%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU352+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:38:32 AM UTC 2026
% Result : Theorem 161.50s 39.12s
% Output : Refutation 163.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 74
% Syntax : Number of formulae : 341 ( 126 unt; 0 typ; 13 def)
% Number of atoms : 1076 ( 180 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 2981 ( 339 ~; 186 |; 263 &;2046 @)
% ( 7 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 11 con; 0-6 aty)
% Number of variables : 581 ( 7 ^; 521 !; 40 ?; 581 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(lattice_decl,type,
lattice: $i > $o ).
thf(complete_latt_str_decl,type,
complete_latt_str: $i > $o ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(lower_bounded_semilattstr_decl,type,
lower_bounded_semilattstr: $i > $o ).
thf(bottom_of_semilattstr_decl,type,
bottom_of_semilattstr: $i > $i ).
thf(join_of_latt_set_decl,type,
join_of_latt_set: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(apply_binary_decl,type,
apply_binary: $i > $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(apply_binary_as_element_decl,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(meet_associative_decl,type,
meet_associative: $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(meet_decl,type,
meet: $i > $i > $i > $i ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(below_decl,type,
below: $i > $i > $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_decl,type,
join_absorbing: $i > $o ).
thf(below_refl_decl,type,
below_refl: $i > $i > $i > $o ).
thf(latt_element_smaller_decl,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(join_associative_decl,type,
join_associative: $i > $o ).
thf(meet_commut_decl,type,
meet_commut: $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ relation_of2 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ relation_of2_as_subset ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] : ( A @ meet_semilatt_str ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] : ( A @ one_sorted_str ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] : ( A @ join_semilatt_str ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] : ( A @ latt_str ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ) ) ) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(160,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(161,plain,
! [A: $i] :
( ( A @ sk10 @ empty )
& ( A @ powerset @ ( A @ sk10 @ element ) ) ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
! [A: $i] : ( A @ powerset @ ( A @ sk10 @ element ) ),
inference(cnfConj,[status(thm)],[161]) ).
thf(163,plain,
! [A: $i] : ( A @ sk10 @ empty ),
inference(cnfConj,[status(thm)],[161]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(259,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(260,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( ( A @ sk10 @ empty )
!= ( B @ empty ) )
| ~ $true
| ( B = empty_set ) ),
inference(paramod_ordered,[status(thm)],[163,261]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( ( A @ sk10 @ empty )
!= ( B @ empty ) )
| ( B = empty_set ) ),
inference(simp,[status(thm)],[732]) ).
thf(734,plain,
! [A: $i] :
( ( A @ sk10 )
= empty_set ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( C )),bind(B,$thf( C @ sk10 ))]]) ).
thf(786,plain,
! [A: $i] :
( ( A @ sk10 )
= empty_set ),
inference(simp,[status(thm)],[734]) ).
thf(1322,plain,
! [A: $i] : ( A @ powerset @ ( empty_set @ element ) ),
inference(rewrite,[status(thm)],[162,786]) ).
thf(39,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(180,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(63,plain,
~ ! [A: $i] :
( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ bottom_of_semilattstr )
= ( empty_set @ ( A @ join_of_latt_set ) ) )
& ( A @ latt_str )
& ( A @ lower_bounded_semilattstr )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(64,plain,
( ( ( ( sk1 @ bottom_of_semilattstr )
!= ( empty_set @ ( sk1 @ join_of_latt_set ) ) )
| ~ ( sk1 @ latt_str )
| ~ ( sk1 @ lower_bounded_semilattstr )
| ~ ( sk1 @ lattice )
| ( sk1 @ empty_carrier ) )
& ( sk1 @ latt_str )
& ( sk1 @ complete_latt_str )
& ( sk1 @ lattice )
& ~ ( sk1 @ empty_carrier ) ),
inference(cnf,[status(esa)],[63]) ).
thf(67,plain,
sk1 @ complete_latt_str,
inference(cnfConj,[status(thm)],[64]) ).
thf(576,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ complete_latt_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,67]) ).
thf(577,plain,
( ( empty_set @ complete_latt_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( sk1 ))]]) ).
thf(803,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ complete_latt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,577]) ).
thf(804,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ complete_latt_str ) ),
inference(simp,[status(thm)],[803]) ).
thf(809,plain,
( ( sk1 != empty_set )
| ( empty_set @ complete_latt_str ) ),
inference(simp,[status(thm)],[804]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(137,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(138,plain,
! [A: $i] :
( ( A @ one_sorted_str )
| ~ ( A @ meet_semilatt_str ) ),
inference(cnf,[status(esa)],[137]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(100,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(101,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) @ element ) )
| ~ ( B @ ( F @ element ) )
| ~ ( A @ ( E @ element ) )
| ~ ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
| ~ ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
| ~ ( D @ function )
| ( B @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[100]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
thf(249,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ meet ) ) )
= ( C @ ( B @ ( A @ the_L_meet @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(83,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)],[8]) ).
thf(84,plain,
( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( F @ relation_of2_as_subset ) ) )
| ~ ( E @ ( D @ ( F @ relation_of2 ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2 ) ) )
| ~ ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
| ~ ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
| ~ ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(65,plain,
sk1 @ latt_str,
inference(cnfConj,[status(thm)],[64]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(223,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
| ~ ( A @ latt_str ) )
& ( ( A @ meet_semilatt_str )
| ~ ( A @ latt_str ) ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
| ~ ( A @ latt_str ) ),
inference(cnfConj,[status(thm)],[224]) ).
thf(478,plain,
! [A: $i] :
( ( ( sk1 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ meet_semilatt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,225]) ).
thf(479,plain,
! [A: $i] :
( ( ( sk1 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ meet_semilatt_str ) ),
inference(simp,[status(thm)],[478]) ).
thf(480,plain,
sk1 @ meet_semilatt_str,
inference(pattern_uni,[status(thm)],[479:[bind(A,$thf( sk1 ))]]) ).
thf(487,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,138]) ).
thf(488,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str ) ),
inference(simp,[status(thm)],[487]) ).
thf(489,plain,
sk1 @ one_sorted_str,
inference(pattern_uni,[status(thm)],[488:[bind(A,$thf( sk1 ))]]) ).
thf(644,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ one_sorted_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,489]) ).
thf(645,plain,
( ( empty_set @ one_sorted_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( sk1 ))]]) ).
thf(69,plain,
~ ( sk1 @ empty_carrier ),
inference(cnfConj,[status(thm)],[64]) ).
thf(18,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(115,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(118,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(119,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[118]) ).
thf(120,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[119]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[145]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[146]) ).
thf(510,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[509:[bind(A,$thf( B ))]]) ).
thf(511,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[510]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(269,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)],[60]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(202,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)],[44]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(116,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[115]) ).
thf(117,plain,
~ ( sk5 @ empty ),
inference(cnf,[status(esa)],[116]) ).
thf(299,plain,
( ( ( sk5 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,117]) ).
thf(300,plain,
( ( sk5 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[299]) ).
thf(301,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[300]) ).
thf(55,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( A @ bottom_of_semilattstr @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(93,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,plain,
sk4 @ empty,
inference(cnf,[status(esa)],[93]) ).
thf(722,plain,
! [A: $i] :
( ( ( sk4 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[94,261]) ).
thf(723,plain,
! [A: $i] :
( ( ( sk4 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
sk4 = empty_set,
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk4 ))]]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
thf(108,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)],[16]) ).
thf(109,plain,
! [A: $i] :
( ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ relation_of2_as_subset ) ) )
| ~ ( A @ meet_semilatt_str ) )
& ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
| ~ ( A @ meet_semilatt_str ) )
& ( ( A @ the_L_meet @ function )
| ~ ( A @ meet_semilatt_str ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(110,plain,
! [A: $i] :
( ( A @ the_L_meet @ function )
| ~ ( A @ meet_semilatt_str ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(123,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(124,plain,
! [A: $i] :
( ( ~ ( A @ sk6 @ empty )
| ( A @ empty ) )
& ( ( A @ powerset @ ( A @ sk6 @ element ) )
| ( A @ empty ) ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk6 @ element ) )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[124]) ).
thf(33,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(156,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(157,plain,
sk9 @ join_semilatt_str,
inference(cnf,[status(esa)],[156]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(95,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ relation )
| ~ ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk6 @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[125,96]) ).
thf(1462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( A @ sk6 @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1461]) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cartesian_product2 ) @ sk6 @ relation )
| ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(pattern_uni,[status(thm)],[1462:[bind(A,$thf( G @ ( F @ cartesian_product2 ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cartesian_product2 ) @ sk6 ))]]) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cartesian_product2 ) @ sk6 @ relation )
| ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(simp,[status(thm)],[1463]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(135,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(136,plain,
! [A: $i] :
( ( A @ one_sorted_str )
| ~ ( A @ join_semilatt_str ) ),
inference(cnf,[status(esa)],[135]) ).
thf(323,plain,
! [A: $i] :
( ( ( sk9 @ join_semilatt_str )
!= ( A @ join_semilatt_str ) )
| ( A @ one_sorted_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[157,136]) ).
thf(324,plain,
! [A: $i] :
( ( ( sk9 @ join_semilatt_str )
!= ( A @ join_semilatt_str ) )
| ( A @ one_sorted_str ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
sk9 @ one_sorted_str,
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sk9 ))]]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(152,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)],[31]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(77,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)],[6]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,79]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( F @ ( G @ unordered_pair ) )),bind(B,$thf( G @ singleton )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(30,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(149,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(150,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(cnf,[status(esa)],[150]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,151]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[326]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[327]) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[82,332]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[396:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= ( C @ ( D @ unordered_pair ) ) )
| ( ( A @ ( B @ ordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[400,397]) ).
thf(1537,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1536:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ unordered_pair ) )),bind(D,$thf( F @ singleton ))]]) ).
thf(1572,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[1537]) ).
thf(36,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(164,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(130,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(131,plain,
sk7 @ meet_semilatt_str,
inference(cnf,[status(esa)],[130]) ).
thf(111,plain,
! [A: $i] :
( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
| ~ ( A @ meet_semilatt_str ) ),
inference(cnfConj,[status(thm)],[109]) ).
thf(2088,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,111]) ).
thf(2089,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[2088]) ).
thf(2090,plain,
sk7 @ the_carrier @ ( sk7 @ the_carrier @ ( sk7 @ the_carrier @ cartesian_product2 ) @ ( sk7 @ the_L_meet @ quasi_total ) ),
inference(pattern_uni,[status(thm)],[2089:[bind(A,$thf( sk7 ))]]) ).
thf(351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ ordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[79,332]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ unordered_pair ) )),bind(D,$thf( G @ singleton ))]]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[352]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(226,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
| ~ ( A @ latt_str ) ),
inference(cnfConj,[status(thm)],[224]) ).
thf(512,plain,
! [A: $i] :
( ( ( sk1 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ join_semilatt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,226]) ).
thf(513,plain,
! [A: $i] :
( ( ( sk1 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ join_semilatt_str ) ),
inference(simp,[status(thm)],[512]) ).
thf(514,plain,
sk1 @ join_semilatt_str,
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( sk1 ))]]) ).
thf(29,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(147,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(61,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(278,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(279,plain,
( ~ ( sk18 @ empty_carrier )
& ( sk18 @ one_sorted_str ) ),
inference(cnf,[status(esa)],[278]) ).
thf(280,plain,
sk18 @ one_sorted_str,
inference(cnfConj,[status(thm)],[279]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ element ) )
& ( A @ ( E @ element ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ relation_of2 ) ) )
& ( C @ ( B @ ( A @ cartesian_product2 ) @ ( D @ quasi_total ) ) )
& ( D @ function )
& ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ apply_binary_as_element ) ) ) ) ) )
= ( F @ ( E @ ( D @ apply_binary ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(89,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
thf(265,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ( A @ meet_absorbing )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( B @ ( C @ ( B @ ( A @ meet_commut ) ) @ ( A @ below ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
<=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
thf(206,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ( A @ latt_str )
& ( A @ complete_latt_str )
& ( A @ lattice )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i,C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) )
=> ( C
= ( B @ ( A @ join_of_latt_set ) ) ) )
& ( ( C
= ( B @ ( A @ join_of_latt_set ) ) )
=> ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( B @ ( D @ ( A @ latt_element_smaller ) ) )
=> ( D @ ( C @ ( A @ below ) ) ) ) )
& ( B @ ( C @ ( A @ latt_element_smaller ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(22,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(127,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(128,plain,
~ ? [A: $i] : ( A @ powerset @ empty ),
inference(miniscope,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnf,[status(esa)],[128]) ).
thf(308,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,129]) ).
thf(309,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[308]) ).
thf(312,plain,
! [A: $i] :
( ( A @ powerset )
!= empty_set ),
inference(simp,[status(thm)],[309]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(74,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[73]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2059,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,111]) ).
thf(2060,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[2059]) ).
thf(2061,plain,
sk1 @ the_carrier @ ( sk1 @ the_carrier @ ( sk1 @ the_carrier @ cartesian_product2 ) @ ( sk1 @ the_L_meet @ quasi_total ) ),
inference(pattern_uni,[status(thm)],[2060:[bind(A,$thf( sk1 ))]]) ).
thf(165,plain,
! [A: $i] : ( A @ ( A @ sk11 @ element ) ),
inference(cnf,[status(esa)],[164]) ).
thf(90,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[89]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
thf(252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ meet_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(582,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( empty_set @ empty_carrier )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,69]) ).
thf(583,plain,
( ~ ( empty_set @ empty_carrier )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(75,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk3 ) @ relation_of2_as_subset ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
| ~ ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(490,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk3 ) @ relation_of2_as_subset ) ) )
!= ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) )
| ( D @ ( C @ ( E @ relation_of2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,86]) ).
thf(491,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk3 ) @ relation_of2_as_subset ) ) )
!= ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) )
| ( D @ ( C @ ( E @ relation_of2 ) ) ) ),
inference(simp,[status(thm)],[490]) ).
thf(492,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2 ) ) ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(493,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2 ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(1908,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,110]) ).
thf(1909,plain,
! [A: $i] :
( ( ( sk1 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1910,plain,
sk1 @ the_L_meet @ function,
inference(pattern_uni,[status(thm)],[1909:[bind(A,$thf( sk1 ))]]) ).
thf(1400,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ empty_carrier )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,583]) ).
thf(1401,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ empty_carrier ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1402,plain,
( ( sk1 != empty_set )
| ~ ( empty_set @ empty_carrier ) ),
inference(simp,[status(thm)],[1401]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_associative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v2_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(369,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,138]) ).
thf(370,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str ) ),
inference(simp,[status(thm)],[369]) ).
thf(371,plain,
sk7 @ one_sorted_str,
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( sk7 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(71,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk2 ) @ relation_of2 ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(521,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk2 ) @ relation_of2 ) ) )
!= ( D @ ( C @ ( E @ relation_of2 ) ) ) )
| ( D @ ( C @ ( E @ relation_of2_as_subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,88]) ).
thf(522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ sk2 ) @ relation_of2 ) ) )
!= ( D @ ( C @ ( E @ relation_of2 ) ) ) )
| ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) ),
inference(simp,[status(thm)],[521]) ).
thf(523,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2_as_subset ) ) ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk2 ) ))]]) ).
thf(530,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2_as_subset ) ) ),
inference(simp,[status(thm)],[523]) ).
thf(538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2_as_subset ) ) )
!= ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) )
| ( D @ ( C @ ( E @ relation_of2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[530,86]) ).
thf(539,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2_as_subset ) ) )
!= ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) )
| ( D @ ( C @ ( E @ relation_of2 ) ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(540,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2 ) ) ),
inference(pattern_uni,[status(thm)],[539:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk2 ) ))]]) ).
thf(541,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk2 ) @ relation_of2 ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(105,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(244,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,plain,
( ( ( sk1 @ bottom_of_semilattstr )
!= ( empty_set @ ( sk1 @ join_of_latt_set ) ) )
| ~ ( sk1 @ latt_str )
| ~ ( sk1 @ lower_bounded_semilattstr )
| ~ ( sk1 @ lattice )
| ( sk1 @ empty_carrier ) ),
inference(cnfConj,[status(thm)],[64]) ).
thf(70,plain,
( ~ ( sk1 @ latt_str )
| ~ ( sk1 @ lower_bounded_semilattstr )
| ~ ( sk1 @ lattice )
| ( sk1 @ empty_carrier )
| ( ( empty_set @ ( sk1 @ join_of_latt_set ) )
!= ( sk1 @ bottom_of_semilattstr ) ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(66,plain,
sk1 @ lattice,
inference(cnfConj,[status(thm)],[64]) ).
thf(297,plain,
( ~ $true
| ~ ( sk1 @ lower_bounded_semilattstr )
| ~ $true
| $false
| ( ( empty_set @ ( sk1 @ join_of_latt_set ) )
!= ( sk1 @ bottom_of_semilattstr ) ) ),
inference(rewrite,[status(thm)],[70,65,66,69]) ).
thf(298,plain,
( ~ ( sk1 @ lower_bounded_semilattstr )
| ( ( empty_set @ ( sk1 @ join_of_latt_set ) )
!= ( sk1 @ bottom_of_semilattstr ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ v1_partfun1 ) ) )
& ( A @ the_carrier @ ( A @ the_L_meet @ v1_binop_1 ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ cartesian_product2 ) @ ( A @ the_L_meet @ quasi_total ) ) )
& ( A @ the_L_meet @ function )
& ( A @ the_L_meet @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(148,plain,
sk8 @ one_sorted_str,
inference(cnf,[status(esa)],[147]) ).
thf(59,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(267,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(268,plain,
sk17 @ latt_str,
inference(cnf,[status(esa)],[267]) ).
thf(484,plain,
! [A: $i] :
( ( ( sk17 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ meet_semilatt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[268,225]) ).
thf(485,plain,
! [A: $i] :
( ( ( sk17 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ meet_semilatt_str ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
sk17 @ meet_semilatt_str,
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( sk17 ))]]) ).
thf(1927,plain,
! [A: $i] :
( ( ( sk17 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[486,110]) ).
thf(1928,plain,
! [A: $i] :
( ( ( sk17 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function ) ),
inference(simp,[status(thm)],[1927]) ).
thf(1929,plain,
sk17 @ the_L_meet @ function,
inference(pattern_uni,[status(thm)],[1928:[bind(A,$thf( sk17 ))]]) ).
thf(281,plain,
~ ( sk18 @ empty_carrier ),
inference(cnfConj,[status(thm)],[279]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(181,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)],[40]) ).
thf(640,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ latt_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,65]) ).
thf(641,plain,
( ( empty_set @ latt_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[640:[bind(A,$thf( sk1 ))]]) ).
thf(611,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ join_semilatt_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,514]) ).
thf(612,plain,
( ( empty_set @ join_semilatt_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( sk1 ))]]) ).
thf(1423,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ join_semilatt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,612]) ).
thf(1424,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ join_semilatt_str ) ),
inference(simp,[status(thm)],[1423]) ).
thf(1428,plain,
( ( sk1 != empty_set )
| ( empty_set @ join_semilatt_str ) ),
inference(simp,[status(thm)],[1424]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ below ) ) )
& ( C @ ( B @ ( A @ below ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
thf(187,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ below ) ) )
& ( C @ ( B @ ( A @ below ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
<=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(230,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) )
=> ( C @ ( B @ ( A @ latt_element_smaller ) ) ) )
& ( ( C @ ( B @ ( A @ latt_element_smaller ) ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ below ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( C @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,79]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[386:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(240,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)],[49]) ).
thf(1458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1322,96]) ).
thf(1459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ powerset @ ( empty_set @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation ) ),
inference(simp,[status(thm)],[1458]) ).
thf(1460,plain,
empty_set @ relation,
inference(pattern_uni,[status(thm)],[1459:[bind(A,$thf( F @ ( E @ cartesian_product2 ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( empty_set ))]]) ).
thf(574,plain,
! [A: $i] :
( ( A != sk18 )
| ~ ( empty_set @ empty_carrier )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,281]) ).
thf(575,plain,
( ~ ( empty_set @ empty_carrier )
| ~ ( sk18 @ empty ) ),
inference(pattern_uni,[status(thm)],[574:[bind(A,$thf( sk18 ))]]) ).
thf(1379,plain,
( ( ( sk18 @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ empty_carrier )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,575]) ).
thf(1380,plain,
( ( ( sk18 @ empty )
!= ( empty_set @ empty ) )
| ~ ( empty_set @ empty_carrier ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1381,plain,
( ( sk18 != empty_set )
| ~ ( empty_set @ empty_carrier ) ),
inference(simp,[status(thm)],[1380]) ).
thf(518,plain,
! [A: $i] :
( ( ( sk17 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ join_semilatt_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[268,226]) ).
thf(519,plain,
! [A: $i] :
( ( ( sk17 @ latt_str )
!= ( A @ latt_str ) )
| ( A @ join_semilatt_str ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
sk17 @ join_semilatt_str,
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( sk17 ))]]) ).
thf(1924,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,110]) ).
thf(1925,plain,
! [A: $i] :
( ( ( sk7 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ the_L_meet @ function ) ),
inference(simp,[status(thm)],[1924]) ).
thf(1926,plain,
sk7 @ the_L_meet @ function,
inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( sk7 ))]]) ).
thf(302,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,120]) ).
thf(303,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[302]) ).
thf(306,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[303]) ).
thf(524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2 ) ) )
!= ( D @ ( C @ ( E @ relation_of2 ) ) ) )
| ( D @ ( C @ ( E @ relation_of2_as_subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[493,88]) ).
thf(525,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2 ) ) )
!= ( D @ ( C @ ( E @ relation_of2 ) ) ) )
| ( D @ ( C @ ( E @ relation_of2_as_subset ) ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(526,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2_as_subset ) ) ),
inference(pattern_uni,[status(thm)],[525:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(531,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ sk3 ) @ relation_of2_as_subset ) ) ),
inference(simp,[status(thm)],[526]) ).
thf(616,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ meet_semilatt_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,480]) ).
thf(617,plain,
( ( empty_set @ meet_semilatt_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[616:[bind(A,$thf( sk1 ))]]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B
= ( A @ bottom_of_semilattstr ) )
<=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(282,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
=> ( B
= ( A @ bottom_of_semilattstr ) ) )
& ( ( B
= ( A @ bottom_of_semilattstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(689,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ lattice )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[261,66]) ).
thf(690,plain,
( ( empty_set @ lattice )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( sk1 ))]]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnf,[status(esa)],[97]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ function )
| ~ ( A @ relation )
| ( ( C @ ( B @ ( A @ apply_binary ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(103,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ empty )
& ( C @ powerset @ ( B @ element ) ) )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[102]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(1455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[165,96]) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ element ) )
!= ( C @ ( B @ cartesian_product2 ) @ powerset @ ( D @ element ) ) )
| ( D @ relation ) ),
inference(simp,[status(thm)],[1455]) ).
thf(1457,plain,
! [B: $i,A: $i] : ( B @ ( A @ cartesian_product2 ) @ powerset @ sk11 @ relation ),
inference(pattern_uni,[status(thm)],[1456:[bind(A,$thf( H @ ( G @ cartesian_product2 ) @ powerset )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ cartesian_product2 ) @ powerset @ sk11 ))]]) ).
thf(1476,plain,
! [B: $i,A: $i] : ( B @ ( A @ cartesian_product2 ) @ powerset @ sk11 @ relation ),
inference(simp,[status(thm)],[1457]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(158,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)],[34]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(139,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)],[27]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
thf(246,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( B @ ( C @ ( A @ meet_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
thf(262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ meet_semilatt_str )
& ( A @ meet_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ meet_commut ) ) )
= ( C @ ( B @ ( A @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ lower_bounded_semilattstr )
<=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(190,plain,
! [A: $i] :
( ( ( A @ meet_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) )
=> ( A @ lower_bounded_semilattstr ) )
& ( ( A @ lower_bounded_semilattstr )
=> ? [B: $i] :
( ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ meet ) ) )
= B )
& ( ( C @ ( B @ ( A @ meet ) ) )
= B ) ) )
& ( A @ the_carrier @ ( B @ element ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(106,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[180,107]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(337,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ ordered_pair ) )
= ( C @ ( D @ unordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,82]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( G )),bind(B,$thf( E )),bind(C,$thf( G @ ( E @ unordered_pair ) )),bind(D,$thf( G @ singleton ))]]) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(494,plain,
! [A: $i] :
( ( ( sk17 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[486,138]) ).
thf(495,plain,
! [A: $i] :
( ( ( sk17 @ meet_semilatt_str )
!= ( A @ meet_semilatt_str ) )
| ( A @ one_sorted_str ) ),
inference(simp,[status(thm)],[494]) ).
thf(496,plain,
sk17 @ one_sorted_str,
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( sk17 ))]]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(254,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)],[54]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( B @ ( A @ join_of_latt_set ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ~ ( B @ ( A @ ordered_pair ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[79,151]) ).
thf(346,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ordered_pair ) @ empty ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ unordered_pair ) )),bind(D,$thf( G @ singleton ))]]) ).
thf(354,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ordered_pair ) @ empty ),
inference(simp,[status(thm)],[346]) ).
thf(46374,plain,
$false,
inference(e,[status(thm)],[1322,809,138,101,249,88,645,69,115,120,511,269,202,185,301,257,724,110,125,157,1479,325,152,261,93,1572,164,2090,353,480,121,514,147,397,280,132,89,265,206,312,74,117,102,2061,160,137,165,92,252,65,97,583,493,1910,1402,156,225,77,489,96,173,129,371,73,541,530,105,244,298,166,148,180,149,1929,577,118,281,259,71,181,86,641,1428,187,113,230,76,387,240,1460,1381,108,520,66,130,1926,278,223,306,135,226,267,80,531,617,123,145,282,95,690,63,67,127,154,72,612,99,104,1476,158,139,786,75,246,82,151,262,146,190,107,136,268,79,400,332,575,131,111,486,337,469,496,100,254,227,354,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU352+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.21/0.46 % Computer : n020.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sat Sep 26 09:18:18 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.24/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.02/1.66 % [INFO] Parsing done (363ms).
% 2.02/1.69 % [INFO] Running in sequential loop mode.
% 3.50/2.30 % [INFO] eprover registered as external prover.
% 3.50/2.31 % [INFO] Scanning for conjecture ...
% 3.73/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 72 axioms. Running axiom selection ...
% 4.10/2.64 % [INFO] Axiom selection finished. Selected 60 axioms (removed 12 axioms).
% 4.63/2.82 % [INFO] Problem is first-order (TPTP FOF).
% 4.63/2.84 % [INFO] Type checking passed.
% 4.63/2.85 % [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 ...
% 161.50/39.11 % External prover 'e' found a proof!
% 161.50/39.11 % [INFO] Killing All external provers ...
% 161.50/39.11 % Time passed: 38445ms (effective reasoning time: 37415ms)
% 161.50/39.11 % 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)>
% 161.50/39.12 % Axioms used in derivation (60): redefinition_m2_relset_1, d13_lattices, dt_m2_relset_1, dt_k2_binop_1, dt_l2_lattices, redefinition_r3_lattices, existence_m2_relset_1, redefinition_k2_binop_1, d2_lattices, fc1_xboole_0, d16_lattices, existence_l1_lattices, d5_tarski, t26_lattices, t1_subset, fc4_subset_1, existence_l3_lattices, dt_k5_lattices, fc4_lattice2, reflexivity_r3_lattices, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, fc3_subset_1, t5_subset, existence_m1_relset_1, dt_l3_lattices, fc2_subset_1, d21_lattice3, t4_subset, t7_boole, d17_lattice3, rc3_struct_0, commutativity_k4_lattices, fc1_subset_1, fc5_lattice2, rc1_subset_1, cc1_lattices, dt_k15_lattice3, t3_subset, cc1_relset_1, dt_u1_lattices, existence_m1_subset_1, commutativity_k2_tarski, fc1_struct_0, dt_k4_lattices, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, dt_k2_lattices, d1_binop_1, rc2_xboole_0, t23_lattices, antisymmetry_r2_hidden, cc2_lattices, redefinition_k4_lattices
% 161.50/39.12 % No. of inferences in proof: 328
% 161.50/39.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38445 ms resp. 37415 ms w/o parsing
% 163.12/39.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 163.12/39.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------