%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n002.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 : Sun Sep 27 08:38:36 AM UTC 2026
% Result : Theorem 10.59s 3.95s
% Output : Refutation 12.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 224 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 1195 ( 34 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 3245 ( 176 ~; 2 |; 762 &;2098 @)
% ( 9 <=>; 198 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 2 con; 0-3 aty)
% Number of variables : 352 ( 0 ^; 296 !; 56 ?; 352 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(boole_POSet_decl,type,
boole_POSet: $i > $i ).
thf(related_reflexive_decl,type,
related_reflexive: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(lower_bounded_semilattstr_decl,type,
lower_bounded_semilattstr: $i > $o ).
thf(upper_bounded_semilattstr_decl,type,
upper_bounded_semilattstr: $i > $o ).
thf(bounded_lattstr_decl,type,
bounded_lattstr: $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(boolean_lattstr_decl,type,
boolean_lattstr: $i > $o ).
thf(distributive_lattstr_decl,type,
distributive_lattstr: $i > $o ).
thf(complemented_lattstr_decl,type,
complemented_lattstr: $i > $o ).
thf(boole_lattice_decl,type,
boole_lattice: $i > $i ).
thf(strict_latt_str_decl,type,
strict_latt_str: $i > $o ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(modular_lattstr_decl,type,
modular_lattstr: $i > $o ).
thf(complete_latt_str_decl,type,
complete_latt_str: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(lower_bounded_relstr_decl,type,
lower_bounded_relstr: $i > $o ).
thf(upper_bounded_relstr_decl,type,
upper_bounded_relstr: $i > $o ).
thf(bounded_relstr_decl,type,
bounded_relstr: $i > $o ).
thf(reflexive_relstr_decl,type,
reflexive_relstr: $i > $o ).
thf(trivial_carrier_decl,type,
trivial_carrier: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(complete_relstr_decl,type,
complete_relstr: $i > $o ).
thf(with_suprema_relstr_decl,type,
with_suprema_relstr: $i > $o ).
thf(with_infima_relstr_decl,type,
with_infima_relstr: $i > $o ).
thf(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(poset_of_lattice_decl,type,
poset_of_lattice: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(latt_str_of_decl,type,
latt_str_of: $i > $i > $i > $i ).
thf(rel_str_of_decl,type,
rel_str_of: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_of_lattice_decl,type,
relation_of_lattice: $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(k2_lattice3_decl,type,
k2_lattice3: $i > $i ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(below_refl_decl,type,
below_refl: $i > $i > $i > $o ).
thf(cast_to_el_of_LattPOSet_decl,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(the_L_join_decl,type,
the_L_join: $i > $i ).
thf(below_decl,type,
below: $i > $i > $i > $o ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(103,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(742,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(482,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(422,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).
thf(138,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
thf(518,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(73,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(582,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(683,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ below_refl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ upper_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_1) ).
thf(449,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ upper_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
thf(597,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_knaster) ).
thf(217,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
thf(276,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ rel_str )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(105,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(747,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(670,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_yellow_0) ).
thf(570,plain,
? [A: $i] :
( ( A @ trivial_carrier )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(719,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(587,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(107,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
thf(751,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ cast_to_el_of_LattPOSet ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(357,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice3) ).
thf(606,plain,
! [A: $i] :
( ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(770,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(25,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(325,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice3) ).
thf(179,plain,
! [A: $i] :
( ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
thf(591,plain,
! [A: $i] :
( ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(443,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(646,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).
thf(121,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(101,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(734,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(37,axiom,
? [A: $i] :
( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).
thf(396,plain,
? [A: $i] :
( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(248,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ below_refl ) ) )
<=> ( C @ ( B @ ( A @ below ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(761,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( ( C @ ( B @ ( A @ below ) ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) )
& ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( C @ ( B @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(63,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(534,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(28,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice3) ).
thf(334,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(392,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
thf(484,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(252,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
thf(329,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,axiom,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
thf(522,plain,
? [A: $i] :
( ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(461,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(57,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(493,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
thf(686,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice )
= ( A @ k2_lattice3 @ ( A @ the_carrier @ rel_str_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(26,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(328,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(471,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_0) ).
thf(256,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ trivial_carrier )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ related ) ) )
<=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
thf(738,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C @ ( B @ ( A @ related ) ) ) )
& ( ( C @ ( B @ ( A @ related ) ) )
=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(654,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(721,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(508,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ rel_str_of ) @ rel_str )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(311,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(765,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_join @ quasi_total ) ) )
& ( A @ the_L_join @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(128,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ complete_relstr )
& ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ bounded_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow_1) ).
thf(298,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ complete_relstr )
& ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ bounded_relstr )
& ( A @ poset_of_lattice @ upper_bounded_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
thf(412,plain,
! [A: $i] :
( ( A @ boole_lattice @ latt_str )
& ( A @ boole_lattice @ strict_latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(41,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(425,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_yellow_1) ).
thf(689,plain,
! [A: $i] :
( ( A @ boole_POSet @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_relstr )
& ( A @ boole_POSet @ bounded_relstr )
& ( A @ boole_POSet @ upper_bounded_relstr )
& ( A @ boole_POSet @ lower_bounded_relstr )
& ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(562,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
thf(772,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ ( B @ element ) )
& ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ poset_of_lattice @ the_carrier @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(641,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
thf(445,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str )
& ~ ( C @ ( B @ ( A @ latt_str_of ) ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
thf(713,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ strict_latt_str )
=> ( A
= ( A @ the_L_meet @ ( A @ the_L_join @ ( A @ the_carrier @ latt_str_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow_1) ).
thf(498,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ lower_bounded_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_POSet @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) )
<=> ( C @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_POSet @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) )
<=> ( C @ ( B @ subset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ! [A: $i,B: $i] :
( ( A @ boole_POSet @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_POSet @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ subset ) )
=> ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) ) )
& ( ( C @ ( B @ ( A @ boole_POSet @ related_reflexive ) ) )
=> ( C @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ boolean_lattstr )
& ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).
thf(230,plain,
? [A: $i] :
( ( A @ boolean_lattstr )
& ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(318,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_1) ).
thf(434,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ poset_of_lattice @ with_infima_relstr )
& ( A @ poset_of_lattice @ with_suprema_relstr )
& ( A @ poset_of_lattice @ antisymmetric_relstr )
& ( A @ poset_of_lattice @ transitive_relstr )
& ( A @ poset_of_lattice @ reflexive_relstr )
& ( A @ poset_of_lattice @ strict_rel_str )
& ~ ( A @ poset_of_lattice @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_0) ).
thf(477,plain,
! [A: $i,B: $i] :
( ( A @ singleton @ ( A @ singleton @ ( B @ relation_of2 ) ) )
=> ( ( B @ ( A @ singleton @ rel_str_of ) @ trivial_carrier )
& ( B @ ( A @ singleton @ rel_str_of ) @ strict_rel_str )
& ~ ( B @ ( A @ singleton @ rel_str_of ) @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).
thf(213,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(626,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).
thf(130,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ boolean_lattstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_lattstr )
& ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ distributive_lattstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(636,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(394,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(431,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_yellow_1) ).
thf(658,plain,
! [A: $i] :
( ( A @ boole_POSet @ antisymmetric_relstr )
& ( A @ boole_POSet @ transitive_relstr )
& ( A @ boole_POSet @ reflexive_relstr )
& ( A @ boole_POSet @ strict_rel_str )
& ~ ( A @ boole_POSet @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(52,axiom,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(473,plain,
? [A: $i] :
( ( A @ strict_rel_str )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(85,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(648,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(749,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(108,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice3) ).
thf(754,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ k2_lattice3 @ v1_partfun1 ) ) )
& ( A @ k2_lattice3 @ transitive )
& ( A @ k2_lattice3 @ antisymmetric )
& ( A @ k2_lattice3 @ reflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
thf(553,plain,
? [A: $i] :
( ( A @ strict_latt_str )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
thf(557,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ k2_lattice3 )
= ( A @ relation_of_lattice ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_yellow_0) ).
thf(263,plain,
? [A: $i] :
( ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(463,plain,
? [A: $i] :
( ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ distributive_lattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ modular_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).
thf(359,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( ( A @ distributive_lattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ modular_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_0) ).
thf(544,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(585,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ modular_lattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).
thf(370,plain,
? [A: $i] :
( ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ modular_lattstr )
& ( A @ distributive_lattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(744,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ strict_rel_str )
=> ( A
= ( A @ the_InternalRel @ ( A @ the_carrier @ rel_str_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ related_reflexive ) ) )
<=> ( C @ ( B @ ( A @ related ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( ( C @ ( B @ ( A @ related ) ) )
=> ( C @ ( B @ ( A @ related_reflexive ) ) ) )
& ( ( C @ ( B @ ( A @ related_reflexive ) ) )
=> ( C @ ( B @ ( A @ related ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(386,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ rel_str_of ) )
= ( D @ ( C @ rel_str_of ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(314,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( C @ ( B @ ( A @ latt_str_of ) ) @ latt_str )
& ( C @ ( B @ ( A @ latt_str_of ) ) @ strict_latt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ boole_lattice @ complete_latt_str )
& ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
thf(143,plain,
! [A: $i] :
( ( A @ boole_lattice @ complete_latt_str )
& ( A @ boole_lattice @ boolean_lattstr )
& ( A @ boole_lattice @ complemented_lattstr )
& ( A @ boole_lattice @ bounded_lattstr )
& ( A @ boole_lattice @ upper_bounded_semilattstr )
& ( A @ boole_lattice @ lower_bounded_semilattstr )
& ( A @ boole_lattice @ modular_lattstr )
& ( A @ boole_lattice @ distributive_lattstr )
& ( A @ boole_lattice @ lattice )
& ( A @ boole_lattice @ join_absorbing )
& ( A @ boole_lattice @ meet_absorbing )
& ( A @ boole_lattice @ meet_associative )
& ( A @ boole_lattice @ meet_commutative )
& ( A @ boole_lattice @ join_associative )
& ( A @ boole_lattice @ join_commutative )
& ( A @ boole_lattice @ strict_latt_str )
& ~ ( A @ boole_lattice @ empty_carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(80,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ below_refl ) ) )
<=> ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
thf(632,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) )
=> ( C @ ( B @ ( A @ below_refl ) ) ) )
& ( ( C @ ( B @ ( A @ below_refl ) ) )
=> ( C @ ( A @ cast_to_el_of_LattPOSet ) @ ( B @ ( A @ cast_to_el_of_LattPOSet ) @ ( A @ poset_of_lattice @ related_reflexive ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ boole_lattice @ poset_of_lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
thf(731,plain,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ boole_lattice @ poset_of_lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_0) ).
thf(418,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complete_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lattice3) ).
thf(346,plain,
? [A: $i] :
( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ( A @ strict_rel_str )
& ~ ( A @ empty_carrier )
& ( A @ rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(66,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(549,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( A @ cartesian_product2 ) @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ latt_str_of ) ) )
= ( F @ ( E @ ( D @ latt_str_of ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ related_reflexive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(716,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ rel_str )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( B @ ( B @ ( A @ related_reflexive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(564,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ relation_of2 ) ) )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ reflexive ) )
=> ( ( B @ ( A @ rel_str_of ) @ antisymmetric_relstr )
& ( B @ ( A @ rel_str_of ) @ transitive_relstr )
& ( B @ ( A @ rel_str_of ) @ reflexive_relstr )
& ( B @ ( A @ rel_str_of ) @ strict_rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).
thf(283,plain,
? [A: $i] :
( ( A @ bounded_lattstr )
& ( A @ upper_bounded_semilattstr )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ( A @ join_absorbing )
& ( A @ meet_absorbing )
& ( A @ meet_associative )
& ( A @ meet_commutative )
& ( A @ join_associative )
& ( A @ join_commutative )
& ( A @ strict_latt_str )
& ~ ( A @ empty_carrier )
& ( A @ latt_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow_0) ).
thf(427,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ bounded_relstr )
=> ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(459,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ boole_lattice @ below ) ) )
<=> ( C @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice3) ).
thf(723,plain,
! [A: $i,B: $i] :
( ( A @ boole_lattice @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ boole_lattice @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ subset ) )
=> ( C @ ( B @ ( A @ boole_lattice @ below ) ) ) )
& ( ( C @ ( B @ ( A @ boole_lattice @ below ) ) )
=> ( C @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_yellow_0) ).
thf(254,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr ) )
=> ( A @ bounded_relstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(322,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(69,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(560,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(90,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(676,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ v1_partfun1 ) ) )
& ( A @ the_InternalRel @ transitive )
& ( A @ the_InternalRel @ antisymmetric )
& ( A @ the_InternalRel @ reflexive )
& ( A @ the_InternalRel @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(491,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( A @ relation_of_lattice @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(801,plain,
$false,
inference(e,[status(thm)],[742,482,422,138,518,582,683,449,597,217,276,747,670,570,719,587,751,125,357,638,606,770,325,179,591,443,646,121,734,396,248,512,761,534,334,392,484,252,329,522,461,493,686,328,471,256,738,654,721,508,311,765,128,343,298,412,425,689,562,772,641,445,713,498,113,230,318,434,477,213,626,130,636,394,431,658,473,648,749,754,553,557,263,463,359,544,585,370,744,727,386,314,143,652,632,731,418,346,549,536,716,564,283,427,459,723,254,322,560,676,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU369+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/0.40 % Computer : n002.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 09:23:35 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.86/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.19 % [INFO] Parsing done (186ms).
% 1.68/1.20 % [INFO] Running in sequential loop mode.
% 2.36/1.42 % [INFO] eprover registered as external prover.
% 2.36/1.42 % [INFO] Scanning for conjecture ...
% 2.78/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 120 axioms. Running axiom selection ...
% 3.04/1.74 % [INFO] Axiom selection finished. Selected 110 axioms (removed 10 axioms).
% 3.39/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 3.63/1.91 % [INFO] Type checking passed.
% 3.63/1.91 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.59/3.95 % External prover 'e' found a proof!
% 10.59/3.95 % [INFO] Killing All external provers ...
% 10.59/3.95 % Time passed: 3395ms (effective reasoning time: 2746ms)
% 10.59/3.95 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.59/3.95 % Axioms used in derivation (110): redefinition_m2_relset_1, fc1_yellow_1, rc2_yellow_0, cc3_lattices, rc2_xboole_0, fc1_xboole_0, rc12_lattices, cc6_lattices, existence_l1_lattices, d5_tarski, t1_subset, fc4_lattice3, fc4_subset_1, existence_l3_lattices, d2_lattice3, rc2_partfun1, cc4_lattices, rc2_orders_2, cc1_lattice3, dt_m2_relset_1, dt_k4_lattice3, dt_u1_orders_2, reflexivity_r3_lattices, d9_orders_2, rc1_lattice3, rc11_lattices, rc3_lattices, dt_l1_lattices, dt_k3_yellow_1, rc2_lattice3, t6_boole, rc2_subset_1, existence_l2_lattices, redefinition_r3_orders_2, t2_lattice3, fc3_subset_1, t5_subset, existence_m1_relset_1, cc2_yellow_0, dt_l3_lattices, fc2_subset_1, fc2_lattice3, fc1_lattice3, dt_l2_lattices, fc8_yellow_1, dt_k3_lattice3, cc5_lattices, t4_subset, dt_k9_filter_1, rc13_lattices, d3_lattice3, fc2_orders_2, t7_boole, existence_l1_orders_2, rc1_orders_2, rc3_struct_0, fc1_subset_1, reflexivity_r3_orders_2, dt_g1_orders_2, rc1_subset_1, fc4_yellow_1, cc1_lattices, abstractness_v1_orders_2, cc4_yellow_0, redefinition_r3_lattices, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, fc3_orders_2, d2_yellow_1, existence_m2_relset_1, fc1_yellow_0, dt_l1_orders_2, fc1_orders_2, free_g1_orders_2, fc1_struct_0, fc2_yellow_1, fc1_knaster, reflexivity_r1_tarski, dt_k2_lattice3, t7_lattice3, cc1_knaster, dt_g3_lattices, rc6_lattices, free_g3_lattices, cc7_lattices, fc3_lattice3, cc5_yellow_0, dt_k1_lattice3, abstractness_v3_lattices, cc1_yellow_0, redefinition_k2_lattice3, fc3_yellow_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, rc1_yellow_0, cc2_lattice3, existence_l1_struct_0, fc7_yellow_1, rc10_lattices, dt_u2_lattices, fc3_lattices, cc3_yellow_0, antisymmetry_r2_hidden, cc2_lattices
% 10.59/3.95 % No. of inferences in proof: 224
% 10.59/3.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3395 ms resp. 2746 ms w/o parsing
% 12.19/4.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.19/4.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------