TSTP Solution File: DAT176^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT176^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Tue May 7 07:39:40 EDT 2024
% Result : Theorem 15.95s 4.71s
% Output : Refutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 337
% Syntax : Number of formulae : 637 ( 236 unt; 39 typ; 0 def)
% Number of atoms : 1954 ( 563 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 7299 ( 101 ~; 14 |; 46 &;6726 @)
% ( 0 <=>; 412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 218 ( 218 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 5 con; 0-5 aty)
% Number of variables : 1766 ( 106 ^1596 !; 26 ?;1766 :)
% ( 38 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_type,type,
bounded_lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(minus_type,type,
minus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bot_type,type,
bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(top_type,type,
top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(distrib_lattice_type,type,
distrib_lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_sup_type,type,
semilattice_sup:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounded_lattice_bot_type,type,
bounded_lattice_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounded_lattice_top_type,type,
bounded_lattice_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounde1561333602nf_top_type,type,
bounde1561333602nf_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bounde1808546759up_bot_type,type,
bounde1808546759up_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coinductive_LCons_type,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(lList2435255213lllsts_type,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList2236698231inlsts_type,type,
lList2236698231inlsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21916056377ts_rec_type,type,
lList21916056377ts_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coinductive_llist @ TA ) > TB > TB ) > ( coinductive_llist @ TA ) > TB ) ).
thf(lList22096119349pslsts_type,type,
lList22096119349pslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21612149805nflsts_type,type,
lList21612149805nflsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(lList21148268032oslsts_type,type,
lList21148268032oslsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ 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(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(disjnt_type,type,
disjnt:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(x_type,type,
x: coinductive_llist @ a ).
thf(216,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_infsubsetall) ).
thf(892,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(127,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_top__conj_I2_J) ).
thf(629,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(170,axiom,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_alllsts_Ocoinduct) ).
thf(760,plain,
! [TA: $tType,A: ( coinductive_llist @ TA ) > $o,B: coinductive_llist @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: coinductive_llist @ TA] :
( ( A @ D )
=> ( ( D
= ( coinductive_LNil @ TA ) )
| ? [E: coinductive_llist @ TA,F: TA] :
( ( D
= ( coinductive_LCons @ TA @ F @ E ) )
& ( ( A @ E )
| ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2435255213lllsts @ TA @ C ) ) )
& ( member @ TA @ F @ C ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(85,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_minus__diff__minus) ).
thf(518,plain,
! [TA: $tType] :
( ( ab_group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(242,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Un__iff) ).
thf(962,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(66,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_sup__bot_Oright__neutral) ).
thf(468,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(523,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(5,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_sup__inf__absorb) ).
thf(308,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(440,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(115,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_compl__eq__compl__iff) ).
thf(597,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(203,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_notfin__inf) ).
thf(861,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) )
= ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_inf__fun__def) ).
thf(384,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(295,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Int__Un__distrib2) ).
thf(1137,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(188,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Int__insert__left__if1) ).
thf(814,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(150,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_inflstsE) ).
thf(698,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(269,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Int__empty__left) ).
thf(1063,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_inf__assoc) ).
thf(340,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Un__empty__left) ).
thf(782,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(213,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_singletonI) ).
thf(885,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(263,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Int__insert__left__if0) ).
thf(1046,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(266,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Int__commute) ).
thf(1055,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_sup__apply) ).
thf(570,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_fin__Un__inf) ).
thf(785,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(32,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_llistE) ).
thf(372,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [B: TA,C: coinductive_llist @ TA] :
( A
!= ( coinductive_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(226,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_finlsts_OLNil__fin) ).
thf(917,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2236698231inlsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(20,axiom,
minus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_28) ).
thf(344,plain,
minus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
uminus @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_27) ).
thf(357,plain,
uminus @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(95,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_inf__commute) ).
thf(542,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(63,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_inf__compl__bot) ).
thf(460,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(101,axiom,
bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_26) ).
thf(559,plain,
bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(130,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Compl__Int) ).
thf(638,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(277,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Un__UNIV__left) ).
thf(1087,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(59,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_sup_Oassoc) ).
thf(448,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(8,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_sup__bot__right) ).
thf(316,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(282,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Diff__Diff__Int) ).
thf(1100,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(189,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_5) ).
thf(817,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(220,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Set_Ois__empty__def) ).
thf(902,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(211,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_DiffI) ).
thf(881,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(48,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inf_Oright__idem) ).
thf(416,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(287,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_ex__in__conv) ).
thf(1115,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(325,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA @ ( type2 @ TA ) )
=> ( uminus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(229,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_inf__top__right) ).
thf(924,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(113,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_inf__cancel__left1) ).
thf(591,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Compl__disjoint) ).
thf(834,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(185,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(806,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(261,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Diff__Un) ).
thf(1040,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(285,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Int__UNIV__left) ).
thf(1109,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(254,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_alllsts_Osimps) ).
thf(1020,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(22,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_inf__sup__aci_I6_J) ).
thf(348,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(221,axiom,
! [TA: $tType] : ( distrib_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Odistrib__lattice_9) ).
thf(905,plain,
! [TA: $tType] : ( distrib_lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(70,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_inf__sup__aci_I5_J) ).
thf(480,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Compl__Diff__eq) ).
thf(687,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(148,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_sup__cancel__left1) ).
thf(692,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ C ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(162,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_UNIV__eq__I) ).
thf(734,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(240,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Compl__eq__Compl__iff) ).
thf(956,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(173,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finsubsetall) ).
thf(774,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_llist_Oinject) ).
thf(396,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounde1808546759up_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot) ).
thf(411,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounde1808546759up_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_finlsts__rec__LNil) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( lList21916056377ts_rec @ TA @ TB @ A @ B @ ( coinductive_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(273,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Un__left__commute) ).
thf(1074,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(83,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_sup_Oleft__commute) ).
thf(512,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(143,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_bot__empty__eq) ).
thf(678,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(180,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_top1I) ).
thf(793,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(35,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_bot__eq__sup__iff) ).
thf(381,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(92,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_sup__bot_Oleft__neutral) ).
thf(534,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(182,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_compl__sup__top) ).
thf(798,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
thf(334,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(223,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_7) ).
thf(910,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(217,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_empty__Collect__eq) ).
thf(894,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Int__absorb) ).
thf(825,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(3,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_inf_Oidem) ).
thf(302,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(290,axiom,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3) ).
thf(1123,plain,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(178,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Int__UNIV__right) ).
thf(788,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_finlsts__rec__LNil__def) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TB ) > TA,B: TA,C: TB > ( coinductive_llist @ TB ) > TA > TA] :
( ( A
= ( lList21916056377ts_rec @ TA @ TB @ B @ C ) )
=> ( ( A @ ( coinductive_LNil @ TB ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(258,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Int__insert__right__if0) ).
thf(1032,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inf__apply) ).
thf(361,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(210,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_infT__simp) ).
thf(879,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(215,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Diff__Int__distrib2) ).
thf(889,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(493,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( boolean_algebra @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Diff__iff) ).
thf(757,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(198,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Un__assoc) ).
thf(842,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(11,axiom,
top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_25) ).
thf(324,plain,
top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(252,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insertCI) ).
thf(1012,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(284,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Diff__disjoint) ).
thf(1106,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ( distrib_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Odistrib__lattice) ).
thf(583,plain,
! [TA: $tType,TB: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ( distrib_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(87,axiom,
bounded_lattice_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__top_18) ).
thf(522,plain,
bounded_lattice_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(551,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA @ ( type2 @ TA ) )
=> ( bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(292,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_bot__set__def) ).
thf(1128,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(165,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_alllsts_Ocases) ).
thf(742,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2435255213lllsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(253,axiom,
! [TA: $tType] :
( ( disjnt @ TA )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_disjnt__def) ).
thf(1017,plain,
! [TA: $tType] :
( ( disjnt @ TA )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) )
= ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) @ ( sup_sup @ ( set @ TA ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Un__Int__crazy) ).
thf(725,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) )
= ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) @ ( sup_sup @ ( set @ TA ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(280,axiom,
! [TA: $tType] : ( bounde1561333602nf_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4) ).
thf(1096,plain,
! [TA: $tType] : ( bounde1561333602nf_top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(250,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Un__empty) ).
thf(1006,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_DiffD2) ).
thf(869,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(288,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_12) ).
thf(1118,plain,
! [TA: $tType] : ( top @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(78,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inf__idem) ).
thf(499,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(247,axiom,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ouminus_14) ).
thf(989,plain,
! [TA: $tType] : ( uminus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(208,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__bot_6) ).
thf(874,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(297,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_Int__Un__distrib) ).
thf(1143,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(134,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Int__Diff) ).
thf(650,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(237,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Compl__partition) ).
thf(948,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(93,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( minus_minus @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_diff__eq) ).
thf(537,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( minus_minus @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(140,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_empty__not__UNIV) ).
thf(669,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(14,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( inf_inf @ TA @ A @ C ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_inf__cancel__left2) ).
thf(328,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( inf_inf @ TA @ A @ C ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(67,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_inf_Ocommute) ).
thf(471,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(196,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_alllstsE) ).
thf(837,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_sup__fun__def) ).
thf(393,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB @ ( type2 @ TB ) )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__iff) ).
thf(647,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finlsts__rec__LCons__def) ).
thf(701,plain,
! [TA: $tType,TB: $tType,A: ( coinductive_llist @ TA ) > TB,B: TB,C: TA > ( coinductive_llist @ TA ) > TB > TB,D: coinductive_llist @ TA,E: set @ TA,F: TA] :
( ( A
= ( lList21916056377ts_rec @ TB @ TA @ B @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ E ) )
=> ( ( A @ ( coinductive_LCons @ TA @ F @ D ) )
= ( C @ F @ D @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_minus__apply) ).
thf(515,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(293,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_IntE) ).
thf(1131,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Compl__disjoint2) ).
thf(984,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(157,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__lemma) ).
thf(721,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ C ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(175,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( sup_sup @ TA @ A @ C ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_sup__cancel__left2) ).
thf(779,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) @ ( sup_sup @ TA @ A @ C ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(118,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( minus_minus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Compl__eq__Diff__UNIV) ).
thf(605,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) )
= ( minus_minus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(268,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Diff__empty) ).
thf(1060,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(62,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_sup__commute) ).
thf(457,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(19,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_24) ).
thf(343,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_UnE) ).
thf(938,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(27,axiom,
bounded_lattice_bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__bot_19) ).
thf(360,plain,
bounded_lattice_bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_inf__sup__aci_I2_J) ).
thf(311,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finlsts__rec__LCons) ).
thf(921,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TB,D: TA > ( coinductive_llist @ TA ) > TB > TB,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( lList21916056377ts_rec @ TB @ TA @ C @ D @ ( coinductive_LCons @ TA @ E @ A ) )
= ( D @ E @ A @ ( lList21916056377ts_rec @ TB @ TA @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(259,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_fin__finite) ).
thf(1035,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(272,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Un__absorb) ).
thf(1071,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(256,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Diff__Compl) ).
thf(1026,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(138,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_inflstsI2) ).
thf(662,plain,
! [TA: $tType,A: TA,B: set @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList21612149805nflsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ C ) @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_DiffE) ).
thf(718,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(243,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finlsts_Oinducts) ).
thf(965,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ ( coinductive_LNil @ TA ) )
=> ( ! [D: coinductive_llist @ TA,E: TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ D )
=> ( ( member @ TA @ E @ B )
=> ( C @ ( coinductive_LCons @ TA @ E @ D ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_UnCI) ).
thf(618,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(51,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_inf__sup__aci_I8_J) ).
thf(425,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(298,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Un__commute) ).
thf(1146,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(283,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Un__insert__right) ).
thf(1103,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sup_Oright__idem) ).
thf(573,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(33,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_sup__left__idem) ).
thf(375,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Compl__Un) ).
thf(819,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(42,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_inf__bot__left) ).
thf(402,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(291,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Un__Diff__Int) ).
thf(1125,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(96,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_inf__bot__right) ).
thf(545,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(47,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inf__left__idem) ).
thf(413,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(108,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ ( inf_inf @ TA @ A @ B ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_inf__compl__bot__left1) ).
thf(577,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ ( inf_inf @ TA @ A @ B ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(154,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inflsts__cases) ).
thf(711,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ D @ ( lList21612149805nflsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( A
!= ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Un__insert__left) ).
thf(641,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(58,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_inf__sup__aci_I7_J) ).
thf(445,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(120,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finT__simp) ).
thf(611,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(267,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_alllsts_OLCons__all) ).
thf(1058,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2435255213lllsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(278,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Compl__partition2) ).
thf(1090,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(540,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA @ ( type2 @ TA ) )
=> ( top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(141,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_inf__top_Oleft__neutral) ).
thf(672,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(227,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_UNIV__I) ).
thf(919,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(184,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_emptyE) ).
thf(804,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(44,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_sup__assoc) ).
thf(406,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Un__Diff__cancel) ).
thf(831,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(144,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Collect__empty__eq) ).
thf(681,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(49,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA,E: TA,F: TA] :
( ( sup_sup @ TA @ D @ ( inf_inf @ TA @ E @ F ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ D @ E ) @ ( sup_sup @ TA @ D @ F ) ) )
=> ( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_distrib__imp2) ).
thf(419,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA,E: TA,F: TA] :
( ( sup_sup @ TA @ D @ ( inf_inf @ TA @ E @ F ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ D @ E ) @ ( sup_sup @ TA @ D @ F ) ) )
=> ( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_uminus__apply) ).
thf(451,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_alllsts_OLNil__all) ).
thf(737,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( lList2435255213lllsts @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_IntD2) ).
thf(616,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(82,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ ( uminus_uminus @ TA @ A ) ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_inf__compl__bot__right) ).
thf(509,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ ( uminus_uminus @ TA @ A ) ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(262,axiom,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_poslsts__def) ).
thf(1043,plain,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( insert @ ( coinductive_llist @ TA ) @ ( coinductive_LNil @ TA ) @ ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(54,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_diff__eq__diff__eq) ).
thf(434,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA,E: TA,F: TA] :
( ( inf_inf @ TA @ D @ ( sup_sup @ TA @ E @ F ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ D @ E ) @ ( inf_inf @ TA @ D @ F ) ) )
=> ( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_distrib__imp1) ).
thf(477,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ! [D: TA,E: TA,F: TA] :
( ( inf_inf @ TA @ D @ ( sup_sup @ TA @ E @ F ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ D @ E ) @ ( inf_inf @ TA @ D @ F ) ) )
=> ( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(114,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_inf__sup__aci_I3_J) ).
thf(594,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_LConsE) ).
thf(621,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ A @ B ) @ ( lList2435255213lllsts @ TA @ C ) )
= ( ( member @ TA @ A @ C )
& ( member @ ( coinductive_llist @ TA ) @ B @ ( lList2435255213lllsts @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_fun__diff__def) ).
thf(483,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB @ ( type2 @ TB ) )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(200,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finlsts_Ocases) ).
thf(848,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( A
!= ( coinductive_LNil @ TA ) )
=> ~ ! [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
=> ( ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
=> ~ ( member @ TA @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Int__assoc) ).
thf(1029,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(299,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Un__empty__right) ).
thf(1149,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(235,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_empty__Diff) ).
thf(943,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(231,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Un__Int__distrib2) ).
thf(932,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(286,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Int__iff) ).
thf(1112,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bex__Un) ).
thf(811,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(37,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( inf_inf @ TA @ A @ B ) )
= ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_compl__inf) ).
thf(387,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( inf_inf @ TA @ A @ B ) )
= ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_neq__LNil__conv) ).
thf(345,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
!= ( coinductive_LNil @ TA ) )
= ( ? [B: TA,C: coinductive_llist @ TA] :
( A
= ( coinductive_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(202,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( bot_bot @ TA ) )
=> ( ( ( sup_sup @ TA @ A @ B )
= ( top_top @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_compl__unique) ).
thf(858,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( bot_bot @ TA ) )
=> ( ( ( sup_sup @ TA @ A @ B )
= ( top_top @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(30,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_neg__equal__iff__equal) ).
thf(367,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inf__right__idem) ).
thf(399,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(241,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_sup__top__right) ).
thf(959,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(171,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_poslsts__UNIV) ).
thf(768,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
= ( A
!= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(149,axiom,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_poslsts__empty) ).
thf(695,plain,
! [TA: $tType] :
( ( lList21148268032oslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(270,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_inf__top__left) ).
thf(1066,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( top_top @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(212,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_UNIV__witness) ).
thf(883,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(119,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_poslsts__iff) ).
thf(608,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21148268032oslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(103,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( sup_sup @ TA @ A @ B ) )
= ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_compl__sup) ).
thf(563,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( sup_sup @ TA @ A @ B ) )
= ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(80,axiom,
bounde1808546759up_bot @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16) ).
thf(505,plain,
bounde1808546759up_bot @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(53,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_sup__bot__left) ).
thf(431,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(135,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Diff__eq) ).
thf(653,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(224,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_iso__tuple__UNIV__I) ).
thf(912,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(86,axiom,
semilattice_inf @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_21) ).
thf(521,plain,
semilattice_inf @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(91,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_equation__minus__iff) ).
thf(531,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(181,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_fin__Int__inf) ).
thf(795,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2236698231inlsts @ TA @ A ) @ ( lList21612149805nflsts @ TA @ A ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(97,axiom,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_inf__sup__distrib2) ).
thf(548,plain,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(230,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Int__emptyI) ).
thf(927,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_bot__fun__def) ).
thf(553,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(264,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_sup__top__left) ).
thf(1049,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(74,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_inf__compl__bot__left2) ).
thf(490,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(142,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inf__eq__top__iff) ).
thf(675,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inf_inf @ TA @ A @ B )
= ( top_top @ TA ) )
= ( ( A
= ( top_top @ TA ) )
& ( B
= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(294,axiom,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_inflsts__empty) ).
thf(1134,plain,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(73,axiom,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_inf__sup__distrib1) ).
thf(487,plain,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(275,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_double__complement) ).
thf(1081,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(166,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_fpslsts__iff) ).
thf(749,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
= ( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
& ( A
!= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Diff__UNIV) ).
thf(776,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(89,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_inf_Oleft__commute) ).
thf(525,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(147,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_IntD1) ).
thf(690,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(152,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Compl__iff) ).
thf(705,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(214,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_UnI1) ).
thf(887,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(13,axiom,
semilattice_sup @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_20) ).
thf(327,plain,
semilattice_sup @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(239,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_DiffD1) ).
thf(954,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(164,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( top_top @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_compl__top__eq) ).
thf(739,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( top_top @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(409,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(281,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_8) ).
thf(1098,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(109,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_sup_Oidem) ).
thf(580,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Int__empty__right) ).
thf(855,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(179,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_13) ).
thf(791,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_fun__Compl__def) ).
thf(331,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB @ ( type2 @ TB ) )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( minus_minus @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_minus__diff__eq) ).
thf(502,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( minus_minus @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(463,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(107,axiom,
distrib_lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Odistrib__lattice_22) ).
thf(576,plain,
distrib_lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(222,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Collect__empty__eq__bot) ).
thf(907,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(111,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_inf__left__commute) ).
thf(585,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(370,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( semilattice_sup @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(238,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Diff__triv) ).
thf(951,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(186,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_top__set__def) ).
thf(808,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Int__insert__right__if1) ).
thf(613,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(116,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ball__Un) ).
thf(600,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(265,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1052,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Diff__Int) ).
thf(864,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(296,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(1140,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__bot) ).
thf(314,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounded_lattice_bot @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(209,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_sup__compl__top) ).
thf(876,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(248,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_finlsts__induct) ).
thf(991,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] :
( ( D
= ( coinductive_LNil @ TA ) )
=> ( C @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ E @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( C @ E )
=> ( ( member @ TA @ D @ B )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Un__Int__distrib) ).
thf(656,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(255,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Un__Diff__cancel2) ).
thf(1023,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(199,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_all__not__in__conv) ).
thf(845,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(65,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_sup_Oleft__idem) ).
thf(465,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(126,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_fin__inf__cases) ).
thf(627,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_top__apply) ).
thf(1084,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB @ ( type2 @ TB ) )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(100,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_inf__sup__aci_I4_J) ).
thf(556,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(76,axiom,
boolean_algebra @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_23) ).
thf(495,plain,
boolean_algebra @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(172,axiom,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_inf__top_Oright__neutral) ).
thf(771,plain,
! [TA: $tType] :
( ( bounde1561333602nf_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( top_top @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(112,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_minus__equation__iff) ).
thf(588,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_llist_Odistinct_I1_J) ).
thf(319,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_LNil @ TA )
!= ( coinductive_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(236,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_alllsts__UNIV) ).
thf(946,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_bot__apply) ).
thf(351,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB @ ( type2 @ TB ) )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(38,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inf_Oleft__idem) ).
thf(390,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(128,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top__empty__eq) ).
thf(632,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(161,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Un__UNIV__right) ).
thf(731,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(274,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equals0D) ).
thf(1077,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(219,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Diff__Int2) ).
thf(899,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Int__left__commute) ).
thf(684,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(155,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_11) ).
thf(716,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(225,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Un__left__absorb) ).
thf(914,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(34,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_inf__sup__aci_I1_J) ).
thf(378,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
( ( ~ ( member @ ( coinductive_llist @ a ) @ x @ ( lList21612149805nflsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
= ( member @ ( coinductive_llist @ a ) @ x @ ( lList2236698231inlsts @ a @ ( top_top @ ( set @ a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ~ ( member @ ( coinductive_llist @ a ) @ x @ ( lList21612149805nflsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
!= ( member @ ( coinductive_llist @ a ) @ x @ ( lList2236698231inlsts @ a @ ( top_top @ ( set @ a ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(300,plain,
( ( ~ ( member @ ( coinductive_llist @ a ) @ x @ ( lList21612149805nflsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
!= ( member @ ( coinductive_llist @ a ) @ x @ ( lList2236698231inlsts @ a @ ( top_top @ ( set @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(167,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finlsts_Osimps) ).
thf(752,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ? [C: coinductive_llist @ TA,D: TA] :
( ( A
= ( coinductive_LCons @ TA @ D @ C ) )
& ( member @ ( coinductive_llist @ TA ) @ C @ ( lList2236698231inlsts @ TA @ B ) )
& ( member @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(43,axiom,
bounded_lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(405,plain,
bounded_lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_sup__left__commute) ).
thf(422,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_IntI) ).
thf(867,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(117,axiom,
! [TA: $tType] : ( minus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ominus_15) ).
thf(603,plain,
! [TA: $tType] : ( minus @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_double__compl) ).
thf(305,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(183,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Un__Diff) ).
thf(801,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(81,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_sup__eq__bot__iff) ).
thf(506,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounde1561333602nf_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__inf__top) ).
thf(358,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA @ ( type2 @ TA ) )
=> ( bounde1561333602nf_top @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(55,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_compl__inf__bot) ).
thf(437,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_fpslsts__cases) ).
thf(664,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList22096119349pslsts @ TA @ B ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( A
= ( coinductive_LCons @ TA @ C @ D ) )
=> ( ( member @ TA @ C @ B )
=> ~ ( member @ ( coinductive_llist @ TA ) @ D @ ( lList2236698231inlsts @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(193,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Diff__idemp) ).
thf(828,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Int__left__absorb) ).
thf(635,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(218,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ComplD) ).
thf(897,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(68,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_inf_Oassoc) ).
thf(474,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(160,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( bot_bot @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_compl__bot__eq) ).
thf(728,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ( ( uminus_uminus @ TA @ ( bot_bot @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(246,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_10) ).
thf(987,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(90,axiom,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_sup__inf__distrib1) ).
thf(528,plain,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ B ) @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(132,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__inter__insert) ).
thf(644,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_ComplI) ).
thf(723,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(191,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Compl__empty__eq) ).
thf(822,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(57,axiom,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_sup__inf__distrib2) ).
thf(442,plain,
! [TA: $tType] :
( ( distrib_lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ ( sup_sup @ TA @ A @ C ) @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_equals0I) ).
thf(871,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(289,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( sup_sup @ TA @ A @ B ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_sup__compl__top__left1) ).
thf(1120,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ ( sup_sup @ TA @ A @ B ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(279,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Diff__Int__distrib) ).
thf(1093,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Int__UNIV) ).
thf(624,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(197,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_disjoint__iff__not__equal) ).
thf(839,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(244,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_empty__iff) ).
thf(982,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(249,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_inflstsI) ).
thf(1004,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ B ) )
=> ( ~ ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) )
=> ( member @ ( coinductive_llist @ TA ) @ A @ ( lList21612149805nflsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA @ ( type2 @ TA ) )
=> ( minus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(322,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA @ ( type2 @ TA ) )
=> ( minus @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,axiom,
bounde1561333602nf_top @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_17) ).
thf(486,plain,
bounde1561333602nf_top @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(17,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_diff__right__commute) ).
thf(337,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(234,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_sup__compl__top__left2) ).
thf(940,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ ( uminus_uminus @ TA @ A ) @ B ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(24,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_sup__idem) ).
thf(354,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(137,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_top__conj_I1_J) ).
thf(659,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(168,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_UnI2) ).
thf(755,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(29,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add_Oinverse__inverse) ).
thf(364,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(153,axiom,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Compl__UNIV__eq) ).
thf(708,plain,
! [TA: $tType] :
( ( uminus_uminus @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(232,axiom,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_inflsts__def) ).
thf(935,plain,
! [TA: $tType] :
( ( lList21612149805nflsts @ TA )
= ( ^ [A: set @ TA] : ( minus_minus @ ( set @ ( coinductive_llist @ TA ) ) @ ( lList2435255213lllsts @ TA @ A ) @ ( lList2236698231inlsts @ TA @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(251,axiom,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_fpslsts__empty) ).
thf(1009,plain,
! [TA: $tType] :
( ( lList22096119349pslsts @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( coinductive_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(260,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Diff__cancel) ).
thf(1037,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(102,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(560,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(77,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_sup_Ocommute) ).
thf(496,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA @ ( type2 @ TA ) )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(61,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_inf__sup__absorb) ).
thf(454,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(271,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_finlsts_OLCons__fin) ).
thf(1069,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: set @ TA,C: TA] :
( ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2236698231inlsts @ TA @ B ) )
=> ( ( member @ TA @ C @ B )
=> ( member @ ( coinductive_llist @ TA ) @ ( coinductive_LCons @ TA @ C @ A ) @ ( lList2236698231inlsts @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1152,plain,
$false,
inference(e,[status(thm)],[892,629,760,518,962,468,523,308,440,597,861,384,1137,814,698,1063,340,782,885,1046,1055,570,785,372,917,344,357,542,460,559,638,1087,448,316,1100,817,902,881,416,1115,325,924,591,834,806,1040,1109,1020,348,905,480,687,692,734,956,774,396,411,428,1074,512,678,793,381,534,798,334,910,894,825,302,1123,788,566,1032,361,879,889,493,757,842,324,1012,1106,583,522,551,1128,742,1017,725,1096,1006,869,1118,499,989,874,1143,650,948,537,669,328,471,837,393,647,701,515,1131,984,721,779,605,1060,457,343,938,360,311,921,1035,1071,1026,662,718,965,618,425,1146,1103,573,375,819,402,1125,545,413,577,711,641,445,611,1058,1090,540,672,919,804,406,831,681,419,451,737,616,509,1043,434,477,594,621,483,848,1029,1149,943,932,1112,811,387,345,858,367,399,959,768,695,1066,883,608,563,505,431,653,912,521,531,795,548,927,553,1049,490,675,1134,487,1081,749,776,525,690,705,887,327,954,739,409,1098,580,855,791,331,502,463,576,907,585,370,951,808,613,600,1052,864,1140,314,876,991,656,1023,845,465,627,1084,556,495,771,588,319,946,351,390,632,731,1077,899,684,716,914,378,300,752,405,422,867,603,305,801,506,358,437,664,828,635,897,474,728,987,528,644,723,822,442,871,1120,1093,624,839,982,1004,322,486,337,940,354,659,755,364,708,935,1009,1037,560,496,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT176^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n016.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 11:38:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.05/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.25 % [INFO] Parsing done (306ms).
% 2.05/1.26 % [INFO] Running in sequential loop mode.
% 2.72/1.49 % [INFO] eprover registered as external prover.
% 2.72/1.49 % [INFO] cvc4 registered as external prover.
% 2.91/1.50 % [INFO] Scanning for conjecture ...
% 3.06/1.62 % [INFO] Found a conjecture and 298 axioms. Running axiom selection ...
% 3.47/1.72 % [INFO] Axiom selection finished. Selected 297 axioms (removed 1 axioms).
% 4.05/1.90 % [INFO] Problem is higher-order (TPTP THF).
% 4.24/1.91 % [INFO] Type checking passed.
% 4.24/1.92 % [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 ...
% 15.95/4.71 % External prover 'e' found a proof!
% 15.95/4.71 % [INFO] Killing All external provers ...
% 15.95/4.71 % Time passed: 4156ms (effective reasoning time: 3447ms)
% 15.95/4.71 % 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)>
% 15.95/4.71 % Axioms used in derivation (297): fact_241_alllsts_Ocases, fact_42_all__not__in__conv, tcon_fun___Orderings_Obot, fact_69_Diff__cancel, tcon_Set_Oset___Lattices_Obounded__semilattice__inf__top_4, fact_70_empty__Diff, fact_109_sup_Ocommute, tcon_fun___Groups_Ominus, fact_139_fpslsts__empty, fact_137_Set_Ois__empty__def, fact_252_Int__insert__right__if0, fact_245_insert__absorb2, fact_102_sup__cancel__left1, fact_51_sup_Oleft__idem, fact_211_Int__left__commute, fact_223_finlsts__rec__LNil__def, fact_21_DiffD1, tcon_HOL_Obool___Lattices_Obounded__lattice__bot_19, tcon_Set_Oset___Lattices_Odistrib__lattice_9, fact_98_Un__left__commute, fact_84_ComplD, fact_232_Compl__Un, tcon_HOL_Obool___Lattices_Osemilattice__inf_21, fact_195_Un__Int__crazy, fact_30_diff__right__commute, fact_114_fun__Compl__def, fact_207_Int__assoc, fact_177_inf__top__right, fact_44_empty__Collect__eq, fact_179_distrib__imp1, fact_107_sup__bot__left, fact_22_DiffD2, fact_192_Int__Un__distrib2, fact_50_sup__left__idem, fact_136_top__conj_I1_J, fact_9_inflstsE, fact_200_Diff__Int__distrib2, fact_224_finlsts__rec__LNil, fact_67_sup__top__right, fact_101_double__complement, tcon_HOL_Obool___Lattices_Osemilattice__sup_20, fact_87_ball__Un, fact_246_insert__iff, fact_88_Un__assoc, fact_31_Diff__UNIV, fact_149_inf_Oleft__idem, fact_26_fin__Un__inf, fact_164_inf__compl__bot__left2, tcon_Set_Oset___Lattices_Obounded__lattice__bot_6, fact_147_inf_Oidem, fact_255_Un__insert__right, fact_254_Un__insert__left, fact_18_Diff__iff, fact_191_Un__Int__distrib2, fact_248_singletonI, fact_228_Diff__triv, tcon_fun___Lattices_Odistrib__lattice, fact_56_Un__iff, fact_92_Un__commute, fact_229_Un__Diff__Int, fact_96_Un__left__absorb, fact_3_fin__finite, fact_231_Diff__Un, fact_55_UnCI, tcon_HOL_Obool___Lattices_Odistrib__lattice_22, fact_113_sup_Oassoc, fact_222_inf__left__commute, fact_225_diff__eq, fact_162_Int__UNIV, fact_89_equals0D, fact_122_Un__UNIV__left, fact_116_inf__sup__aci_I5_J, fact_197_Diff__Int2, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_129_inflsts__cases, fact_59_Compl__eq__Compl__iff, fact_187_Int__empty__left, fact_58_Compl__iff, fact_238_finlsts_Oinducts, tcon_HOL_Obool___Orderings_Obot_26, fact_124_Un__Diff, fact_15_infsubsetall, tcon_HOL_Obool___Lattices_Obounded__lattice__top_18, fact_25_minus__apply, fact_66_sup__top__left, fact_196_Int__Diff, fact_10_alllstsE, fact_104_sup__bot__right, fact_77_sup__compl__top, fact_33_LConsE, fact_40_uminus__apply, fact_62_sup__bot_Oright__neutral, fact_39_add_Oinverse__inverse, fact_150_inf__left__idem, fact_74_compl__bot__eq, fact_212_inf__sup__aci_I4_J, fact_72_Un__Diff__cancel, fact_46_Collect__mem__eq, fact_1_finT__simp, fact_19_Diff__idemp, fact_250_Int__insert__left__if1, fact_144_poslsts__iff, fact_106_sup_Oleft__commute, fact_247_insertCI, fact_85_bex__Un, fact_230_Diff__Int, tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16, fact_243_Collect__empty__eq__bot, fact_16_finite__lemma, fact_32_Compl__eq__Diff__UNIV, fact_119_inf__sup__aci_I8_J, fact_146_inf__apply, tcon_fun___Lattices_Obounded__lattice_2, fact_105_sup__left__commute, fact_108_sup__commute, fact_53_sup_Oidem, fact_28_fun__diff__def, fact_38_neg__equal__iff__equal, fact_35_bot__apply, fact_121_Compl__UNIV__eq, tcon_Set_Oset___Lattices_Obounded__lattice__top_5, fact_153_IntI, tcon_fun___Lattices_Osemilattice__sup, fact_215_inf__sup__aci_I1_J, fact_174_poslsts__UNIV, fact_100_bot__fun__def, fact_20_DiffE, tcon_Set_Oset___Lattices_Oboolean__algebra_10, fact_23_top__set__def, fact_13_alllsts__UNIV, tcon_Set_Oset___Groups_Ominus_15, fact_103_sup__cancel__left2, fact_199_Diff__Int__distrib, fact_128_inflstsI2, fact_57_ComplI, fact_151_inf_Oright__idem, tcon_Set_Oset___Orderings_Otop_12, fact_95_Un__empty__right, fact_182_inf__sup__distrib2, tcon_fun___Lattices_Osemilattice__inf, fact_110_minus__equation__iff, fact_226_inf__cancel__left2, tcon_HOL_Obool___Lattices_Obounded__semilattice__inf__top_17, fact_205_IntD1, tcon_HOL_Obool___Groups_Ouminus_27, fact_63_sup__bot_Oleft__neutral, fact_198_Diff__Diff__Int, fact_240_alllsts_Osimps, fact_45_mem__Collect__eq, fact_185_disjoint__iff__not__equal, fact_239_alllsts_Ocoinduct, fact_159_inf__eq__top__iff, fact_158_inf__top_Oleft__neutral, fact_7_top__apply, fact_138_poslsts__empty, fact_0_notfin__inf, tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, fact_160_inf__sup__absorb, fact_90_equals0I, fact_68_Un__empty, fact_251_insert__inter__insert, fact_54_sup__apply, tcon_fun___Lattices_Obounded__lattice__bot, tcon_Set_Oset___Lattices_Olattice_11, fact_131_minus__diff__minus, fact_188_Int__emptyI, fact_236_finlsts_Osimps, fact_184_sup__inf__distrib2, fact_209_Int__commute, fact_47_Collect__cong, fact_220_inf__commute, fact_155_inf__bot__left, fact_112_sup__assoc, fact_189_Int__UNIV__right, tcon_Set_Oset___Lattices_Obounded__lattice_1, tcon_fun___Lattices_Oboolean__algebra, fact_78_sup__compl__top__left1, tcon_fun___Orderings_Otop, fact_75_compl__top__eq, fact_94_Un__empty__left, tcon_fun___Lattices_Obounded__lattice__top, fact_202_finlsts_OLNil__fin, fact_204_IntE, fact_156_inf__bot__right, fact_14_inflsts__def, fact_125_empty__not__UNIV, fact_6_iso__tuple__UNIV__I, fact_141_bot__set__def, fact_183_sup__inf__distrib1, fact_221_inf_Oleft__commute, fact_8_inflstsI, fact_49_sup_Oright__idem, tcon_HOL_Obool___Lattices_Oboolean__algebra_23, fact_214_inf__sup__aci_I2_J, fact_134_finlsts__rec__LCons__def, fact_142_compl__unique, fact_213_inf__sup__aci_I3_J, fact_83_UnI2, tcon_HOL_Obool___Orderings_Otop_25, fact_176_llist_Odistinct_I1_J, fact_172_Compl__disjoint2, fact_123_Un__UNIV__right, fact_173_Diff__Compl, fact_61_minus__diff__eq, tcon_Set_Oset___Lattices_Osemilattice__inf_8, fact_217_inf_Oassoc, fact_181_inf__sup__distrib1, fact_80_Compl__Diff__eq, fact_234_Diff__eq, fact_71_Un__Diff__cancel2, fact_135_top__conj_I2_J, fact_218_inf__assoc, fact_52_sup__idem, tcon_HOL_Obool___Lattices_Olattice_24, fact_81_UnE, fact_237_finlsts__induct, fact_178_inf__top__left, fact_186_Int__empty__right, fact_37_double__compl, fact_4_fin__inf__cases, fact_127_alllsts_OLCons__all, fact_143_fin__Int__inf, fact_170_Diff__disjoint, fact_41_empty__iff, fact_99_Compl__partition2, fact_253_Int__insert__right__if1, fact_73_inflsts__empty, fact_163_inf__compl__bot__right, fact_193_Un__Int__distrib, fact_2_infT__simp, fact_5_UNIV__I, fact_43_Collect__empty__eq, fact_86_emptyE, fact_169_compl__inf, fact_208_Int__absorb, tcon_Set_Oset___Orderings_Obot_13, fact_126_finlsts_OLCons__fin, fact_132_fpslsts__cases, fact_166_inf__compl__bot, fact_82_UnI1, fact_154_Int__iff, fact_130_llist_Oinject, fact_242_disjnt__def, fact_97_Compl__partition, fact_34_Diff__empty, fact_180_distrib__imp2, fact_157_inf__top_Oright__neutral, fact_249_Int__insert__left__if0, fact_29_diff__eq__diff__eq, fact_91_Un__absorb, fact_168_compl__sup, fact_117_inf__sup__aci_I6_J, tcon_HOL_Obool___Groups_Ominus_28, fact_161_sup__inf__absorb, tcon_Set_Oset___Groups_Ouminus_14, fact_201_llistE, fact_17_DiffI, tcon_fun___Lattices_Obounded__semilattice__inf__top, fact_171_Compl__disjoint, fact_12_UNIV__witness, tcon_fun___Groups_Ouminus, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_79_sup__compl__top__left2, fact_111_equation__minus__iff, fact_227_inf__cancel__left1, fact_93_ex__in__conv, fact_190_Int__UNIV__left, fact_233_Compl__Int, fact_244_poslsts__def, fact_167_compl__inf__bot, fact_235_finlsts_Ocases, fact_76_compl__sup__top, fact_203_alllsts_OLNil__all, fact_65_bot__eq__sup__iff, tcon_Set_Oset___Lattices_Osemilattice__sup_7, fact_152_inf__right__idem, fact_206_IntD2, fact_140_bot__empty__eq, fact_216_inf__fun__def, fact_194_Int__Un__distrib, fact_36_compl__eq__compl__iff, fact_133_finlsts__rec__LCons, fact_148_inf__idem, fact_27_top__empty__eq, fact_118_inf__sup__aci_I7_J, fact_175_neq__LNil__conv, tcon_fun___Lattices_Olattice, fact_145_fpslsts__iff, fact_24_finsubsetall, fact_165_inf__compl__bot__left1, fact_120_Compl__empty__eq, fact_210_Int__left__absorb, fact_64_sup__eq__bot__iff, fact_219_inf_Ocommute, fact_11_UNIV__eq__I, fact_60_top1I, fact_115_sup__fun__def
% 15.95/4.71 % No. of inferences in proof: 598
% 15.95/4.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4156 ms resp. 3447 ms w/o parsing
% 16.59/4.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.59/4.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------