%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP124^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:51 AM UTC 2026
% Result : Theorem 26.13s 10.20s
% Output : Refutation 32.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 263
% Syntax : Number of formulae : 528 ( 230 unt; 0 typ; 0 def)
% Number of atoms : 1666 ( 445 equ; 8 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 5160 ( 106 ~; 14 |; 70 &;4398 @)
% ( 0 <=>; 572 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 124 ( 124 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 7 con; 0-6 aty)
% Number of variables : 1376 ( 30 ^;1322 !; 24 ?;1376 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(condit2040224947_above_decl,type,
condit2040224947_above:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(condit1201339847_below_decl,type,
condit1201339847_below:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(finite_comp_fun_idem_decl,type,
finite_comp_fun_idem:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(finite_finite2_decl,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(abel_semigroup_decl,type,
abel_semigroup:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(semigroup_decl,type,
semigroup:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(semilattice_decl,type,
semilattice:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(lattic1263571978nf_fin_decl,type,
lattic1263571978nf_fin:
!>[TA: $tType] : ( ( TA > TA > TA ) > ( set @ TA ) > TA ) ).
thf(lattic35693393ce_set_decl,type,
lattic35693393ce_set:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(lattic1039401930up_fin_decl,type,
lattic1039401930up_fin:
!>[TA: $tType] : ( ( TA > TA > TA ) > ( set @ TA ) > TA ) ).
thf(modula1221160330_d_aux_decl,type,
modula1221160330_d_aux:
!>[TA: $tType] : ( ( TA > TA > TA ) > ( TA > TA > TA ) > TA > TA > TA > TA ) ).
thf(modula1593167561_e_aux_decl,type,
modula1593167561_e_aux:
!>[TA: $tType] : ( ( TA > TA > TA ) > ( TA > TA > TA ) > TA > TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(least_decl,type,
least:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > TA ) ).
thf(max_decl,type,
max:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(min_decl,type,
min:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(greatest_decl,type,
greatest:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > TA ) ).
thf(antimono_decl,type,
antimono:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > $o ) ).
thf(mono_decl,type,
mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > $o ) ).
thf(transp_decl,type,
transp:
!>[TA: $tType] : ( ( TA > TA > $o ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(set_atLeast_decl,type,
set_atLeast:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_atLeastAtMost_decl,type,
set_atLeastAtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atMost_decl,type,
set_atMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(inf_decl,type,
inf: a > a > a ).
thf(less_eq_decl,type,
less_eq: a > a > $o ).
thf(sup_decl,type,
sup: a > a > a ).
thf(123,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_local_Osup_Oabsorb1) ).
thf(645,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(39,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_187_all__not__in__conv) ).
thf(365,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)],[39]) ).
thf(160,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_local_Oinf_Ocobounded2) ).
thf(760,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(254,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_local_Osup_Oleft__commute) ).
thf(1105,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(180,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_local_Oinf_OorderE) ).
thf(846,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(166,axiom,
abel_semigroup @ a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_local_Osup_Oabel__semigroup__axioms) ).
thf(777,plain,
abel_semigroup @ a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(130,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_local_Osup_OorderE) ).
thf(666,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(35,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_semilattice_Oidem) ).
thf(352,plain,
! [TA: $tType,A: TA > TA > TA,B: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(195,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_Osup__Inf__absorb) ).
thf(909,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( sup @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_subset__eq) ).
thf(333,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(248,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_local_Oinf_OboundedE) ).
thf(1083,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_insert__subset) ).
thf(468,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(44,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ( semilattice @ TA @ A )
=> ( lattic35693393ce_set @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_semilattice__set_Ointro) ).
thf(379,plain,
! [TA: $tType,A: TA > TA > TA] :
( ( semilattice @ TA @ A )
=> ( lattic35693393ce_set @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(134,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_local_OIcc__eq__Icc) ).
thf(677,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(106,axiom,
condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_local_Obdd__above__empty) ).
thf(597,plain,
condit2040224947_above @ a @ less_eq @ ( bot_bot @ ( set @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(89,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_local_Odual__order_Otrans) ).
thf(523,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(161,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_local_Ole__infI2) ).
thf(762,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(247,axiom,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_local_Obdd__belowI) ).
thf(1078,plain,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(92,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_local_Osup__least) ).
thf(533,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(97,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_local_Oinf_Ocommute) ).
thf(550,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(72,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ( semilattice @ TA @ A )
=> ( abel_semigroup @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_semilattice_Oaxioms_I1_J) ).
thf(472,plain,
! [TA: $tType,A: TA > TA > TA] :
( ( semilattice @ TA @ A )
=> ( abel_semigroup @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(196,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_local_Ole__supI2) ).
thf(913,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(242,axiom,
! [A: a] :
( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_local_OInf__fin_Osingleton) ).
thf(1063,plain,
! [A: a] :
( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(29,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_185_empty__Collect__eq) ).
thf(340,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)],[29]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_equalityE) ).
thf(404,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(223,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_local_Ole__iff__sup) ).
thf(1001,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(261,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_local_Osup_OcoboundedI2) ).
thf(1127,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(144,axiom,
! [TA: $tType] :
( ( modula1593167561_e_aux @ TA )
= ( modula1593167561_e_aux @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lattice_Oe__aux_Ocong) ).
thf(709,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(57,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_local_Oeq__iff) ).
thf(417,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(191,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_local_Oinf__left__commute) ).
thf(885,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(23,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_local_Oord__le__eq__trans) ).
thf(320,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(102,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ~ ( member @ a @ B @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ B @ A ) )
= ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_local_OInf__fin_Oinsert__not__elem) ).
thf(565,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ~ ( member @ a @ B @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ B @ A ) )
= ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(48,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_local_Oorder_Otrans) ).
thf(389,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(239,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_local_Osup__left__commute) ).
thf(1055,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(168,axiom,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_local_Obdd__below__Icc) ).
thf(785,plain,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(201,axiom,
semigroup @ a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Osup_Osemigroup__axioms) ).
thf(934,plain,
semigroup @ a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(114,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_local_Odistrib__inf__le) ).
thf(619,plain,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(177,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( mono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_local_OmonoD) ).
thf(838,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( mono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(171,axiom,
transp @ a @ less_eq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_local_Otransp__le) ).
thf(817,plain,
transp @ a @ less_eq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(100,axiom,
! [A: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_local_Obdd__below__def) ).
thf(559,plain,
! [A: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(121,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_local_Oinf_Oabsorb__iff2) ).
thf(638,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(249,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_local_Osup_Omono) ).
thf(1087,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(188,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ C @ B ) )
=> ( ( greatest @ a @ less_eq @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_local_OGreatest__equality) ).
thf(870,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ C @ B ) )
=> ( ( greatest @ a @ less_eq @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(212,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_local_Oinf_Oassoc) ).
thf(969,plain,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(24,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_local_Oantisym) ).
thf(325,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_singletonD) ).
thf(289,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_insert__not__empty) ).
thf(492,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(159,axiom,
! [A: a] :
( ( bot_bot @ ( set @ a ) )
!= ( set_atLeast @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_local_Onot__empty__eq__Ici__eq__empty) ).
thf(756,plain,
! [A: a] :
( ( bot_bot @ ( set @ a ) )
!= ( set_atLeast @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(234,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_local_OInf__fin_Obounded__iff) ).
thf(1040,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(43,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_semigroup_Ointro) ).
thf(376,plain,
! [TA: $tType,A: TA > TA > TA] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(211,axiom,
! [A: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ A )
= ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_local_OatLeastAtMost__singleton) ).
thf(966,plain,
! [A: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ A )
= ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(173,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_local_Oinf__greatest) ).
thf(821,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(75,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_Oord__eq__le__trans) ).
thf(480,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(76,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_186_Collect__empty__eq) ).
thf(485,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)],[76]) ).
thf(264,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Oinf_OboundedI) ).
thf(1136,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(229,axiom,
! [A: a,B: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( bot_bot @ ( set @ a ) ) )
= ( ~ ( less_eq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_local_OatLeastatMost__empty__iff) ).
thf(1020,plain,
! [A: a,B: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( bot_bot @ ( set @ a ) ) )
= ( ~ ( less_eq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(32,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_4) ).
thf(348,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(280,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(186,axiom,
finite_comp_fun_idem @ a @ a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_local_Ocomp__fun__idem__sup) ).
thf(866,plain,
finite_comp_fun_idem @ a @ a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(245,axiom,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_d__b__c__a) ).
thf(1072,plain,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( modula1221160330_d_aux @ a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(165,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_local_Ole__supI) ).
thf(774,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(221,axiom,
semilattice @ a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Oinf_Osemilattice__axioms) ).
thf(998,plain,
semilattice @ a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_subsetI) ).
thf(428,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_insert__mono) ).
thf(507,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(20,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_singletonI) ).
thf(312,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
( ( modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2 )
= ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2 )
!= ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(265,plain,
( ( modula1593167561_e_aux @ a @ inf @ sup @ b @ c @ a2 )
!= ( modula1593167561_e_aux @ a @ inf @ sup @ a2 @ b @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(181,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_local_Oinf_Oabsorb2) ).
thf(849,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_singleton__insert__inj__eq_H) ).
thf(292,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_subset__insertI) ).
thf(452,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(85,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_local_Oantisym__conv) ).
thf(512,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(45,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_in__mono) ).
thf(381,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(236,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_local_Oinf_Obounded__iff) ).
thf(1047,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(4,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(270,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(91,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_local_OSup__fin_Oin__idem) ).
thf(529,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(208,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ( antimono @ a @ TA @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_local_Oantimono__def) ).
thf(957,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ( antimono @ a @ TA @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(156,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_local_Osup__commute) ).
thf(746,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(167,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ? [C: a] :
( ( member @ a @ C @ A )
& ( less_eq @ C @ B )
& ! [D: a] :
( ( member @ a @ D @ A )
=> ( ( less_eq @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_local_Ofinite__has__minimal2) ).
thf(778,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ? [C: a] :
( ( member @ a @ C @ A )
& ( less_eq @ C @ B )
& ! [D: a] :
( ( member @ a @ D @ A )
=> ( ( less_eq @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_singleton__inject) ).
thf(302,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [TA: $tType] :
( ( lattic1263571978nf_fin @ TA )
= ( lattic1263571978nf_fin @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_semilattice__inf_OInf__fin_Ocong) ).
thf(349,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(107,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Osup__absorb2) ).
thf(598,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_subsetD) ).
thf(392,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_local_Oorder_Oeq__iff) ).
thf(297,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(140,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_local_OSup__fin_OboundedI) ).
thf(693,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(118,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_local_Oinf__absorb2) ).
thf(630,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(197,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_local_Osup_OcoboundedI1) ).
thf(916,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(189,axiom,
! [A: set @ a,B: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( condit2040224947_above @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_local_Obdd__above__mono) ).
thf(879,plain,
! [A: set @ a,B: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( condit2040224947_above @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(182,axiom,
! [A: a] :
( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_local_OSup__fin_Osingleton) ).
thf(852,plain,
! [A: a] :
( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(136,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_local_OatMost__iff) ).
thf(682,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(145,axiom,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_local_Osup_Oright__idem) ).
thf(710,plain,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TA] :
( ( finite_comp_fun_idem @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_comp__fun__idem_Ofun__left__idem) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: TA] :
( ( finite_comp_fun_idem @ TB @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_equalityD2) ).
thf(285,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_local_Oorder__trans) ).
thf(317,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(125,axiom,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_local_Oinf_OorderI) ).
thf(650,plain,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(113,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_local_Ole__infE) ).
thf(615,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(259,axiom,
! [A: set @ a,B: set @ a] :
( ( ord_less_eq @ ( set @ a ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( finite_finite2 @ a @ B )
=> ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ ( lattic1039401930up_fin @ a @ sup @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_local_OSup__fin_Osubset__imp) ).
thf(1121,plain,
! [A: set @ a,B: set @ a] :
( ( ord_less_eq @ ( set @ a ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( finite_finite2 @ a @ B )
=> ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ ( lattic1039401930up_fin @ a @ sup @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(256,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_local_Osup_Oabsorb__iff2) ).
thf(1111,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(148,axiom,
! [A: set @ a,B: set @ a] :
( ( ord_less_eq @ ( set @ a ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( finite_finite2 @ a @ B )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B ) @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_local_OInf__fin_Osubset__imp) ).
thf(725,plain,
! [A: set @ a,B: set @ a] :
( ( ord_less_eq @ ( set @ a ) @ A @ B )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( finite_finite2 @ a @ B )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ B ) @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(225,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_local_Osup_Oorder__iff) ).
thf(1006,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(218,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( mono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_local_OmonoE) ).
thf(989,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( mono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(155,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
=> ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_local_OInf__fin_OboundedE) ).
thf(742,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
=> ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(104,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_local_Ole__inf__iff) ).
thf(578,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__trans) ).
thf(488,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(131,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Osup_Obounded__iff) ).
thf(669,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(246,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_local_Ole__infI) ).
thf(1075,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(90,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_local_Osup__left__idem) ).
thf(526,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,axiom,
! [A: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_local_Obdd__above__def) ).
thf(706,plain,
! [A: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_finite__set__choice) ).
thf(328,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(71,axiom,
! [TA: $tType] :
( ( modula1221160330_d_aux @ TA )
= ( modula1221160330_d_aux @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_lattice_Od__aux_Ocong) ).
thf(471,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(257,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_local_Oinf__absorb1) ).
thf(1114,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(86,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_local_Oorder__refl) ).
thf(515,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(154,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ( mono @ a @ TA @ less_eq @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_local_OmonoI) ).
thf(738,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ( mono @ a @ TA @ less_eq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(237,axiom,
! [A: a,B: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ ( insert @ a @ A @ B ) )
= ( condit1201339847_below @ a @ less_eq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_local_Obdd__below__insert) ).
thf(1050,plain,
! [A: a,B: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ ( insert @ a @ A @ B ) )
= ( condit1201339847_below @ a @ less_eq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(103,axiom,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ D @ ( A @ D @ E ) )
=> ( ! [D: a,E: a] : ( less_eq @ E @ ( A @ D @ E ) )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ E @ D )
=> ( ( less_eq @ F @ D )
=> ( less_eq @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Osup__unique) ).
thf(569,plain,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ D @ ( A @ D @ E ) )
=> ( ! [D: a,E: a] : ( less_eq @ E @ ( A @ D @ E ) )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ E @ D )
=> ( ( less_eq @ F @ D )
=> ( less_eq @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_subset__refl) ).
thf(343,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(203,axiom,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_local_Obdd__aboveI) ).
thf(938,plain,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(119,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_local_Oinf_OcoboundedI2) ).
thf(633,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(162,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_local_Osup_Oabsorb2) ).
thf(765,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(51,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_local_Oorder_Oantisym) ).
thf(398,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(231,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_local_Oinf_Oleft__idem) ).
thf(1026,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(170,axiom,
! [A: a > $o] :
( ? [B: a] :
( ( A @ B )
& ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
& ! [C: a] :
( ( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( less_eq @ C @ D ) ) )
=> ( C = B ) ) )
=> ( A @ ( least @ a @ less_eq @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_local_OLeast1I) ).
thf(794,plain,
! [A: a > $o] :
( ? [B: a] :
( ( A @ B )
& ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
& ! [C: a] :
( ( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( less_eq @ C @ D ) ) )
=> ( C = B ) ) )
=> ( A @ ( least @ a @ less_eq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(192,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Oinf__assoc) ).
thf(888,plain,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(55,axiom,
! [TA: $tType] :
( ( lattic35693393ce_set @ TA )
= ( semilattice @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_semilattice__set__def) ).
thf(412,plain,
! [TA: $tType] :
( ( lattic35693393ce_set @ TA )
= ( semilattice @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(60,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( abel_semigroup @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_abel__semigroup_Oleft__commute) ).
thf(425,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( abel_semigroup @ TA @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(174,axiom,
! [A: a > $o,B: a] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( less_eq @ C @ D ) )
& ! [D: a] :
( ( ( A @ D )
& ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) ) )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( less_eq @ ( least @ a @ less_eq @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_OLeast1__le) ).
thf(824,plain,
! [A: a > $o,B: a] :
( ? [C: a] :
( ( A @ C )
& ! [D: a] :
( ( A @ D )
=> ( less_eq @ C @ D ) )
& ! [D: a] :
( ( ( A @ D )
& ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) ) )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( less_eq @ ( least @ a @ less_eq @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(108,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( less_eq @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_OSup__fin_OcoboundedI) ).
thf(601,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( less_eq @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(101,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_local_Oinf_Oidem) ).
thf(562,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(53,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_subset__insertI2) ).
thf(402,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(179,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_local_Osup_Ocommute) ).
thf(843,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(164,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( antimono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_local_OantimonoE) ).
thf(772,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( antimono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(260,axiom,
! [A: a,B: a] :
( ( ( bot_bot @ ( set @ a ) )
= ( set_atLeastAtMost @ a @ less_eq @ A @ B ) )
= ( ~ ( less_eq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_local_OatLeastatMost__empty__iff2) ).
thf(1124,plain,
! [A: a,B: a] :
( ( ( bot_bot @ ( set @ a ) )
= ( set_atLeastAtMost @ a @ less_eq @ A @ B ) )
= ( ~ ( less_eq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(95,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atMost @ a @ less_eq @ C ) )
= ( ~ ( less_eq @ A @ B )
| ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_local_OIcc__subset__Iic__iff) ).
thf(545,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atMost @ a @ less_eq @ C ) )
= ( ~ ( less_eq @ A @ B )
| ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(122,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B )
=> ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_local_OSup__fin_OboundedE) ).
thf(641,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B )
=> ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(240,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) )
=> ( antimono @ a @ TA @ less_eq @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_local_OantimonoI) ).
thf(1058,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) )
=> ( antimono @ a @ TA @ less_eq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(69,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_empty__iff) ).
thf(466,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(250,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [B: a,C: a] : ( member @ a @ ( sup @ B @ C ) @ ( insert @ a @ B @ ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) ) )
=> ( member @ a @ ( lattic1039401930up_fin @ a @ sup @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_local_OSup__fin_Oclosed) ).
thf(1090,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [B: a,C: a] : ( member @ a @ ( sup @ B @ C ) @ ( insert @ a @ B @ ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) ) )
=> ( member @ a @ ( lattic1039401930up_fin @ a @ sup @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(198,axiom,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ D )
=> ( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ E )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ D @ E )
=> ( ( less_eq @ D @ F )
=> ( less_eq @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Oinf__unique) ).
thf(919,plain,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ D )
=> ( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ E )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ D @ E )
=> ( ( less_eq @ D @ F )
=> ( less_eq @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(205,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_local_Oinf_Oorder__iff) ).
thf(947,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(34,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_local_Oorder_Orefl) ).
thf(350,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(132,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_local_Osup_OboundedI) ).
thf(672,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(112,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_local_Osup_OboundedE) ).
thf(611,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(169,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ? [C: a] :
( ( member @ a @ C @ A )
& ( less_eq @ B @ C )
& ! [D: a] :
( ( member @ a @ D @ A )
=> ( ( less_eq @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_local_Ofinite__has__maximal2) ).
thf(787,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ? [C: a] :
( ( member @ a @ C @ A )
& ( less_eq @ B @ C )
& ! [D: a] :
( ( member @ a @ D @ A )
=> ( ( less_eq @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(146,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
=> ( ( least @ a @ less_eq @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_local_OLeast__equality) ).
thf(713,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
=> ( ( least @ a @ less_eq @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_singleton__insert__inj__eq) ).
thf(498,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,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(274,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)],[6]) ).
thf(258,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( inf @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_local_Oinf__Sup__absorb) ).
thf(1117,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( inf @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_doubleton__eq__iff) ).
thf(419,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(152,axiom,
semilattice @ a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_local_Osup_Osemilattice__axioms) ).
thf(736,plain,
semilattice @ a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subset__singleton__iff) ).
thf(362,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(153,axiom,
lattic35693393ce_set @ a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_local_OInf__fin_Osemilattice__set__axioms) ).
thf(737,plain,
lattic35693393ce_set @ a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(84,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_semilattice_Oright__idem) ).
thf(509,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(216,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_local_OInf__fin_OboundedI) ).
thf(979,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( less_eq @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(109,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_local_Oinf_Oright__idem) ).
thf(604,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_singleton__iff) ).
thf(477,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(111,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Osup__ge1) ).
thf(609,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(115,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_local_OInf__fin__le__Sup__fin) ).
thf(621,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(232,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_local_Omax__def) ).
thf(1029,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(204,axiom,
! [A: set @ a,B: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( B
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B ) @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_local_OInf__fin_Osubset) ).
thf(943,plain,
! [A: set @ a,B: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( B
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( ( inf @ ( lattic1263571978nf_fin @ a @ inf @ B ) @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(31,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( abel_semigroup @ TA @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_abel__semigroup_Ocommute) ).
thf(345,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( abel_semigroup @ TA @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(184,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ? [B: a] :
( ( member @ a @ B @ A )
& ! [C: a] :
( ( member @ a @ C @ A )
=> ( ( less_eq @ C @ B )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_local_Ofinite__has__minimal) ).
thf(858,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ? [B: a] :
( ( member @ a @ B @ A )
& ! [C: a] :
( ( member @ a @ C @ A )
=> ( ( less_eq @ C @ B )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(141,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_local_Oinf_Oabsorb__iff1) ).
thf(700,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(88,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_set__eq__subset) ).
thf(520,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(137,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_local_Oinf__commute) ).
thf(685,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(163,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ B @ A ) )
= ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_local_OInf__fin_Oinsert) ).
thf(768,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1263571978nf_fin @ a @ inf @ ( insert @ a @ B @ A ) )
= ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(16,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_semilattice_Oleft__idem) ).
thf(299,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA] :
( ( semilattice @ TA @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,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(267,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(126,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_local_Osup__inf__absorb) ).
thf(653,plain,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(120,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_local_Obdd__below__finite) ).
thf(636,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(235,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_local_Oinf_Oleft__commute) ).
thf(1044,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(243,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_local_Osup_Oassoc) ).
thf(1066,plain,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(8,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_1) ).
thf(278,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(50,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_198_equals0D) ).
thf(394,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)],[50]) ).
thf(217,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_Oinf__idem) ).
thf(986,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(147,axiom,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( modula1221160330_d_aux @ a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_d__c__a__b) ).
thf(722,plain,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( modula1221160330_d_aux @ a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(135,axiom,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_local_Obdd__above__Iic) ).
thf(680,plain,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(124,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_local_Osup__ge2) ).
thf(648,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(157,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Osup_Oidem) ).
thf(749,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(36,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subset__singletonD) ).
thf(355,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(98,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_local_OatLeastAtMost__iff) ).
thf(553,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_empty__subsetI) ).
thf(490,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(133,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_local_Oinf__le1) ).
thf(675,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(129,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Osup_Oleft__idem) ).
thf(663,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(96,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_local_Oinf__le2) ).
thf(548,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(183,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atLeast @ a @ less_eq @ C ) )
= ( ~ ( less_eq @ A @ B )
| ( less_eq @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_local_OIcc__subset__Ici__iff) ).
thf(855,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atLeast @ a @ less_eq @ C ) )
= ( ~ ( less_eq @ A @ B )
| ( less_eq @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(139,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_local_Ole__iff__inf) ).
thf(690,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(14,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_finite) ).
thf(295,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_subset__insert) ).
thf(282,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(207,axiom,
! [A: a,B: a,C: a] :
( ( modula1593167561_e_aux @ a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_e__aux__def) ).
thf(954,plain,
! [A: a,B: a,C: a] :
( ( modula1593167561_e_aux @ a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(238,axiom,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_local_Obdd__above__Icc) ).
thf(1053,plain,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_finite__insert) ).
thf(370,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( finite_finite2 @ TA @ ( insert @ TA @ A @ B ) )
= ( finite_finite2 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(178,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [B: a,C: a] : ( member @ a @ ( inf @ B @ C ) @ ( insert @ a @ B @ ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) ) )
=> ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_local_OInf__fin_Oclosed) ).
thf(840,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ! [B: a,C: a] : ( member @ a @ ( inf @ B @ C ) @ ( insert @ a @ B @ ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) ) )
=> ( member @ a @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subset__iff) ).
thf(463,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(28,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ( abel_semigroup @ TA @ A )
=> ( semigroup @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_abel__semigroup_Oaxioms_I1_J) ).
thf(338,plain,
! [TA: $tType,A: TA > TA > TA] :
( ( abel_semigroup @ TA @ A )
=> ( semigroup @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(262,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_local_Osup_Oabsorb__iff1) ).
thf(1130,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(94,axiom,
abel_semigroup @ a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_local_Oinf_Oabel__semigroup__axioms) ).
thf(544,plain,
abel_semigroup @ a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(194,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ A @ ( inf @ B @ C ) ) @ ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_local_Odistrib__sup__le) ).
thf(907,plain,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ A @ ( inf @ B @ C ) ) @ ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(27,axiom,
! [TA: $tType,A: TA > TA > TA] :
( ( lattic35693393ce_set @ TA @ A )
=> ( semilattice @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_semilattice__set_Oaxioms) ).
thf(336,plain,
! [TA: $tType,A: TA > TA > TA] :
( ( lattic35693393ce_set @ TA @ A )
=> ( semilattice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(142,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( inf @ A @ C ) @ ( inf @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_local_Oinf__mono) ).
thf(703,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( inf @ A @ C ) @ ( inf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(185,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( antimono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_local_OantimonoD) ).
thf(864,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA,B: a,C: a] :
( ( antimono @ a @ TA @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(21,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_197_equals0I) ).
thf(314,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)],[21]) ).
thf(219,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_local_OatLeastAtMost__singleton_H) ).
thf(991,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( insert @ a @ A @ ( bot_bot @ ( set @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(127,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_local_Oinf_Oabsorb1) ).
thf(656,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(230,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_local_Oinf__sup__absorb) ).
thf(1023,plain,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(215,axiom,
condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_local_Obdd__below__empty) ).
thf(978,plain,
condit1201339847_below @ a @ less_eq @ ( bot_bot @ ( set @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(47,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_finite__code) ).
thf(386,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(117,axiom,
! [A: set @ a,B: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( condit1201339847_below @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_local_Obdd__below__mono) ).
thf(627,plain,
! [A: set @ a,B: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( condit1201339847_below @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(63,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_emptyE) ).
thf(450,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(99,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_local_Osup__absorb1) ).
thf(556,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(200,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_local_Ole__infI1) ).
thf(931,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(105,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( greatest @ a @ less_eq @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_local_OGreatestI2__order) ).
thf(581,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( greatest @ a @ less_eq @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semigroup @ TA )
= ( ^ [A: TA > TA > TA] :
! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_semigroup__def) ).
thf(495,plain,
! [TA: $tType] :
( ( semigroup @ TA )
= ( ^ [A: TA > TA > TA] :
! [B: TA,C: TA,D: TA] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(193,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ B @ D ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) )
=> ( C @ D ) ) )
=> ( C @ ( least @ a @ less_eq @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_local_OLeastI2__order) ).
thf(891,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ B @ D ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) )
=> ( C @ D ) ) )
=> ( C @ ( least @ a @ less_eq @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(227,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_local_Ole__supE) ).
thf(1010,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(368,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(255,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_local_Osup__idem) ).
thf(1108,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(214,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_local_Oinf_Ocobounded1) ).
thf(976,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(138,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_local_Osup_Ocobounded2) ).
thf(688,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(241,axiom,
finite_comp_fun_idem @ a @ a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_Ocomp__fun__idem__inf) ).
thf(1062,plain,
finite_comp_fun_idem @ a @ a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(253,axiom,
! [A: set @ a,B: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( B
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B ) @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_local_OSup__fin_Osubset) ).
thf(1101,plain,
! [A: set @ a,B: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( B
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( ord_less_eq @ ( set @ a ) @ B @ A )
=> ( ( sup @ ( lattic1039401930up_fin @ a @ sup @ B ) @ ( lattic1039401930up_fin @ a @ sup @ A ) )
= ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(52,axiom,
! [TA: $tType] :
( ( lattic1039401930up_fin @ TA )
= ( lattic1039401930up_fin @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_semilattice__sup_OSup__fin_Ocong) ).
thf(401,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(150,axiom,
! [A: a] :
( ( bot_bot @ ( set @ a ) )
!= ( set_atMost @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_local_Onot__empty__eq__Iic__eq__empty) ).
thf(731,plain,
! [A: a] :
( ( bot_bot @ ( set @ a ) )
!= ( set_atMost @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(220,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_local_Oinf_OcoboundedI1) ).
thf(995,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(210,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_local_OatLeast__iff) ).
thf(963,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(87,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_196_ex__in__conv) ).
thf(517,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)],[87]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_subset__antisym) ).
thf(383,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(175,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_local_Oinf__right__idem) ).
thf(832,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(93,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Omin__def) ).
thf(536,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(263,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ~ ( less_eq @ A @ B )
| ( ( less_eq @ C @ A )
& ( less_eq @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_local_OatLeastatMost__subset__iff) ).
thf(1133,plain,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq @ ( set @ a ) @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) @ ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ~ ( less_eq @ A @ B )
| ( ( less_eq @ C @ A )
& ( less_eq @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(222,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_local_Osup_Ocobounded1) ).
thf(999,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(158,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ~ ( member @ a @ B @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ B @ A ) )
= ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_local_OSup__fin_Oinsert__not__elem) ).
thf(752,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ~ ( member @ a @ B @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ B @ A ) )
= ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: ( set @ TA ) > $o,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ! [F: TA] :
( ( member @ TA @ F @ E )
=> ( ord_less_eq @ TB @ ( C @ F ) @ ( C @ D ) ) )
=> ( ( B @ E )
=> ( B @ ( insert @ TA @ D @ E ) ) ) ) )
=> ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_finite__ranking__induct) ).
thf(432,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: set @ TA,B: ( set @ TA ) > $o,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( B @ ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA,E: set @ TA] :
( ( finite_finite2 @ TA @ E )
=> ( ! [F: TA] :
( ( member @ TA @ F @ E )
=> ( ord_less_eq @ TB @ ( C @ F ) @ ( C @ D ) ) )
=> ( ( B @ E )
=> ( B @ ( insert @ TA @ D @ E ) ) ) ) )
=> ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(172,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Ole__sup__iff) ).
thf(818,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(59,axiom,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( semigroup @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_semigroup_Oassoc) ).
thf(422,plain,
! [TA: $tType,A: TA > TA > TA,B: TA,C: TA,D: TA] :
( ( semigroup @ TA @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(42,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_local_Odual__order_Oantisym) ).
thf(373,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(151,axiom,
lattic35693393ce_set @ a @ sup,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_local_OSup__fin_Osemilattice__set__axioms) ).
thf(735,plain,
lattic35693393ce_set @ a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(206,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_local_OInf__fin_Oin__idem) ).
thf(950,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( ( inf @ B @ ( lattic1263571978nf_fin @ a @ inf @ A ) )
= ( lattic1263571978nf_fin @ a @ inf @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(252,axiom,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( sup @ D @ ( inf @ E @ F ) )
= ( inf @ ( sup @ D @ E ) @ ( sup @ D @ F ) ) )
=> ( ( inf @ A @ ( sup @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_local_Odistrib__imp2) ).
thf(1097,plain,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( sup @ D @ ( inf @ E @ F ) )
= ( inf @ ( sup @ D @ E ) @ ( sup @ D @ F ) ) )
=> ( ( inf @ A @ ( sup @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(176,axiom,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_local_Osup_OorderI) ).
thf(835,plain,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(187,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_local_OInf__fin_OcoboundedI) ).
thf(867,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( member @ a @ B @ A )
=> ( less_eq @ ( lattic1263571978nf_fin @ a @ inf @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(5,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_3) ).
thf(273,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_equalityD1) ).
thf(305,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_Oeq__refl) ).
thf(358,plain,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Collect__mono__iff) ).
thf(474,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(209,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_local_Ole__supI1) ).
thf(960,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(199,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_local_Oinf__left__idem) ).
thf(928,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(56,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_local_Odual__order_Oeq__iff) ).
thf(415,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(149,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Osup__mono) ).
thf(728,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(67,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Collect__mono) ).
thf(459,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(224,axiom,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_local_Obdd__below__Ici) ).
thf(1004,plain,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(7,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(277,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(82,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_order__class_Ofinite__has__minimal2) ).
thf(501,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(110,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_local_Obdd__above__finite) ).
thf(607,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(251,axiom,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( inf @ D @ ( sup @ E @ F ) )
= ( sup @ ( inf @ D @ E ) @ ( inf @ D @ F ) ) )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_local_Odistrib__imp1) ).
thf(1093,plain,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( inf @ D @ ( sup @ E @ F ) )
= ( sup @ ( inf @ D @ E ) @ ( inf @ D @ F ) ) )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(116,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_local_Osup__assoc) ).
thf(624,plain,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(233,axiom,
! [A: a,B: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ ( insert @ a @ A @ B ) )
= ( condit2040224947_above @ a @ less_eq @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_local_Obdd__above__insert) ).
thf(1037,plain,
! [A: a,B: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ ( insert @ a @ A @ B ) )
= ( condit2040224947_above @ a @ less_eq @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(190,axiom,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_d__aux__def) ).
thf(882,plain,
! [A: a,B: a,C: a] :
( ( modula1221160330_d_aux @ a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(202,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ( mono @ a @ TA @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_local_Omono__def) ).
thf(935,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: a > TA] :
( ( mono @ a @ TA @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(226,axiom,
semigroup @ a @ inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_local_Oinf_Osemigroup__axioms) ).
thf(1009,plain,
semigroup @ a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(19,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__empty) ).
thf(309,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(128,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ B @ A ) )
= ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_local_OSup__fin_Oinsert) ).
thf(659,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( lattic1039401930up_fin @ a @ sup @ ( insert @ a @ B @ A ) )
= ( sup @ B @ ( lattic1039401930up_fin @ a @ sup @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(65,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_2) ).
thf(454,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(244,axiom,
! [A: a,B: a,C: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) )
= ( ( A = B )
& ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_local_OatLeastAtMost__singleton__iff) ).
thf(1069,plain,
! [A: a,B: a,C: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( insert @ a @ C @ ( bot_bot @ ( set @ a ) ) ) )
= ( ( A = B )
& ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(228,axiom,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ? [B: a] :
( ( member @ a @ B @ A )
& ! [C: a] :
( ( member @ a @ C @ A )
=> ( ( less_eq @ B @ C )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_local_Ofinite__has__maximal) ).
thf(1014,plain,
! [A: set @ a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ? [B: a] :
( ( member @ a @ B @ A )
& ! [C: a] :
( ( member @ a @ C @ A )
=> ( ( less_eq @ B @ C )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(213,axiom,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B )
= ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_local_OSup__fin_Obounded__iff) ).
thf(972,plain,
! [A: set @ a,B: a] :
( ( finite_finite2 @ a @ A )
=> ( ( A
!= ( bot_bot @ ( set @ a ) ) )
=> ( ( less_eq @ ( lattic1039401930up_fin @ a @ sup @ A ) @ B )
= ( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1857,plain,
$false,
inference(e,[status(thm)],[645,365,760,1105,846,777,666,352,909,333,1083,468,379,677,597,523,762,1078,533,550,472,913,1063,340,404,1001,1127,709,417,885,320,565,389,1055,785,934,619,838,817,559,638,1087,870,969,325,289,492,756,1040,376,966,821,480,485,1136,1020,348,280,866,1072,774,998,428,507,312,265,849,292,452,512,381,1047,270,529,957,746,778,302,349,598,392,297,693,630,916,879,852,682,710,456,285,317,650,615,1121,1111,725,1006,989,742,578,488,669,1075,526,706,328,471,1114,515,738,1050,569,343,938,633,765,398,1026,794,888,412,425,824,601,562,402,843,772,1124,545,641,1058,466,1090,919,947,350,672,611,787,713,498,274,1117,419,736,362,737,509,979,604,477,609,621,1029,943,345,858,700,520,685,768,299,267,653,636,1044,1066,278,394,986,722,680,648,749,355,553,490,675,663,548,855,690,295,282,954,1053,370,840,463,338,1130,544,907,336,703,864,314,991,656,1023,978,386,627,450,556,931,581,495,891,1010,368,1108,976,688,1062,1101,401,731,995,963,517,383,832,536,1133,999,752,432,818,422,373,735,950,1097,835,867,273,305,358,474,960,928,415,728,459,1004,277,501,607,1093,624,1037,882,935,1009,309,659,454,1069,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP124^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n018.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:59:26 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.00/1.17 % [INFO] Parsing done (379ms).
% 2.00/1.19 % [INFO] Running in sequential loop mode.
% 3.30/1.57 % [INFO] eprover registered as external prover.
% 3.30/1.58 % [INFO] Scanning for conjecture ...
% 3.69/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 263 axioms. Running axiom selection ...
% 3.89/1.85 % [INFO] Axiom selection finished. Selected 262 axioms (removed 1 axioms).
% 4.49/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 4.49/2.12 % [INFO] Type checking passed.
% 4.76/2.13 % [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 ...
% 26.13/10.19 % External prover 'e' found a proof!
% 26.13/10.19 % [INFO] Killing All external provers ...
% 26.13/10.19 % Time passed: 9829ms (effective reasoning time: 9000ms)
% 26.13/10.19 % 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)>
% 26.13/10.20 % Axioms used in derivation (262): fact_41_local_OInf__fin_Osemilattice__set__axioms, fact_150_local_Ofinite__has__minimal2, fact_149_local_Ofinite__has__maximal2, fact_88_local_Osup__least, fact_168_local_OSup__fin_Osubset__imp, fact_13_local_Odistrib__imp2, fact_113_local_Oorder__refl, fact_237_finite__ranking__induct, tcon_fun___Finite__Set_Ofinite, fact_59_local_Oorder_Otrans, fact_3_local_Oinf__assoc, fact_205_subset__iff, fact_18_local_Oinf__idem, fact_224_local_OInf__fin_Oinsert, fact_179_local_OSup__fin_OboundedE, fact_214_local_OInf__fin_Oclosed, fact_140_abel__semigroup_Ocommute, fact_97_local_Osup_OcoboundedI2, fact_148_local_Obdd__above__finite, fact_21_local_Osup_Oidem, fact_143_semigroup_Oassoc, fact_17_local_Oinf_Oright__idem, fact_98_local_Osup_OcoboundedI1, fact_117_local_Omin__def, fact_235_subset__insert, fact_26_local_Oinf__sup__absorb, fact_209_equalityE, fact_247_local_OatLeastatMost__subset__iff, fact_114_local_OGreatestI2__order, fact_54_local_Oeq__refl, fact_129_semilattice__set_Ointro, fact_172_local_OInf__fin_Osubset, fact_96_local_Osup_Omono, fact_70_local_Oinf__greatest, fact_186_Collect__empty__eq, fact_72_local_Oinf__absorb1, fact_110_local_Ole__supE, fact_248_local_OatLeastAtMost__singleton, fact_223_local_OSup__fin_Osingleton, fact_141_semilattice_Oidem, fact_68_local_Oinf__le2, fact_58_local_Oorder_Oeq__iff, tcon_HOL_Obool___Orderings_Olinorder, fact_71_local_Oinf__absorb2, fact_246_local_Obdd__above__Icc, fact_221_local_Obdd__below__insert, fact_105_local_Osup_Oabsorb2, fact_64_local_Ole__infE, fact_76_local_Oinf_OcoboundedI2, fact_254_comp__fun__idem_Ofun__left__idem, fact_187_all__not__in__conv, fact_167_local_OInf__fin__le__Sup__fin, fact_134_local_Otransp__le, fact_61_local_Ole__infI2, fact_34_local_Osup_Osemigroup__axioms, fact_228_singletonD, fact_225_local_OSup__fin_Oinsert, fact_46_Collect__mem__eq, fact_155_local_OmonoD, fact_161_local_OSup__fin_Oin__idem, fact_208_subset__eq, fact_108_local_Ole__supI1, fact_101_local_Osup_OboundedI, fact_233_subset__insertI2, fact_29_d__b__c__a, fact_164_local_Osup__Inf__absorb, fact_25_local_Osup__left__idem, fact_207_equalityD1, fact_16_local_Oinf_Oleft__idem, fact_102_local_Osup_OboundedE, fact_5_local_Oinf__left__commute, fact_193_local_OatMost__iff, fact_253_finite__set__choice, fact_87_local_Osup__mono, fact_103_local_Osup_Oabsorb__iff2, fact_60_local_Oorder__trans, fact_104_local_Osup_Oabsorb__iff1, fact_219_singleton__insert__inj__eq, fact_44_local_Oantisym, fact_82_local_Oinf_Oabsorb__iff2, fact_52_local_Odual__order_Otrans, fact_180_local_Obdd__above__empty, fact_111_local_Ole__iff__sup, fact_147_local_Obdd__below__finite, fact_182_local_Onot__empty__eq__Iic__eq__empty, fact_146_local_Obdd__above__mono, fact_55_local_Oord__eq__le__trans, fact_27_local_Osup__inf__absorb, fact_206_equalityD2, fact_118_local_Ole__inf__iff, fact_122_local_OLeast1I, fact_81_local_Oinf_OboundedE, fact_49_local_Oantisym__conv, fact_63_local_Ole__infI, fact_191_empty__subsetI, fact_38_local_Osup_Oabel__semigroup__axioms, fact_90_local_Osup__ge1, fact_181_local_Obdd__below__empty, fact_156_local_OmonoE, fact_229_singleton__iff, fact_201_set__eq__subset, fact_152_local_OantimonoE, fact_178_local_OSup__fin_OboundedI, fact_213_local_OSup__fin_Oinsert__not__elem, fact_92_local_Osup__absorb1, fact_199_emptyE, fact_86_local_Osup__unique, fact_162_local_OInf__fin_Oin__idem, fact_9_local_Osup__assoc, fact_238_local_OatLeastAtMost__singleton_H, fact_151_local_OantimonoD, fact_251_local_OIcc__subset__Iic__iff, fact_217_insert__subset, fact_69_local_Oinf__le1, fact_252_finite, fact_200_Collect__mono__iff, fact_137_abel__semigroup_Oleft__commute, fact_116_local_Omax__def, fact_45_mem__Collect__eq, fact_109_local_Ole__supI, fact_89_local_Osup__ge2, fact_240_finite__code, fact_83_local_Oinf_Oabsorb__iff1, fact_123_local_OLeast1__le, fact_119_local_Oinf_Obounded__iff, fact_194_local_Obdd__below__Ici, fact_2_local_Oinf_Oleft__commute, fact_144_semigroup__def, fact_100_local_Osup_Ocobounded1, fact_31_lattice_Oe__aux_Ocong, fact_173_local_OSup__fin_Osubset, fact_222_local_OInf__fin_Osingleton, fact_216_singletonI, fact_106_local_Osup_Oabsorb1, fact_93_local_Osup_Oorder__iff, fact_50_local_Odual__order_Oantisym, fact_170_local_Ofinite__has__minimal, fact_99_local_Osup_Ocobounded2, fact_243_local_OatLeastatMost__empty__iff, fact_85_local_Oinf_Oabsorb1, fact_77_local_Oinf_OcoboundedI1, fact_112_local_Oorder_Orefl, tcon_HOL_Obool___Finite__Set_Ofinite_3, fact_15_local_Oinf_Oidem, fact_40_local_OSup__fin_Osemilattice__set__axioms, fact_226_subset__singletonD, fact_42_local_Odistrib__inf__le, fact_47_Collect__cong, fact_10_local_Osup__commute, fact_139_semilattice_Oleft__idem, fact_121_local_Ole__sup__iff, fact_23_local_Osup_Oright__idem, fact_241_local_OIcc__eq__Icc, fact_32_local_Ocomp__fun__idem__sup, fact_158_local_Omono__def, fact_183_local_Onot__empty__eq__Ici__eq__empty, fact_37_local_Oinf_Osemilattice__axioms, fact_231_insert__not__empty, fact_165_semilattice__inf_OInf__fin_Ocong, fact_128_semilattice__set__def, fact_203_Collect__mono, fact_11_local_Osup__left__commute, fact_131_semilattice_Oaxioms_I1_J, fact_255_order__class_Ofinite__has__minimal2, fact_124_local_OLeastI2__order, fact_127_abel__semigroup_Oaxioms_I1_J, fact_126_lattice_Od__aux_Ocong, fact_75_local_Oinf_OorderE, fact_163_local_Oinf__Sup__absorb, fact_74_local_Oinf_OorderI, fact_73_local_Oinf_Oorder__iff, fact_234_subset__insertI, fact_1_local_Oinf_Ocommute, fact_20_local_Oinf__right__idem, fact_145_local_Obdd__below__mono, fact_39_local_Oinf_Oabel__semigroup__axioms, fact_22_local_Osup_Oleft__idem, fact_250_local_OIcc__subset__Ici__iff, fact_95_local_Osup_OorderE, fact_227_subset__singleton__iff, fact_19_local_Oinf__left__idem, fact_195_local_Obdd__above__Iic, fact_236_insert__mono, fact_57_local_Oorder_Oantisym, fact_79_local_Oinf_Ocobounded1, fact_169_local_OInf__fin_Osubset__imp, fact_94_local_Osup_OorderI, fact_84_local_Oinf_Oabsorb2, tcon_Set_Oset___Orderings_Oorder_2, fact_62_local_Ole__infI1, fact_215_local_OInf__fin_Oinsert__not__elem, fact_115_local_OGreatest__equality, fact_171_local_Ofinite__has__maximal, fact_166_semilattice__sup_OSup__fin_Ocong, fact_159_local_OSup__fin_OcoboundedI, fact_249_local_OatLeastAtMost__singleton__iff, fact_198_equals0D, tcon_Set_Oset___Finite__Set_Ofinite_1, tcon_HOL_Obool___Orderings_Oorder_4, fact_174_local_OInf__fin_Obounded__iff, fact_130_semilattice__set_Oaxioms, fact_212_local_OSup__fin_Oclosed, fact_142_semigroup_Ointro, fact_184_subset__empty, fact_244_local_OatLeastatMost__empty__iff2, fact_67_local_Oinf__mono, fact_135_local_Obdd__belowI, fact_138_semilattice_Oright__idem, fact_153_local_OantimonoI, fact_220_local_Obdd__above__insert, fact_133_local_Obdd__below__def, fact_7_local_Osup_Ocommute, fact_210_subsetD, fact_125_local_OLeast__equality, fact_196_ex__in__conv, fact_0_local_Oinf_Oassoc, fact_43_local_Odistrib__sup__le, fact_6_local_Osup_Oassoc, tcon_fun___Orderings_Oorder, fact_197_equals0I, fact_56_local_Oord__le__eq__trans, fact_136_local_Obdd__aboveI, fact_53_local_Oeq__iff, fact_211_in__mono, fact_190_subsetI, fact_160_local_OInf__fin_OcoboundedI, fact_188_empty__iff, fact_91_local_Osup__absorb2, fact_28_d__aux__def, fact_192_local_OatLeast__iff, fact_245_local_Obdd__below__Icc, fact_242_local_OatLeastAtMost__iff, fact_24_local_Osup__idem, fact_14_e__aux__def, fact_66_local_Oinf__unique, fact_202_subset__trans, fact_189_subset__antisym, fact_33_local_Ocomp__fun__idem__inf, fact_177_local_OSup__fin_Obounded__iff, fact_4_local_Oinf__commute, fact_78_local_Oinf_Ocobounded2, fact_239_finite__insert, fact_80_local_Oinf_OboundedI, fact_65_local_Ole__iff__inf, fact_232_singleton__inject, fact_30_d__c__a__b, fact_230_doubleton__eq__iff, fact_185_empty__Collect__eq, fact_35_local_Oinf_Osemigroup__axioms, fact_8_local_Osup_Oleft__commute, fact_218_singleton__insert__inj__eq_H, fact_157_local_OmonoI, fact_154_local_Oantimono__def, fact_36_local_Osup_Osemilattice__axioms, fact_175_local_OInf__fin_OboundedI, fact_51_local_Odual__order_Oeq__iff, fact_120_local_Osup_Obounded__iff, fact_204_subset__refl, fact_132_local_Obdd__above__def, fact_176_local_OInf__fin_OboundedE, fact_107_local_Ole__supI2, fact_12_local_Odistrib__imp1
% 26.13/10.20 % No. of inferences in proof: 528
% 26.13/10.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9829 ms resp. 9000 ms w/o parsing
% 32.30/10.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.30/10.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------