%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP123^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:51 AM UTC 2026
% Result : Theorem 38.20s 10.45s
% Output : Refutation 39.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 255
% Syntax : Number of formulae : 588 ( 286 unt; 0 typ; 1 def)
% Number of atoms : 1347 ( 452 equ; 8 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4311 ( 196 ~; 56 |; 73 &;3523 @)
% ( 0 <=>; 463 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 500 ( 500 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 12 con; 0-6 aty)
% Number of variables : 1498 ( 75 ^;1413 !; 9 ?;1498 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(condit1627435690bove_a_decl,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(condit1001553558elow_a_decl,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(finite40241356em_a_a_decl,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(abel_semigroup_a_decl,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(semigroup_a_decl,type,
semigroup_a: ( a > a > a ) > $o ).
thf(lattice_a_decl,type,
lattice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > ( a > a > a ) > $o ).
thf(semilattice_a_decl,type,
semilattice_a: ( a > a > a ) > $o ).
thf(semilattice_order_a_decl,type,
semilattice_order_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(lattic655834328_set_a_decl,type,
lattic655834328_set_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(lattic1885654924_set_a_decl,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(modula1376131916tice_a_decl,type,
modula1376131916tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(modula397570059tice_a_decl,type,
modula397570059tice_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(modula17988509_aux_a_decl,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1373251614_aux_a_decl,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula581031071_aux_a_decl,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1936294176_aux_a_decl,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1144073633_aux_a_decl,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1727524044comp_a_decl,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(modula1962211574trib_a_decl,type,
modula1962211574trib_a: ( a > a > a ) > ( a > a > $o ) > ( a > a > a ) > a > a > a > $o ).
thf(least_a_decl,type,
least_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(max_a_decl,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(min_a_decl,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(greatest_a_decl,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(ordering_a_decl,type,
ordering_a: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(set_gr1491433118Than_a_decl,type,
set_gr1491433118Than_a: ( a > a > $o ) > a > a > set_a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(inf_decl,type,
inf: a > a > a ).
thf(less_decl,type,
less: a > a > $o ).
thf(less_eq_decl,type,
less_eq: a > a > $o ).
thf(sup_decl,type,
sup: a > a > a ).
thf(x_decl,type,
x: a ).
thf(y_decl,type,
y: a ).
thf(z_decl,type,
z: a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk39_decl,type,
sk39: a ).
thf(sk40_decl,type,
sk40: a ).
thf(sk41_decl,type,
sk41: a ).
thf(sk42_decl,type,
sk42: a ).
thf(sk43_decl,type,
sk43: a ).
thf(sk44_decl,type,
sk44: a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
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(645,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(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(629,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(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(760,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(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(846,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(207,axiom,
semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_local_Oinf_Osemigroup__axioms) ).
thf(893,plain,
semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(75,axiom,
less_eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(468,plain,
less_eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
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(909,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(247,axiom,
semilattice_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_local_Osup_Osemilattice__axioms) ).
thf(1031,plain,
semilattice_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
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(977,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(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(523,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(10,axiom,
modula17988509_aux_a = modula17988509_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_lattice_Oa__aux_Ocong) ).
thf(276,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(1065,plain,
( ~ $true
| ( ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) )
!= ( less_eq @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[468,256]) ).
thf(1066,plain,
( ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) )
!= ( less_eq @ x @ y ) ),
inference(simp,[status(thm)],[1065]) ).
thf(1067,plain,
( ( x != x )
| ( ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z )
!= y ) ),
inference(simp,[status(thm)],[1066]) ).
thf(1068,plain,
( ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z )
!= y ),
inference(simp,[status(thm)],[1067]) ).
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(741,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(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(449,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(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(379,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(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(861,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(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(614,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(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(269,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( abel_semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(533,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(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(715,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(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(472,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(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(929,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(930,plain,
( ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) )
= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[929]) ).
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(898,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(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(709,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
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(1046,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
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(285,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(286,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ! [D: a,E: a] :
( ( C @ D @ E )
= ( ( D
= ( A @ D @ E ) )
& ( D != E ) ) ) ),
inference(miniscope,[status(thm)],[285]) ).
thf(287,plain,
! [E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ~ ( semilattice_order_a @ A @ B @ C )
| ( ( C @ D @ E )
= ( ( D
= ( A @ D @ E ) )
& ( D != E ) ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(288,plain,
! [E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ( ( C @ D @ E )
= ( ( D
= ( A @ D @ E ) )
& ( D != E ) ) )
| ~ ( semilattice_order_a @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[287]) ).
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(320,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
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 > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(119,axiom,
abel_semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_local_Osup_Oabel__semigroup__axioms) ).
thf(607,plain,
abel_semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(8,axiom,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_abel__semigroup_Oleft__commute) ).
thf(271,plain,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(272,plain,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ! [B: a,C: a,D: a] :
( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [D: a,C: a,B: a,A: a > a > a] :
( ~ ( abel_semigroup_a @ A )
| ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [D: a,C: a,B: a,A: a > a > a] :
( ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) )
| ~ ( abel_semigroup_a @ A ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(1401,plain,
! [D: a,C: a,B: a,A: a > a > a] :
( ~ ( abel_semigroup_a @ A )
| ( ( A @ C @ ( A @ B @ D ) )
!= y )
| ( ( A @ B @ ( A @ C @ D ) )
!= ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) ),
inference(paramod_ordered,[status(thm)],[274,1068]) ).
thf(1536,plain,
! [A: a] :
( ~ ( abel_semigroup_a
@ ^ [B: a,C: a] : B )
| ( A != y ) ),
inference(pre_uni,[status(thm)],[1401:[bind(A,$thf( ^ [E: a] : ^ [F: a] : E )),bind(B,$thf( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ))]]) ).
thf(1540,plain,
~ ( abel_semigroup_a
@ ^ [A: a,B: a] : A ),
inference(pattern_uni,[status(thm)],[1536:[bind(A,$thf( y ))]]) ).
thf(2003,plain,
( ~ $true
| ( ( abel_semigroup_a @ sup )
!= ( abel_semigroup_a
@ ^ [A: a,B: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[607,1540]) ).
thf(2004,plain,
( ( abel_semigroup_a @ sup )
!= ( abel_semigroup_a
@ ^ [A: a,B: a] : A ) ),
inference(simp,[status(thm)],[2003]) ).
thf(2006,plain,
( sup
!= ( ^ [A: a,B: a] : A ) ),
inference(simp,[status(thm)],[2004]) ).
thf(2020,plain,
( ( sup @ sk41 @ sk42 )
!= sk41 ),
inference(func_ext,[status(esa)],[2006]) ).
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(417,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(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(724,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
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(570,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(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(372,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(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(504,plain,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
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(587,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(255,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_local_Oorder__refl) ).
thf(1059,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
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(949,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(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(542,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(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(802,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
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(344,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(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(817,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(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(969,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(14,axiom,
modula1936294176_aux_a = modula1936294176_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_lattice_Od__aux_Ocong) ).
thf(284,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(881,plain,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
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(325,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(16,axiom,
modula397570059tice_a = modula397570059tice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lattice_ON5__lattice_Ocong) ).
thf(289,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(67,axiom,
modula1727524044comp_a = modula1727524044comp_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_lattice_Oincomp_Ocong) ).
thf(448,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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(261,plain,
! [B: a,A: a] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ A ) ),
inference(cnf,[status(esa)],[260]) ).
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(475,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(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(492,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(646,plain,
! [B: a,A: a] : ( condit1001553558elow_a @ less_eq @ ( set_gr1491433118Than_a @ less @ A @ B ) ),
inference(cnf,[status(esa)],[645]) ).
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(834,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(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(348,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(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(353,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(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(480,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(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(397,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(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(734,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
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(988,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(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(428,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(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(507,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
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(877,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(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(692,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(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(263,plain,
! [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
=> ! [D: a,E: a,F: a] :
( ( C @ D @ ( A @ E @ F ) )
=> ~ ( ( C @ D @ E )
=> ~ ( C @ D @ F ) ) ) ),
inference(miniscope,[status(thm)],[262]) ).
thf(264,plain,
! [F: a,E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ( ~ ( semilattice_order_a @ A @ B @ C )
| ~ ( C @ D @ ( A @ E @ F ) )
| ( C @ D @ E ) )
& ( ~ ( semilattice_order_a @ A @ B @ C )
| ~ ( C @ D @ ( A @ E @ F ) )
| ( C @ D @ F ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(265,plain,
! [F: a,E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ~ ( semilattice_order_a @ A @ B @ C )
| ~ ( C @ D @ ( A @ E @ F ) )
| ( C @ D @ E ) ),
inference(cnfConj,[status(thm)],[264]) ).
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(849,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(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(307,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(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(292,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(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(942,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
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(793,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(209,axiom,
less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(897,plain,
less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1197,plain,
! [B: a,A: a] :
( ~ $true
| ~ ( less @ B @ A )
| ( ( less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ) )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[897,261]) ).
thf(1198,plain,
! [B: a,A: a] :
( ~ ( less @ B @ A )
| ( ( less @ ( sup @ x @ ( inf @ y @ z ) ) @ ( inf @ y @ ( sup @ x @ z ) ) )
!= ( less @ A @ B ) ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1199,plain,
~ ( less @ ( inf @ y @ ( sup @ x @ z ) ) @ ( sup @ x @ ( inf @ y @ z ) ) ),
inference(pattern_uni,[status(thm)],[1198:[bind(A,$thf( sup @ x @ ( inf @ y @ z ) )),bind(B,$thf( inf @ y @ ( sup @ x @ z ) ))]]) ).
thf(270,plain,
! [A: a > a > a] :
( ~ ( semilattice_a @ A )
| ( abel_semigroup_a @ A ) ),
inference(cnf,[status(esa)],[269]) ).
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(529,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
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(894,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(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(825,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(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(302,plain,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ( semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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(820,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
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(424,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9,axiom,
modula1376131916tice_a = modula1376131916tice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_lattice_OM5__lattice_Ocong) ).
thf(275,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(815,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
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(729,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(349,plain,
( semigroup_a
= ( ^ [A: a > a > a] :
! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[348]) ).
thf(248,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_local_Osup_Oidem) ).
thf(1032,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(126,axiom,
finite40241356em_a_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_local_Ocomp__fun__idem__sup) ).
thf(625,plain,
finite40241356em_a_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
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(852,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(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(329,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
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(665,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(163,axiom,
semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_local_Osup_Osemigroup__axioms) ).
thf(757,plain,
semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
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(551,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(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(456,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(2315,plain,
! [E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ( ( D
= ( A @ D @ E ) )
& ( D != E ) )
| ~ ( semilattice_order_a @ A @ B @ C )
| ( ( semilattice_a @ sup )
!= ( C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[1031,288]) ).
thf(2432,plain,
! [D: a,C: a,B: a > a > $o,A: a > a > a] :
( ( ( C
= ( A @ C @ D ) )
& ( C != D ) )
| ~ ( semilattice_order_a @ A @ B
@ ^ [E: a,F: a] : ( semilattice_a @ sup ) ) ),
inference(pre_uni,[status(thm)],[2315:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [F: a] : ^ [G: a] : ( semilattice_a @ sup ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(2437,plain,
! [D: a,C: a,B: a > a > $o,A: a > a > a] :
( ( ( C
= ( A @ C @ D ) )
| ~ ( semilattice_order_a @ A @ B
@ ^ [E: a,F: a] : ( semilattice_a @ sup ) ) )
& ( ( C != D )
| ~ ( semilattice_order_a @ A @ B
@ ^ [E: a,F: a] : ( semilattice_a @ sup ) ) ) ),
inference(cnf,[status(esa)],[2432]) ).
thf(2439,plain,
! [D: a,C: a,B: a > a > $o,A: a > a > a] :
( ( C != D )
| ~ ( semilattice_order_a @ A @ B
@ ^ [E: a,F: a] : ( semilattice_a @ sup ) ) ),
inference(cnfConj,[status(thm)],[2437]) ).
thf(2442,plain,
! [D: a,C: a,B: a > a > $o,A: a > a > a] :
( ( C != D )
| ~ ( semilattice_order_a @ A @ B
@ ^ [E: a,F: a] : ( semilattice_a @ sup ) ) ),
inference(lifteq,[status(thm)],[2439]) ).
thf(2443,plain,
! [B: a > a > $o,A: a > a > a] :
~ ( semilattice_order_a @ A @ B
@ ^ [C: a,D: a] : ( semilattice_a @ sup ) ),
inference(simp,[status(thm)],[2442]) ).
thf(2758,plain,
! [B: a > a > $o,A: a > a > a] :
~ ( semilattice_order_a @ A @ B
@ ^ [C: a,D: a] : $true ),
inference(rewrite,[status(thm)],[2443,1031]) ).
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(484,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(111,axiom,
lattic1885654924_set_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_local_OInf__fin_Osemilattice__set__axioms) ).
thf(583,plain,
lattic1885654924_set_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(91,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_local_Oinf_Oidem) ).
thf(520,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(521,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(cnf,[status(esa)],[520]) ).
thf(522,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(lifteq,[status(thm)],[521]) ).
thf(90,axiom,
semilattice_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_local_Oinf_Osemilattice__axioms) ).
thf(519,plain,
semilattice_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
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(874,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( inf @ A @ B ) )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
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(317,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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(650,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(40,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Oorder_Oirrefl) ).
thf(356,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
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(593,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(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(857,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
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(980,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(55,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Oless__irrefl) ).
thf(403,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
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(884,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(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(1028,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
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(339,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
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(933,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(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(642,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( less_eq @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
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(526,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(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(590,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(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(901,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(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(686,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(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(393,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(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(647,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( B
= ( sup @ B @ A ) )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(239,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_local_Osup__idem) ).
thf(985,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
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(738,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(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(1002,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(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(779,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
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(622,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
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(837,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(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(721,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(35,axiom,
modula1373251614_aux_a = modula1373251614_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_lattice_Ob__aux_Ocong) ).
thf(343,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(266,plain,
! [F: a,E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ~ ( semilattice_order_a @ A @ B @ C )
| ~ ( C @ D @ ( A @ E @ F ) )
| ( C @ D @ F ) ),
inference(cnfConj,[status(thm)],[264]) ).
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(805,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
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(311,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(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(1035,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(227,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_local_Oorder_Orefl) ).
thf(953,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
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(926,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
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(662,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(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(718,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(213,axiom,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(906,plain,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(20,axiom,
modula581031071_aux_a = modula581031071_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_lattice_Oc__aux_Ocong) ).
thf(298,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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(618,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(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(745,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
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(279,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(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(573,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(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(375,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(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(601,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(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(689,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(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(296,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
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(584,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(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(843,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(109,axiom,
finite40241356em_a_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_local_Ocomp__fun__idem__inf) ).
thf(579,plain,
finite40241356em_a_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
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(958,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
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(281,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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(545,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(258,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(259,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(lifteq,[status(thm)],[258]) ).
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(413,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
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(904,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(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(975,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
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(382,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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(498,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(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(335,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(954,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(cnf,[status(esa)],[953]) ).
thf(1217,plain,
! [A: a] :
( ~ $true
| ( ( less_eq @ A @ A )
!= ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[954,256]) ).
thf(1218,plain,
! [A: a] :
( ( less_eq @ A @ A )
!= ( less_eq @ x @ ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1221,plain,
! [A: a] :
( ( A != x )
| ( A
!= ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z ) ) ),
inference(simp,[status(thm)],[1218]) ).
thf(1224,plain,
( ( sup @ ( inf @ y @ ( sup @ x @ z ) ) @ z )
!= x ),
inference(simp,[status(thm)],[1221]) ).
thf(195,axiom,
abel_semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_local_Oinf_Oabel__semigroup__axioms) ).
thf(860,plain,
abel_semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(2001,plain,
( ~ $true
| ( ( abel_semigroup_a @ inf )
!= ( abel_semigroup_a
@ ^ [A: a,B: a] : A ) ) ),
inference(paramod_ordered,[status(thm)],[860,1540]) ).
thf(2002,plain,
( ( abel_semigroup_a @ inf )
!= ( abel_semigroup_a
@ ^ [A: a,B: a] : A ) ),
inference(simp,[status(thm)],[2001]) ).
thf(2005,plain,
( inf
!= ( ^ [A: a,B: a] : A ) ),
inference(simp,[status(thm)],[2002]) ).
thf(2019,plain,
( ( inf @ sk39 @ sk40 )
!= sk39 ),
inference(func_ext,[status(esa)],[2005]) ).
thf(2100,plain,
! [A: a] :
( ( A != sk39 )
| ( ( inf @ A @ A )
!= ( inf @ sk39 @ sk40 ) ) ),
inference(paramod_ordered,[status(thm)],[522,2019]) ).
thf(2113,plain,
( ( sk39 != sk39 )
| ( sk40 != sk39 ) ),
inference(simp,[status(thm)],[2100]) ).
thf(2148,plain,
sk40 != sk39,
inference(simp,[status(thm)],[2113]) ).
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(350,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(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(540,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
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(445,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
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(936,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(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(611,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(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(787,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(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(604,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(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(406,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(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(831,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(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(784,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
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(996,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(158,axiom,
lattic1885654924_set_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_local_OSup__fin_Osemilattice__set__axioms) ).
thf(737,plain,
lattic1885654924_set_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(250,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_local_Oinf__idem) ).
thf(1043,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
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(451,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(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(567,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(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(890,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(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(758,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(43,axiom,
modula1962211574trib_a = modula1962211574trib_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lattice_Ono__distrib_Ocong) ).
thf(367,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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(964,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
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(668,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(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(799,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(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(726,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
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(700,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(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(626,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
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(915,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(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(462,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(11,axiom,
lattic1885654924_set_a = semilattice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semilattice__set__def) ).
thf(277,plain,
lattic1885654924_set_a = semilattice_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(278,plain,
lattic1885654924_set_a = semilattice_a,
inference(lifteq,[status(thm)],[277]) ).
thf(1061,plain,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
= ( semilattice_a @ A ) ),
inference(func_ext,[status(esa)],[278]) ).
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(912,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(197,axiom,
semilattice_order_a @ inf @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_local_Oinf_Osemilattice__order__axioms) ).
thf(864,plain,
semilattice_order_a @ inf @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2761,plain,
! [B: a > a > $o,A: a > a > a] :
( ~ $true
| ( ( semilattice_order_a @ inf @ less_eq @ less )
!= ( semilattice_order_a @ A @ B
@ ^ [C: a,D: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[864,2758]) ).
thf(2762,plain,
! [B: a > a > $o,A: a > a > a] :
( ( semilattice_order_a @ inf @ less_eq @ less )
!= ( semilattice_order_a @ A @ B
@ ^ [C: a,D: a] : $true ) ),
inference(simp,[status(thm)],[2761]) ).
thf(2765,plain,
! [B: a > a > $o,A: a > a > a] :
( ( inf != A )
| ( less_eq != B )
| ( less
!= ( ^ [C: a,D: a] : $true ) ) ),
inference(simp,[status(thm)],[2762]) ).
thf(2770,plain,
( less
!= ( ^ [A: a,B: a] : $true ) ),
inference(simp,[status(thm)],[2765]) ).
thf(53,axiom,
modula1144073633_aux_a = modula1144073633_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_lattice_Oe__aux_Ocong) ).
thf(399,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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(636,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
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(868,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(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(608,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
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(299,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(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(267,plain,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
=> ( semilattice_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(438,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
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(653,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(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(944,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(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(548,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
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(487,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(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(812,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(123,axiom,
ordering_a @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_local_Oorder_Oordering__axioms) ).
thf(617,plain,
ordering_a @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
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(939,plain,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(340,plain,
! [B: a,A: a] :
( ~ ( less @ A @ B )
| ( B != A ) ),
inference(cnf,[status(esa)],[339]) ).
thf(341,plain,
! [B: a,A: a] :
( ( B != A )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(342,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[341]) ).
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(1049,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
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(776,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
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(712,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(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(887,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(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(409,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(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(993,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
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(580,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
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(855,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
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(1025,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(293,plain,
! [A: a > a > a,B: a > a > $o] :
( ? [C: a > a > $o] : ( semilattice_order_a @ A @ B @ C )
=> ! [C: a,D: a] :
( ( C
= ( A @ C @ D ) )
=> ( B @ C @ D ) ) ),
inference(miniscope,[status(thm)],[292]) ).
thf(294,plain,
! [E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ~ ( semilattice_order_a @ A @ B @ C )
| ( D
!= ( A @ D @ E ) )
| ( B @ D @ E ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [E: a,D: a,C: a > a > $o,B: a > a > $o,A: a > a > a] :
( ( ( A @ D @ E )
!= D )
| ~ ( semilattice_order_a @ A @ B @ C )
| ( B @ D @ E ) ),
inference(lifteq,[status(thm)],[294]) ).
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(331,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(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(840,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(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(576,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
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(808,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(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(359,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(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(656,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( ~ ( less @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
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(1052,plain,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
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(386,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(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(314,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(280,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(lifteq,[status(thm)],[279]) ).
thf(1372,plain,
( lattic655834328_set_a
= ( ^ [A: a > a > a,B: a > a > $o,C: a > a > $o] :
( ( semilattice_order_a @ A @ B @ C )
& ( semilattice_a @ A ) ) ) ),
inference(rewrite,[status(thm)],[280,1061]) ).
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(465,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(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(363,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(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(931,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
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(495,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(759,plain,
( ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) )
= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[758]) ).
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(368,plain,
! [A: a > a > a,B: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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(961,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(318,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[317]) ).
thf(319,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[318]) ).
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(748,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(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(304,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(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(390,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(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(632,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
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(731,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(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(781,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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(290,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( lattic1885654924_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(478,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
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(684,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
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(433,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(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(510,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(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(536,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(986,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(cnf,[status(esa)],[985]) ).
thf(987,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(lifteq,[status(thm)],[986]) ).
thf(2189,plain,
! [A: a] :
( ( A != sk41 )
| ( ( sup @ A @ A )
!= ( sup @ sk41 @ sk42 ) ) ),
inference(paramod_ordered,[status(thm)],[987,2020]) ).
thf(2246,plain,
( ( sk41 != sk41 )
| ( sk42 != sk41 ) ),
inference(simp,[status(thm)],[2189]) ).
thf(2258,plain,
sk42 != sk41,
inference(simp,[status(thm)],[2246]) ).
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(999,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(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(967,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(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(865,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(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(422,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
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(790,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(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(564,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(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(1056,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(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(400,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(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(828,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(130,axiom,
lattice_a @ inf @ less_eq @ less @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(635,plain,
lattice_a @ inf @ less_eq @ less @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
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(532,plain,
lattic655834328_set_a @ inf @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
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(955,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
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(796,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
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(596,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(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(459,plain,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(907,plain,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
inference(polarity_switch,[status(thm)],[906]) ).
thf(908,plain,
( ( sup @ x @ ( inf @ y @ z ) )
!= ( inf @ y @ ( sup @ x @ z ) ) ),
inference(lifteq,[status(thm)],[907]) ).
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(822,plain,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
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(982,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(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(442,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(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(871,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(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(501,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(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(322,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(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(469,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(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(923,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
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(659,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(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(560,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(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(639,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(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(454,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
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(972,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(2771,plain,
~ ( less @ sk43 @ sk44 ),
inference(func_ext,[status(esa)],[2770]) ).
thf(3150,plain,
$false,
inference(e,[status(thm)],[645,629,760,846,893,468,909,1031,977,523,276,1068,741,449,379,861,614,269,533,715,472,930,898,709,1046,288,320,257,2020,417,724,570,372,504,587,1059,949,542,802,344,817,969,284,881,325,289,448,261,475,492,646,834,348,353,480,397,734,988,428,507,877,692,265,849,307,292,942,793,1199,270,529,894,825,302,820,424,275,815,729,260,349,1032,625,852,329,665,757,551,456,285,2758,484,583,522,519,874,317,650,1540,356,593,857,980,403,256,884,1028,339,933,642,526,590,901,686,393,647,985,738,1002,779,622,837,2006,721,343,266,805,311,1035,953,926,662,718,906,298,618,745,279,573,375,601,689,296,584,843,579,958,281,545,259,413,904,975,382,498,335,1224,2148,350,540,445,936,611,787,604,406,831,274,784,996,737,1043,271,451,567,890,758,367,964,668,799,726,700,520,626,915,462,1061,912,2770,399,636,868,608,299,267,438,653,2005,944,548,487,812,617,939,342,1049,776,712,887,954,409,993,580,855,1025,295,331,840,576,808,359,656,1052,864,386,314,1372,465,363,931,495,759,368,961,319,748,304,390,632,731,781,290,929,478,684,433,510,536,2019,2258,999,967,262,865,422,790,564,897,1056,400,828,635,532,955,796,987,860,596,459,908,822,982,277,442,871,501,607,322,469,923,659,560,639,454,972,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP123^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:00:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.95/1.17 % [INFO] Parsing done (386ms).
% 1.95/1.19 % [INFO] Running in sequential loop mode.
% 2.78/1.57 % [INFO] eprover registered as external prover.
% 2.78/1.58 % [INFO] Scanning for conjecture ...
% 3.17/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 253 axioms. Running axiom selection ...
% 3.36/1.84 % [INFO] Axiom selection finished. Selected 253 axioms (removed 0 axioms).
% 3.92/2.07 % [INFO] Problem is higher-order (TPTP THF).
% 3.92/2.09 % [INFO] Type checking passed.
% 3.92/2.10 % [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 ...
% 38.20/10.44 % External prover 'e' found a proof!
% 38.20/10.44 % [INFO] Killing All external provers ...
% 38.20/10.44 % Time passed: 10099ms (effective reasoning time: 9245ms)
% 38.20/10.44 % 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)>
% 38.20/10.44 % 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
% 38.20/10.44 % No. of inferences in proof: 587
% 38.20/10.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10099 ms resp. 9245 ms w/o parsing
% 39.16/10.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.16/10.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------