TSTP Solution File: ITP123^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP123^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:08 EDT 2024
% Result : Theorem 10.59s 3.34s
% Output : Refutation 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 290
% Syntax : Number of formulae : 546 ( 248 unt; 36 typ; 0 def)
% Number of atoms : 1152 ( 363 equ; 6 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3742 ( 96 ~; 8 |; 62 &;3120 @)
% ( 0 <=>; 456 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 548 ( 548 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 6 con; 0-6 aty)
% Number of variables : 1308 ( 22 ^1278 !; 8 ?;1308 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(condit1627435690bove_a_type,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(condit1001553558elow_a_type,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(finite40241356em_a_a_type,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(abel_semigroup_a_type,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(semigroup_a_type,type,
semigroup_a: ( a > a > a ) > $o ).
thf(lattice_a_type,type,
lattice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > ( a > a > a ) > $o ).
thf(semilattice_a_type,type,
semilattice_a: ( a > a > a ) > $o ).
thf(semilattice_order_a_type,type,
semilattice_order_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(lattic655834328_set_a_type,type,
lattic655834328_set_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(lattic1885654924_set_a_type,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(modula1376131916tice_a_type,type,
modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(modula397570059tice_a_type,type,
modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(modula17988509_aux_a_type,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1373251614_aux_a_type,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula581031071_aux_a_type,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1936294176_aux_a_type,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1144073633_aux_a_type,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1727524044comp_a_type,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(modula1962211574trib_a_type,type,
modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(least_a_type,type,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(max_a_type,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(min_a_type,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(greatest_a_type,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(ordering_a_type,type,
ordering_a: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(set_gr1491433118Than_a_type,type,
set_gr1491433118Than_a: ( a > a > $o ) > a > a > set_a ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(inf_type,type,
inf: a > a > a ).
thf(less_type,type,
less: a > a > $o ).
thf(less_eq_type,type,
less_eq: a > a > $o ).
thf(sup_type,type,
sup: a > a > a ).
thf(x_type,type,
x: a ).
thf(y_type,type,
y: a ).
thf(z_type,type,
z: a ).
thf(137,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_local_Oe__c__a__b) ).
thf(645,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(173,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_local_Ole__imp__less__or__eq) ).
thf(760,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(37,axiom,
( semigroup_a
= ( ^ [A: a > a > a] :
! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_semigroup__def) ).
thf(347,plain,
( semigroup_a
= ( ^ [A: a > a > a] :
! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(131,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_local_Ole__neq__trans) ).
thf(628,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(220,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_local_Oeq__iff) ).
thf(893,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(92,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_local_Osup_Oabsorb2) ).
thf(518,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',fact_164_local_OLeast1I) ).
thf(962,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)],[244]) ).
thf(237,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_local_Osup_Ocobounded2) ).
thf(941,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(81,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_local_Oinf_Oassoc) ).
thf(481,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)],[81]) ).
thf(39,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( B @ ( A @ D @ E ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_semilattice__order_Ocobounded1) ).
thf(352,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( B @ ( A @ D @ E ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(57,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( A @ E @ D )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_semilattice__order_Oabsorb2) ).
thf(408,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( A @ E @ D )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ( semilattice_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_semilattice__order_Oaxioms_I1_J) ).
thf(449,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ( semilattice_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(125,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_local_Oinf_Oorder__iff) ).
thf(614,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(118,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_local_Osup_Oleft__commute) ).
thf(597,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)],[118]) ).
thf(210,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_local_Oinf_OboundedI) ).
thf(861,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)],[210]) ).
thf(163,axiom,
semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_local_Osup_Osemigroup__axioms) ).
thf(730,plain,
semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(11,axiom,
lattic1885654924_set_a = semilattice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semilattice__set__def) ).
thf(276,plain,
lattic1885654924_set_a = semilattice_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',fact_153_local_Omax__def) ).
thf(878,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)],[216]) ).
thf(65,axiom,
! [A: a > a > a] :
( ! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_semigroup_Ointro) ).
thf(440,plain,
! [A: a > a > a] :
( ! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(49,axiom,
! [A: a > a > a,B: a,C: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_abel__semigroup_Ocommute) ).
thf(385,plain,
! [A: a > a > a,B: a,C: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(87,axiom,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_local_Osup_OorderI) ).
thf(500,plain,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(158,axiom,
lattic1885654924_set_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_local_OSup__fin_Osemilattice__set__axioms) ).
thf(715,plain,
lattic1885654924_set_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(233,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_local_Osup__left__commute) ).
thf(930,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)],[233]) ).
thf(198,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Odual__order_Oantisym) ).
thf(829,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(222,axiom,
! [A: a,B: a,C: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
= ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_local_Ono__distrib__def) ).
thf(898,plain,
! [A: a,B: a,C: a] :
( ( modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C )
= ( less @ ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(156,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_local_Osup_Ostrict__coboundedI2) ).
thf(709,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(202,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_local_Osup_OboundedE) ).
thf(841,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)],[202]) ).
thf(217,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_local_Oinf_Oabsorb__iff2) ).
thf(885,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(16,axiom,
modula397570059tice_a = modula397570059tice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lattice_ON5__lattice_Ocong) ).
thf(288,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ( semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_abel__semigroup_Oaxioms_I1_J) ).
thf(301,plain,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ( semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Oless__imp__not__eq) ).
thf(436,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',fact_119_local_Osup__mono) ).
thf(651,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)],[139]) ).
thf(3,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(257,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Odual__order_Ostrict__trans) ).
thf(389,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(160,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Ole__supE) ).
thf(719,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)],[160]) ).
thf(201,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_local_Oinf_Ostrict__order__iff) ).
thf(838,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(240,axiom,
! [A: set_a,B: a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit1627435690bove_a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_local_Obdd__aboveI) ).
thf(949,plain,
! [A: set_a,B: a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit1627435690bove_a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(153,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_Oless__imp__le) ).
thf(702,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(170,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_local_Oa__join__d) ).
thf(751,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(101,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_local_Osup__left__idem) ).
thf(542,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(73,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_local_Ob__aux__def) ).
thf(460,plain,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(206,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_local_Osup_Obounded__iff) ).
thf(853,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)],[206]) ).
thf(245,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_local_Ole__sup__iff) ).
thf(969,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)],[245]) ).
thf(15,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
= ( ( D
= ( A @ D @ E ) )
& ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_semilattice__order_Ostrict__order__iff) ).
thf(284,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
= ( ( D
= ( A @ D @ E ) )
& ( D != E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ ( A @ E @ F ) )
=> ~ ( ( B @ D @ E )
=> ~ ( B @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_semilattice__order_OboundedE) ).
thf(416,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ ( A @ E @ F ) )
=> ~ ( ( B @ D @ E )
=> ~ ( B @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( lattic1885654924_set_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_semilattice__set_Ointro) ).
thf(289,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( lattic1885654924_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(316,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(183,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_local_Osup__assoc) ).
thf(789,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)],[183]) ).
thf(66,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(443,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_local_Oorder_Ostrict__trans) ).
thf(321,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(90,axiom,
semilattice_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_local_Oinf_Osemilattice__axioms) ).
thf(514,plain,
semilattice_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(194,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Oless__le) ).
thf(821,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(175,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_local_Oinf_Oabsorb1) ).
thf(766,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(148,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_local_Oinf__right__idem) ).
thf(687,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(13,axiom,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Oless__imp__triv) ).
thf(280,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(133,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( less_eq @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_local_Oantisym__conv1) ).
thf(634,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( less_eq @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(242,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_local_Osup_Oorder__iff) ).
thf(956,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(52,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( lattic1885654924_set_a @ A )
=> ( lattic655834328_set_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_semilattice__order__set_Ointro) ).
thf(396,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( lattic1885654924_set_a @ A )
=> ( lattic655834328_set_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_166_local_OLeastI2__order) ).
thf(660,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)],[142]) ).
thf(95,axiom,
lattic655834328_set_a @ inf @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_local_OInf__fin_Osemilattice__order__set__axioms) ).
thf(527,plain,
lattic655834328_set_a @ inf @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(70,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_Oless__asym) ).
thf(452,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(8,axiom,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_abel__semigroup_Oleft__commute) ).
thf(270,plain,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(231,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_local_Oinf_Oleft__idem) ).
thf(925,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(190,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Ole__supI1) ).
thf(810,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)],[190]) ).
thf(48,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_local_Odual__order_Ostrict__implies__not__eq) ).
thf(381,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(43,axiom,
modula1962211574trib_a = modula1962211574trib_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lattice_Ono__distrib_Ocong) ).
thf(366,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(98,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_local_Osup__ge1) ).
thf(534,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_110_local_Osup_Omono) ).
thf(798,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)],[186]) ).
thf(33,axiom,
! [A: a > a > a,B: a,C: a,D: a] :
( ( semigroup_a @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_semigroup_Oassoc) ).
thf(334,plain,
! [A: a > a > a,B: a,C: a,D: a] :
( ( semigroup_a @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(196,axiom,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
=> ( modula1727524044comp_a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_local_OM5__lattice__incomp) ).
thf(825,plain,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
=> ( modula1727524044comp_a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(51,axiom,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_semilattice_Oleft__idem) ).
thf(392,plain,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(20,axiom,
modula581031071_aux_a = modula581031071_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_lattice_Oc__aux_Ocong) ).
thf(297,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(150,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_local_Ole__supI) ).
thf(693,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)],[150]) ).
thf(10,axiom,
modula17988509_aux_a = modula17988509_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_lattice_Oa__aux_Ocong) ).
thf(275,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Oless__imp__not__less) ).
thf(260,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
=> ( C @ ( A @ D @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_semilattice__order_Ostrict__coboundedI1) ).
thf(349,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
=> ( C @ ( A @ D @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(114,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_local_Oless__infI1) ).
thf(583,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(172,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_local_Ole__less) ).
thf(757,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_152_local_OGreatest__equality) ).
thf(682,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)],[147]) ).
thf(30,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( A @ D @ E )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_semilattice__order_Oabsorb1) ).
thf(324,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( A @ D @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(228,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_local_Oorder_Onot__eq__order__implies__strict) ).
thf(916,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(76,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_local_Ole__supI2) ).
thf(467,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)],[76]) ).
thf(204,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_local_Od__aux__def) ).
thf(847,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_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)],[204]) ).
thf(107,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_local_Oorder_Oantisym) ).
thf(566,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(82,axiom,
! [A: set_a,B: a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1001553558elow_a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_local_Obdd__belowI) ).
thf(484,plain,
! [A: set_a,B: a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1001553558elow_a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_167_local_OLeast__equality) ).
thf(725,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)],[162]) ).
thf(213,axiom,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(869,plain,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(123,axiom,
ordering_a @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_local_Oorder_Oordering__axioms) ).
thf(610,plain,
ordering_a @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(60,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_local_Oless__not__sym) ).
thf(420,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(252,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_local_Odual__order_Onot__eq__order__implies__strict) ).
thf(989,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(208,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_local_Oinf_Ostrict__coboundedI2) ).
thf(857,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(83,axiom,
! [A: a,B: a,C: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ C )
= ( inf @ B @ C ) )
& ( less @ A @ B )
& ( ( sup @ A @ C )
= ( sup @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_local_ON5__lattice__def) ).
thf(488,plain,
! [A: a,B: a,C: a] :
( ( modula397570059tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ C )
= ( inf @ B @ C ) )
& ( less @ A @ B )
& ( ( sup @ A @ C )
= ( sup @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(234,axiom,
! [A: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_local_Obdd__below__def) ).
thf(933,plain,
! [A: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(144,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_local_Ole__infI) ).
thf(669,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)],[144]) ).
thf(136,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_local_Oless__infI2) ).
thf(642,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(134,axiom,
! [A: a,B: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_local_Obdd__below__Ioo) ).
thf(637,plain,
! [A: a,B: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(31,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Oless__asym_H) ).
thf(328,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1,conjecture,
less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(256,plain,
~ ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(223,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_local_Oinf__sup__absorb) ).
thf(901,plain,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(79,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_local_Oinf__le2) ).
thf(476,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(91,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_local_Oinf_Oidem) ).
thf(515,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(140,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_local_Odual__order_Otrans) ).
thf(654,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)],[140]) ).
thf(72,axiom,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_local_Oinf_OorderI) ).
thf(457,plain,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(226,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_local_Ole__infE) ).
thf(911,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)],[226]) ).
thf(108,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_local_Osup_OorderE) ).
thf(569,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(179,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_local_OleD) ).
thf(779,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(45,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( B @ ( A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_semilattice__order_Ocobounded2) ).
thf(371,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( B @ ( A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_local_Osup_Oabsorb1) ).
thf(503,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(36,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( ( A @ E @ D )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_semilattice__order_Oabsorb__iff2) ).
thf(343,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( ( A @ E @ D )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(184,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_local_Oinf__left__idem) ).
thf(792,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
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/sandbox/benchmark/theBenchmark.p',fact_157_local_Oinf_Obounded__iff) ).
thf(938,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(6,axiom,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
=> ( semilattice_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_semilattice__set_Oaxioms) ).
thf(266,plain,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
=> ( semilattice_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(141,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_local_Osup__commute) ).
thf(657,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(53,axiom,
modula1144073633_aux_a = modula1144073633_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_lattice_Oe__aux_Ocong) ).
thf(398,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(241,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_local_Oinf__absorb2) ).
thf(953,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(115,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ A @ C ) )
= ( inf @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_local_Ob__meet__e) ).
thf(586,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ A @ C ) )
= ( inf @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(218,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Oinf_Oabsorb2) ).
thf(888,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(225,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_local_Oord__le__eq__trans) ).
thf(906,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)],[225]) ).
thf(21,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a,G: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( B @ F @ G )
=> ( B @ ( A @ D @ F ) @ ( A @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_semilattice__order_Omono) ).
thf(298,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a,G: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( B @ F @ G )
=> ( B @ ( A @ D @ F ) @ ( A @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(58,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_local_Oorder_Ostrict__implies__not__eq) ).
thf(412,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(127,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_local_Oorder_Oorder__iff__strict) ).
thf(618,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(195,axiom,
abel_semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_local_Oinf_Oabel__semigroup__axioms) ).
thf(824,plain,
abel_semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(207,axiom,
semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_local_Oinf_Osemigroup__axioms) ).
thf(856,plain,
semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(168,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_local_Osup__absorb2) ).
thf(745,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(110,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_local_Oinf_Oright__idem) ).
thf(573,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_151_local_OGreatestI2__order) ).
thf(733,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)],[165]) ).
thf(120,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_local_Oinf_OorderE) ).
thf(601,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(193,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_local_Oinf__le1) ).
thf(819,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(55,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Oless__irrefl) ).
thf(402,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_134_local_Odistrib__imp2) ).
thf(772,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)],[177]) ).
thf(167,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_local_Oorder_Ostrict__implies__order) ).
thf(743,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(18,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( D
= ( A @ D @ E ) )
=> ( B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_semilattice__order_OorderI) ).
thf(291,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( D
= ( A @ D @ E ) )
=> ( B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_120_local_Osup__unique) ).
thf(545,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)],[102]) ).
thf(224,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_local_Osup__ge2) ).
thf(904,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(247,axiom,
semilattice_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_local_Osup_Osemilattice__axioms) ).
thf(975,plain,
semilattice_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(215,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_local_Ole__less__trans) ).
thf(875,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(112,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_local_Oorder_Ostrict__trans2) ).
thf(577,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(235,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_local_Oinf_Ocobounded1) ).
thf(936,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(109,axiom,
finite40241356em_a_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_local_Ocomp__fun__idem__inf) ).
thf(572,plain,
finite40241356em_a_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( lattic655834328_set_a @ A @ B @ C )
=> ( lattic1885654924_set_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semilattice__order__set_Oaxioms_I2_J) ).
thf(313,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( lattic655834328_set_a @ A @ B @ C )
=> ( lattic1885654924_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(124,axiom,
! [A: a,B: a,C: a] :
( ( less @ ( sup @ A @ B ) @ C )
=> ~ ( ( less @ A @ C )
=> ~ ( less @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_local_Osup_Ostrict__boundedE) ).
thf(611,plain,
! [A: a,B: a,C: a] :
( ( less @ ( sup @ A @ B ) @ C )
=> ~ ( ( less @ A @ C )
=> ~ ( less @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(75,axiom,
less_eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(466,plain,
less_eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(154,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_local_Osup_Oabsorb__iff2) ).
thf(704,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(145,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_local_Osup__least) ).
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)],[145]) ).
thf(229,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Oorder_Ostrict__iff__order) ).
thf(919,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(188,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_local_Osup_OboundedI) ).
thf(804,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)],[188]) ).
thf(9,axiom,
modula1376131916tice_a = modula1376131916tice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_lattice_OM5__lattice_Ocong) ).
thf(274,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(181,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_local_Oinf_Ocobounded2) ).
thf(784,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(254,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_local_Ole__inf__iff) ).
thf(996,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)],[254]) ).
thf(42,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( D
= ( A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_semilattice__order_Oorder__iff) ).
thf(362,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( D
= ( A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( B @ ( A @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_semilattice__order_OcoboundedI2) ).
thf(303,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( B @ ( A @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_165_local_OLeast1__le) ).
thf(979,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)],[249]) ).
thf(121,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_local_Oinf_Ostrict__coboundedI1) ).
thf(604,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(85,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_local_Oorder__trans) ).
thf(494,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)],[85]) ).
thf(132,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_local_Oinf__left__commute) ).
thf(631,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)],[132]) ).
thf(44,axiom,
! [A: a > a > a,B: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_semilattice_Oidem) ).
thf(367,plain,
! [A: a > a > a,B: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(192,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_local_Ob__a) ).
thf(816,plain,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(117,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_local_Osup_Oassoc) ).
thf(594,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)],[117]) ).
thf(128,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_local_Osup_OcoboundedI2) ).
thf(621,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)],[128]) ).
thf(221,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_local_Odual__order_Ostrict__trans2) ).
thf(895,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(176,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_local_Osup__absorb1) ).
thf(769,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(238,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_local_Od__b__c__a) ).
thf(943,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(32,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( D
= ( A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_semilattice__order_OorderE) ).
thf(330,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( D
= ( A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_local_Oe__aux__def) ).
thf(521,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_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)],[93]) ).
thf(250,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_local_Oinf__idem) ).
thf(983,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(54,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_local_Oless__trans) ).
thf(399,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',fact_88_local_Oinf__mono) ).
thf(959,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)],[243]) ).
thf(12,axiom,
( lattic655834328_set_a
= ( ^ [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
& ( lattic1885654924_set_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_semilattice__order__set__def) ).
thf(278,plain,
( lattic655834328_set_a
= ( ^ [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
& ( lattic1885654924_set_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(106,axiom,
! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_local_Oa__aux__def) ).
thf(563,plain,
! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(63,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_local_Oord__less__eq__trans) ).
thf(431,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(230,axiom,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ B )
= ( inf @ B @ C ) )
& ( ( inf @ C @ A )
= ( inf @ B @ C ) )
& ( ( sup @ A @ B )
= ( sup @ B @ C ) )
& ( ( sup @ C @ A )
= ( sup @ B @ C ) )
& ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_local_OM5__lattice__def) ).
thf(922,plain,
! [A: a,B: a,C: a] :
( ( modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C )
= ( ( ( inf @ A @ B )
= ( inf @ B @ C ) )
& ( ( inf @ C @ A )
= ( inf @ B @ C ) )
& ( ( sup @ A @ B )
= ( sup @ B @ C ) )
& ( ( sup @ C @ A )
= ( sup @ B @ C ) )
& ( less @ ( inf @ A @ B ) @ ( sup @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(251,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_local_Oinf_Oabsorb__iff1) ).
thf(986,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(24,axiom,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_semilattice_Oright__idem) ).
thf(306,plain,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_local_Ole__infI1) ).
thf(473,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)],[78]) ).
thf(161,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_local_Osup_Oleft__idem) ).
thf(722,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',fact_154_local_Omin__def) ).
thf(675,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)],[146]) ).
thf(62,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_local_Oord__eq__less__trans) ).
thf(426,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(116,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_local_Oord__eq__le__trans) ).
thf(589,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)],[116]) ).
thf(97,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ ( inf @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_local_Oinf_Ostrict__boundedE) ).
thf(531,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ ( inf @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(185,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_local_Oorder_Ostrict__trans1) ).
thf(795,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(46,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( ( A @ D @ E )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_semilattice__order_Oabsorb__iff1) ).
thf(374,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
= ( ( A @ D @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(138,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( ~ ( less @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_local_Oantisym__conv2) ).
thf(648,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( ~ ( less @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(126,axiom,
finite40241356em_a_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_local_Ocomp__fun__idem__sup) ).
thf(617,plain,
finite40241356em_a_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(35,axiom,
modula1373251614_aux_a = modula1373251614_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_lattice_Ob__aux_Ocong) ).
thf(342,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Oorder_Oirrefl) ).
thf(355,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(171,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_local_Oinf__greatest) ).
thf(754,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)],[171]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_133_local_Odistrib__imp1) ).
thf(553,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)],[103]) ).
thf(178,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_local_Oinf_OcoboundedI1) ).
thf(776,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)],[178]) ).
thf(113,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_local_Odual__order_Oorder__iff__strict) ).
thf(580,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(149,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_local_Oless__le__not__le) ).
thf(690,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(19,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_local_Oorder_Oasym) ).
thf(295,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(214,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_local_Oa__meet__e) ).
thf(872,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(155,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_local_Odual__order_Ostrict__implies__order) ).
thf(707,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(25,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( B @ ( A @ D @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_semilattice__order_OcoboundedI1) ).
thf(310,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( B @ ( A @ D @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(157,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_local_Osup_Ocommute) ).
thf(712,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(104,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_local_Oc__a) ).
thf(557,plain,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(74,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_local_Oinf__assoc) ).
thf(463,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)],[74]) ).
thf(34,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Oless__imp__not__eq2) ).
thf(338,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(77,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_local_Osup_Ostrict__coboundedI1) ).
thf(470,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(111,axiom,
lattic1885654924_set_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_local_OInf__fin_Osemilattice__set__axioms) ).
thf(576,plain,
lattic1885654924_set_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(119,axiom,
abel_semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_local_Osup_Oabel__semigroup__axioms) ).
thf(600,plain,
abel_semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(211,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_local_Oc__meet__e) ).
thf(864,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(67,axiom,
modula1727524044comp_a = modula1727524044comp_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_lattice_Oincomp_Ocong) ).
thf(446,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(86,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_local_Osup_OcoboundedI1) ).
thf(497,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)],[86]) ).
thf(130,axiom,
lattice_a @ inf @ less_eq @ less @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(627,plain,
lattice_a @ inf @ less_eq @ less @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(100,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_local_Od__c__a__b) ).
thf(539,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(248,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_local_Osup_Oidem) ).
thf(976,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(94,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_local_Odual__order_Ostrict__iff__order) ).
thf(524,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(219,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Odual__order_Oeq__iff) ).
thf(891,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(203,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_local_Osup__inf__absorb) ).
thf(844,plain,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(152,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_local_Oorder_Otrans) ).
thf(699,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)],[152]) ).
thf(191,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ A @ ( inf @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_local_Ob__join__d) ).
thf(813,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ A @ ( inf @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(28,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_local_Odual__order_Oasym) ).
thf(319,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(169,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_local_Ole__iff__inf) ).
thf(748,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(239,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_local_Osup__idem) ).
thf(946,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(180,axiom,
! [A: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_local_Obdd__above__def) ).
thf(781,plain,
! [A: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(164,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_local_Oorder_Oeq__iff) ).
thf(731,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(182,axiom,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_local_Osup_Oright__idem) ).
thf(786,plain,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(143,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_local_Osup_Ocobounded1) ).
thf(667,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(80,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_local_Oinf_OboundedE) ).
thf(478,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)],[80]) ).
thf(174,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_local_Ole__infI2) ).
thf(763,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)],[174]) ).
thf(199,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_local_Odual__order_Ostrict__trans1) ).
thf(832,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(99,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_local_Oinf_Oleft__commute) ).
thf(536,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)],[99]) ).
thf(159,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Oantisym) ).
thf(716,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(227,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_local_Oorder_Orefl) ).
thf(914,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(47,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( B @ D @ ( A @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_semilattice__order_OboundedI) ).
thf(378,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( B @ D @ ( A @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(255,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_local_Oorder__refl) ).
thf(999,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(68,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( lattic655834328_set_a @ A @ B @ C )
=> ( semilattice_order_a @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_semilattice__order__set_Oaxioms_I1_J) ).
thf(447,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( lattic655834328_set_a @ A @ B @ C )
=> ( semilattice_order_a @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(56,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
=> ( C @ ( A @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_semilattice__order_Ostrict__coboundedI2) ).
thf(405,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ E )
=> ( C @ ( A @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Oless__imp__neq) ).
thf(422,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(212,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ A @ ( inf @ B @ C ) ) @ ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_local_Odistrib__sup__le) ).
thf(867,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)],[212]) ).
thf(200,axiom,
! [A: a,B: a] :
( ( modula1727524044comp_a @ less_eq @ A @ B )
= ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_local_Oincomp__def) ).
thf(835,plain,
! [A: a,B: a] :
( ( modula1727524044comp_a @ less_eq @ A @ B )
= ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(5,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ ( A @ E @ F ) )
=> ~ ( ( C @ D @ E )
=> ~ ( C @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_semilattice__order_Ostrict__boundedE) ).
thf(262,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( C @ D @ ( A @ E @ F ) )
=> ~ ( ( C @ D @ E )
=> ~ ( C @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(187,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_local_Oinf_OcoboundedI2) ).
thf(801,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)],[187]) ).
thf(197,axiom,
semilattice_order_a @ inf @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_local_Oinf_Osemilattice__order__axioms) ).
thf(828,plain,
semilattice_order_a @ inf @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(151,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_local_Oless__supI2) ).
thf(696,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(14,axiom,
modula1936294176_aux_a = modula1936294176_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_lattice_Od__aux_Ocong) ).
thf(283,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(232,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_local_Odistrib__inf__le) ).
thf(928,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)],[232]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_89_local_Oinf__unique) ).
thf(506,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)],[89]) ).
thf(7,axiom,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( abel_semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_semilattice_Oaxioms_I1_J) ).
thf(268,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( abel_semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,axiom,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ ( A @ E @ F ) )
= ( ( B @ D @ E )
& ( B @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_semilattice__order_Obounded__iff) ).
thf(358,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o,D: a,E: a,F: a] :
( ( semilattice_order_a @ A @ B @ C )
=> ( ( B @ D @ ( A @ E @ F ) )
= ( ( B @ D @ E )
& ( B @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(189,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_local_Oless__le__trans) ).
thf(807,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(129,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_local_Oinf__absorb1) ).
thf(624,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(166,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_local_Oinf_Ocommute) ).
thf(740,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(209,axiom,
less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(860,plain,
less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(96,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_local_Oless__supI1) ).
thf(528,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(253,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Oeq__refl) ).
thf(992,plain,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(205,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_local_Oc__aux__def) ).
thf(850,plain,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(122,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_local_Oe__b__c__a) ).
thf(607,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(105,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Oantisym__conv) ).
thf(560,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(135,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( B
= ( sup @ B @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_local_Osup_Ostrict__order__iff) ).
thf(639,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( B
= ( sup @ B @ A ) )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(84,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_local_Osup_Oabsorb__iff1) ).
thf(491,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(71,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_local_Ole__iff__sup) ).
thf(454,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(246,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_local_Oinf__commute) ).
thf(972,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1020,plain,
$false,
inference(cvc4,[status(thm)],[645,760,347,628,893,518,962,941,481,352,408,449,614,597,861,730,276,878,440,385,500,715,930,829,898,709,841,885,288,301,436,651,257,389,719,838,949,702,751,542,460,853,969,284,416,289,316,789,443,321,514,821,766,687,280,634,956,396,660,527,452,270,925,810,381,366,534,798,334,825,392,297,693,275,260,349,583,757,682,324,916,467,847,566,484,725,869,610,420,989,857,488,933,669,642,637,328,256,901,476,515,654,457,911,569,779,371,503,343,792,938,266,657,398,953,586,888,906,298,412,618,824,856,745,573,733,601,819,402,772,743,291,545,904,975,875,577,936,572,313,611,466,704,672,919,804,274,784,996,362,303,979,604,494,631,367,816,594,621,895,769,943,330,521,983,399,959,278,563,431,922,986,306,473,722,675,426,589,531,795,374,648,617,342,355,754,553,776,580,690,295,872,707,310,712,557,463,338,470,576,600,864,446,497,627,539,976,524,891,844,699,813,319,748,946,781,731,786,667,478,763,832,536,716,914,378,999,447,405,422,867,835,262,801,828,696,283,928,506,268,358,807,624,740,860,528,992,850,607,560,639,491,454,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : ITP123^1 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.09 % Command : run_Leo-III %s %d
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sat May 18 17:08:54 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.64/0.67 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/0.87 % [INFO] Parsing done (192ms).
% 1.32/0.87 % [INFO] Running in sequential loop mode.
% 1.71/1.08 % [INFO] eprover registered as external prover.
% 1.71/1.08 % [INFO] cvc4 registered as external prover.
% 1.88/1.08 % [INFO] Scanning for conjecture ...
% 1.88/1.16 % [INFO] Found a conjecture (or negated_conjecture) and 253 axioms. Running axiom selection ...
% 2.30/1.23 % [INFO] Axiom selection finished. Selected 253 axioms (removed 0 axioms).
% 2.57/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.39 % [INFO] Type checking passed.
% 2.76/1.39 % [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 ...
% 10.59/3.33 % External prover 'cvc4' found a proof!
% 10.59/3.34 % [INFO] Killing All external provers ...
% 10.59/3.34 % Time passed: 2937ms (effective reasoning time: 2460ms)
% 10.59/3.34 % 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)>
% 10.59/3.34 % Axioms used in derivation (253): fact_158_local_Ole__inf__iff, fact_139_local_Oorder__refl, fact_130_local_Osup_Ostrict__coboundedI1, fact_57_local_Ole__less, fact_95_local_Ole__iff__sup, fact_156_local_Ono__distrib__def, fact_206_abel__semigroup_Oaxioms_I1_J, fact_65_local_Oorder_Oorder__iff__strict, fact_93_local_Ole__infI1, fact_42_local_Osup__commute, fact_79_local_Oinf_OcoboundedI2, fact_127_local_Oless__supI1, fact_148_local_Osup_Oright__idem, fact_149_local_Osup__idem, fact_146_local_Osup_Oidem, fact_90_local_Ole__iff__inf, fact_34_local_Oinf_Oleft__commute, fact_246_local_Obdd__belowI, fact_131_local_Osup_Ostrict__coboundedI2, fact_195_local_Oc__a, fact_63_local_Oless__le__trans, fact_227_semilattice__order_OboundedI, fact_175_local_Oc__meet__e, fact_114_local_Osup__absorb1, fact_64_local_Oorder_Onot__eq__order__implies__strict, fact_13_local_Odual__order_Oasym, fact_141_local_Oinf_Oleft__idem, fact_165_local_OLeast1__le, fact_209_semigroup_Ointro, fact_140_local_Oinf_Oidem, fact_245_local_Obdd__above__def, fact_120_local_Osup__unique, fact_238_semilattice__order_Ostrict__coboundedI1, fact_48_local_Oantisym__conv2, fact_204_local_Oinf_Oabel__semigroup__axioms, fact_164_local_OLeast1I, fact_229_semilattice__order_Ocobounded1, fact_60_local_Oless__imp__le, fact_233_semilattice__order_Obounded__iff, fact_96_local_Ole__supE, fact_109_local_Osup_OcoboundedI2, fact_1_local_Oantisym__conv, conj_3, fact_66_local_Oorder_Ostrict__iff__order, fact_40_local_Osup_Oleft__commute, fact_224_semilattice__order_Oabsorb1, fact_28_local_Oorder_Oasym, fact_189_lattice_Od__aux_Ocong, fact_8_local_Oord__le__eq__trans, fact_75_local_Oinf_OboundedI, fact_170_local_Od__aux__def, fact_161_local_Oinf__sup__absorb, fact_191_local_Oorder_Oordering__axioms, fact_136_local_Odistrib__sup__le, fact_153_local_Omax__def, fact_3_local_Odual__order_Oeq__iff, fact_117_local_Osup__ge2, fact_241_semilattice_Oleft__idem, fact_30_local_Oorder_Ostrict__implies__not__eq, fact_134_local_Odistrib__imp2, fact_222_semilattice__order_OorderE, fact_21_local_Oless__imp__not__less, fact_205_semilattice__order__set_Oaxioms_I1_J, fact_218_semilattice__set_Oaxioms, fact_197_lattice_Ob__aux_Ocong, fact_188_lattice_Oe__aux_Ocong, fact_225_semilattice__order_Oabsorb2, fact_145_local_Oinf__right__idem, fact_163_local_OM5__lattice__def, fact_22_local_Oless__imp__triv, fact_247_local_Obdd__aboveI, fact_157_local_Oinf_Obounded__iff, fact_27_local_Oord__less__eq__trans, fact_176_local_Oe__aux__def, fact_97_local_Ole__supI, fact_92_local_Ole__infI, fact_135_local_Odistrib__inf__le, fact_178_local_Oe__c__a__b, fact_12_local_Oorder__trans, fact_107_local_Osup_Ocobounded2, fact_41_local_Osup__assoc, fact_108_local_Osup_OcoboundedI1, fact_124_local_Oinf_Ostrict__order__iff, fact_198_lattice_Oa__aux_Ocong, fact_196_lattice_Oc__aux_Ocong, fact_54_local_Odual__order_Ostrict__trans2, fact_213_local_OSup__fin_Osemilattice__set__axioms, fact_155_local_ON5__lattice__def, fact_46_Collect__mem__eq, fact_202_local_Oinf_Osemilattice__axioms, fact_73_local_Oinf_Oabsorb__iff2, fact_212_semilattice_Oaxioms_I1_J, fact_115_local_Osup__absorb2, fact_211_semigroup__def, fact_248_local_Obdd__below__Ioo, fact_230_semilattice__order_Ocobounded2, fact_62_local_Oless__le__not__le, fact_15_local_Odual__order_Ostrict__trans, fact_85_local_Oinf__greatest, fact_103_local_Osup_Oabsorb__iff2, fact_137_local_Oincomp__def, fact_58_local_Ole__less__trans, fact_32_local_Oinf_Oassoc, fact_81_local_Oinf_OorderI, fact_190_local_Oinf_Osemilattice__order__axioms, fact_232_semilattice__order_Oabsorb__iff2, conj_2, fact_154_local_Omin__def, fact_244_local_Obdd__below__def, fact_147_local_Osup_Oleft__idem, fact_84_local_Oinf__absorb2, fact_100_local_Osup_Oabsorb1, fact_102_local_Osup_Oabsorb__iff1, fact_129_local_Osup_Ostrict__boundedE, fact_180_local_OM5__lattice__incomp, fact_20_local_Oless__imp__not__eq2, fact_19_local_Oless__imp__not__eq, fact_94_local_Ole__infI2, fact_104_local_Osup_OboundedE, fact_44_local_Oantisym__conv1, fact_31_local_Oorder_Ostrict__trans, fact_138_local_Oorder_Orefl, fact_201_local_Osup_Osemilattice__axioms, fact_123_local_Oinf_Ostrict__coboundedI2, fact_77_local_Oinf_Ocobounded2, fact_239_semilattice__order_Ostrict__coboundedI2, fact_142_local_Oinf_Oright__idem, fact_69_local_Oorder_Ostrict__trans2, fact_228_semilattice__order_Oorder__iff, fact_61_local_Oless__le, fact_215_semilattice__order__set_Oaxioms_I2_J, fact_18_local_Oless__imp__neq, fact_174_local_Ob__meet__e, fact_25_local_Oless__trans, fact_194_local_Ob__a, fact_52_local_Odual__order_Ostrict__implies__order, fact_223_semilattice__order_OorderI, fact_70_local_Oinf_Oabsorb1, fact_80_local_Oinf_OorderE, fact_226_semilattice__order_OboundedE, fact_29_local_Oorder_Oirrefl, fact_37_local_Oinf__left__commute, fact_171_local_Od__b__c__a, fact_2_local_Odual__order_Oantisym, fact_221_semilattice__order_Omono, fact_231_semilattice__order_Oabsorb__iff1, fact_50_local_Odual__order_Oorder__iff__strict, fact_214_local_OInf__fin_Osemilattice__set__axioms, fact_45_mem__Collect__eq, fact_10_local_Oorder_Oeq__iff, fact_118_local_Osup__least, fact_38_local_Osup_Oassoc, fact_87_local_Oinf__le2, fact_7_local_Oord__eq__le__trans, fact_168_local_Oa__join__d, fact_76_local_Oinf_Ocobounded1, fact_210_semigroup_Oassoc, fact_24_local_Oless__not__sym, fact_83_local_Oinf__absorb1, fact_35_local_Oinf__assoc, fact_192_local_Ocomp__fun__idem__sup, fact_160_local_Osup_Obounded__iff, fact_106_local_Osup_Ocobounded1, fact_125_local_Oless__infI1, fact_162_local_Osup__inf__absorb, fact_242_semilattice_Oright__idem, fact_220_semilattice__order__set_Ointro, fact_5_local_Oeq__iff, fact_59_local_Ole__neq__trans, fact_88_local_Oinf__mono, fact_144_local_Oinf__left__idem, fact_186_lattice_OM5__lattice_Ocong, fact_167_local_OLeast__equality, fact_172_local_Od__c__a__b, fact_121_local_Oinf_Ostrict__boundedE, fact_72_local_Oinf_Oabsorb__iff1, fact_11_local_Oorder_Otrans, fact_47_Collect__cong, fact_216_semilattice__set__def, fact_203_local_Osup_Oabel__semigroup__axioms, fact_86_local_Oinf__le1, fact_119_local_Osup__mono, fact_23_local_Oless__irrefl, fact_39_local_Osup_Ocommute, fact_105_local_Osup_OboundedI, fact_132_local_Osup_Ostrict__order__iff, fact_183_local_Oa__aux__def, fact_51_local_Odual__order_Ostrict__iff__order, fact_199_local_Osup_Osemigroup__axioms, fact_98_local_Ole__supI1, fact_26_local_Oord__eq__less__trans, fact_82_local_Oinf_Oorder__iff, fact_143_local_Oinf__idem, fact_200_local_Oinf_Osemigroup__axioms, fact_207_abel__semigroup_Oleft__commute, fact_234_semilattice__order_OcoboundedI1, fact_111_local_Osup_OorderE, fact_126_local_Oless__infI2, conj_1, fact_159_local_Ole__sup__iff, fact_179_local_OInf__fin_Osemilattice__order__set__axioms, fact_16_local_Oless__asym, fact_55_local_OleD, fact_177_local_Oe__b__c__a, fact_243_semilattice__order_Oaxioms_I1_J, fact_184_lattice_Ono__distrib_Ocong, fact_236_semilattice__order_Ostrict__boundedE, fact_89_local_Oinf__unique, fact_91_local_Ole__infE, fact_173_local_Oa__meet__e, fact_110_local_Osup_Omono, fact_53_local_Odual__order_Ostrict__trans1, fact_182_local_Ob__aux__def, fact_33_local_Oinf_Ocommute, fact_152_local_OGreatest__equality, fact_217_semilattice__set_Ointro, fact_187_lattice_Oincomp_Ocong, fact_237_semilattice__order_Ostrict__order__iff, fact_113_local_Osup_Oorder__iff, fact_219_semilattice__order__set__def, fact_68_local_Oorder_Ostrict__trans1, fact_151_local_OGreatestI2__order, fact_133_local_Odistrib__imp1, fact_122_local_Oinf_Ostrict__coboundedI1, fact_71_local_Oinf_Oabsorb2, fact_17_local_Oless__asym_H, fact_6_local_Oeq__refl, fact_208_abel__semigroup_Ocommute, fact_43_local_Osup__left__commute, fact_128_local_Oless__supI2, fact_181_local_Oc__aux__def, fact_99_local_Ole__supI2, fact_166_local_OLeastI2__order, fact_78_local_Oinf_OcoboundedI1, fact_14_local_Odual__order_Ostrict__implies__not__eq, fact_56_local_Ole__imp__less__or__eq, fact_36_local_Oinf__commute, conj_0, fact_4_local_Odual__order_Otrans, fact_116_local_Osup__ge1, fact_193_local_Ocomp__fun__idem__inf, fact_0_local_Oantisym, fact_185_lattice_ON5__lattice_Ocong, fact_9_local_Oorder_Oantisym, fact_49_local_Odual__order_Onot__eq__order__implies__strict, fact_74_local_Oinf_OboundedE, fact_67_local_Oorder_Ostrict__implies__order, fact_112_local_Osup_OorderI, fact_150_local_Osup__left__idem, fact_101_local_Osup_Oabsorb2, fact_235_semilattice__order_OcoboundedI2, fact_169_local_Ob__join__d, fact_240_semilattice_Oidem
% 10.59/3.34 % No. of inferences in proof: 510
% 10.59/3.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2937 ms resp. 2460 ms w/o parsing
% 11.26/3.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.26/3.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------