%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU306+2 : 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 : n019.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 08:38:24 AM UTC 2026
% Result : Theorem 13.14s 4.42s
% Output : Refutation 14.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 133
% Syntax : Number of formulae : 268 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 1129 ( 189 equ; 0 cnn)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 3565 ( 155 ~; 6 |; 427 &;2549 @)
% ( 38 <=>; 390 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 2 con; 0-6 aty)
% Number of variables : 793 ( 0 ^; 676 !; 117 ?; 793 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_dom_as_subset_decl,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(cast_to_subset_decl,type,
cast_to_subset: $i > $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(relation_rng_as_subset_decl,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(union_of_subsets_decl,type,
union_of_subsets: $i > $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(complements_of_subsets_decl,type,
complements_of_subsets: $i > $i > $i ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $i > $i ).
thf(meet_of_subsets_decl,type,
meet_of_subsets: $i > $i > $i ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(set_meet_decl,type,
set_meet: $i > $i ).
thf(apply_binary_as_element_decl,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(meet_semilatt_str_decl,type,
meet_semilatt_str: $i > $o ).
thf(apply_binary_decl,type,
apply_binary: $i > $i > $i > $i ).
thf(join_semilatt_str_decl,type,
join_semilatt_str: $i > $o ).
thf(latt_str_decl,type,
latt_str: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(meet_absorbing_decl,type,
meet_absorbing: $i > $o ).
thf(join_decl,type,
join: $i > $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i > $i ).
thf(join_commutative_decl,type,
join_commutative: $i > $o ).
thf(join_commut_decl,type,
join_commut: $i > $i > $i > $i ).
thf(below_decl,type,
below: $i > $i > $i > $o ).
thf(meet_commutative_decl,type,
meet_commutative: $i > $o ).
thf(meet_commut_decl,type,
meet_commut: $i > $i > $i > $i ).
thf(the_L_meet_decl,type,
the_L_meet: $i > $i ).
thf(the_L_join_decl,type,
the_L_join: $i > $i ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(809,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(47,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(518,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(67,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(666,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
thf(352,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
( ! [D: $i,E: $i] :
( ( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( D = F ) )
& ( A @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
& ( C @ function )
& ( C @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(333,plain,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ cartesian_product2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(249,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ cartesian_product2 ) ) ) )
& ( ( C
= ( B @ ( A @ cartesian_product2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ ordered_pair ) ) )
& ( B @ ( F @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(741,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(132,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ below ) ) )
<=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(878,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( ( C @ ( B @ ( A @ join ) ) )
= C )
=> ( C @ ( B @ ( A @ below ) ) ) )
& ( ( C @ ( B @ ( A @ below ) ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(85,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(730,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(217,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(384,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(114,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(829,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)],[114]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ relation )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(320,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) )
=> ( A @ relation ) )
& ( ( A @ relation )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(81,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(702,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)],[81]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
thf(460,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= F ) )
& ( D = F )
& ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ? [F: $i] :
( ? [G: $i,H: $i] :
( ? [I: $i] :
( ! [J: $i] :
( ( I @ ( J @ in ) )
=> ( B @ ( J @ ( H @ ordered_pair ) @ in ) ) )
& ( I @ ( H @ in ) )
& ( G = I ) )
& ( A @ ( G @ in ) )
& ( ( H @ ( G @ ordered_pair ) )
= E ) )
& ( F = E )
& ( C @ ( A @ cartesian_product2 ) @ ( F @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(448,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(316,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(687,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(734,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(128,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(866,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)],[128]) ).
thf(44,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(507,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)],[44]) ).
thf(71,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(678,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(661,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(297,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(693,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(111,axiom,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ meet_absorbing )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
thf(815,plain,
! [A: $i] :
( ( ( A @ latt_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) )
=> ( A @ meet_absorbing ) )
& ( ( A @ meet_absorbing )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( C @ ( B @ ( A @ meet ) ) @ ( A @ join ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(126,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(862,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(26,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(349,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(121,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(847,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)],[121]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(435,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(49,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(522,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(73,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(682,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)],[73]) ).
thf(53,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(551,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( C = empty_set ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(710,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( ( C = empty_set )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( C = empty_set ) ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(119,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(842,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ function )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(285,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) )
=> ( A @ function ) )
& ( ( A @ function )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(79,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(697,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
<=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( ( C @ ( B @ ( A @ relation_rng_as_subset ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(783,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(124,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(857,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)],[124]) ).
thf(133,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(884,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ relation_of2_as_subset ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
<=> ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(193,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( ( C @ ( A @ ( B @ relation_dom_as_subset ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( D @ ( E @ in ) )
<=> ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
thf(637,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ( ? [F: $i,G: $i] :
( ? [H: $i] :
( ! [I: $i] :
( ( H @ ( I @ in ) )
=> ( B @ ( I @ ( G @ ordered_pair ) @ in ) ) )
& ( H @ ( G @ in ) )
& ( F = H ) )
& ( A @ ( F @ in ) )
& ( ( G @ ( F @ ordered_pair ) )
= E ) )
& ( C @ ( A @ cartesian_product2 ) @ ( E @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(837,plain,
! [A: $i] :
( ( A @ meet_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(515,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ union_of_subsets ) )
= ( B @ ( A @ meet_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(654,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(457,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(605,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(792,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(107,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(805,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(765,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(558,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cartesian_product2 ) @ ( A @ ( C @ cartesian_product2 ) @ subset ) )
& ( C @ ( B @ cartesian_product2 ) @ ( C @ ( A @ cartesian_product2 ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(70,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(674,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( B @ ( C @ ( A @ join_commut ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
thf(888,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( B @ ( C @ ( A @ join_commut ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(102,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(794,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(93,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(750,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,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(689,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(58,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(601,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(513,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(430,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(31,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(402,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(732,plain,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(33,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(413,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(445,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(144,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(419,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(737,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(318,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(109,axiom,
? [A: $i] : ( A @ latt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(811,plain,
? [A: $i] : ( A @ latt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(140,plain,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(799,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ powerset @ ( C @ ( B @ ( A @ relation_rng_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(61,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(626,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(769,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(68,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(668,plain,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(330,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(80,axiom,
? [A: $i] : ( A @ meet_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(700,plain,
? [A: $i] : ( A @ meet_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(520,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join_commut ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
thf(827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join_commut ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(129,axiom,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
thf(868,plain,
! [A: $i] :
( ( ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ join ) ) )
= ( C @ ( B @ ( A @ the_L_join @ ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_binary_as_element ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ powerset @ ( C @ element ) )
=> ( ( C
= ( B @ ( A @ complements_of_subsets ) ) )
<=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(608,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ powerset @ ( C @ element ) )
=> ( ( ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ subset_complement ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ complements_of_subsets ) ) ) )
& ( ( C
= ( B @ ( A @ complements_of_subsets ) ) )
=> ! [D: $i] :
( ( A @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ subset_complement ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ subset_complement ) @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(135,plain,
~ ! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,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(680,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(24,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(342,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(112,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(823,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)],[112]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(855,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(89,axiom,
? [A: $i] : ( A @ join_semilatt_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(739,plain,
? [A: $i] : ( A @ join_semilatt_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(82,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(705,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(282,plain,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(91,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(744,plain,
! [A: $i] :
( ( A @ latt_str )
=> ( ( A @ join_semilatt_str )
& ( A @ meet_semilatt_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
<=> ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(656,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(864,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ join ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(386,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(314,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(131,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(876,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)],[131]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(859,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ cast_as_carrier_subset )
= ( A @ the_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(450,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ subset ) )
& ( B @ ( D @ in ) ) )
=> ( D = C ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(203,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( B @ ( A @ subset ) ) )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(671,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( B @ ( A @ subset ) ) )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(50,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(524,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(120,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(844,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)],[120]) ).
thf(110,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(813,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(92,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(748,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)],[92]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(390,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(786,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)],[100]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( A = empty_set )
=> ( ( B
= ( A @ set_meet ) )
<=> ( B = empty_set ) ) )
& ( ( A != empty_set )
=> ( ( B
= ( A @ set_meet ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(568,plain,
! [A: $i,B: $i] :
( ( ( A = empty_set )
=> ( ( ( B = empty_set )
=> ( B
= ( A @ set_meet ) ) )
& ( ( B
= ( A @ set_meet ) )
=> ( B = empty_set ) ) ) )
& ( ( A != empty_set )
=> ( ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ set_meet ) ) )
& ( ( B
= ( A @ set_meet ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( D @ ( C @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(25,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(346,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(549,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(115,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(832,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)],[115]) ).
thf(74,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(684,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(432,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(835,plain,
! [A: $i] :
( ( A @ join_semilatt_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ( ( C @ ( B @ disjoint ) )
<=> ( C @ ( A @ subset_complement ) @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(564,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ( ( ( C @ ( A @ subset_complement ) @ ( B @ subset ) )
=> ( C @ ( B @ disjoint ) ) )
& ( ( C @ ( B @ disjoint ) )
=> ( C @ ( A @ subset_complement ) @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(801,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(437,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(767,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(635,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( C @ ( B @ ( A @ join ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
thf(839,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ the_carrier @ ( C @ element ) )
& ( A @ the_carrier @ ( B @ element ) )
& ( A @ join_semilatt_str )
& ( A @ join_commutative )
& ~ ( A @ empty_carrier ) )
=> ( ( C @ ( B @ ( A @ join_commut ) ) )
= ( C @ ( B @ ( A @ join ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(728,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(528,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ~ ( A @ empty ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( E @ ordered_pair ) @ in ) ) )
& ( F @ ( E @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) )
& ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( C = F ) )
& ( A @ ( C @ in ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ? [F: $i] :
( ! [G: $i] :
( ( F @ ( G @ in ) )
=> ( B @ ( G @ ( D @ ordered_pair ) @ in ) ) )
& ( F @ ( D @ in ) )
& ( E = F ) )
& ( A @ ( E @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(122,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(850,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)],[122]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(691,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
thf(871,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)],[130]) ).
thf(106,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(803,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)],[106]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( B @ empty ) ) )
& ( ~ ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( A @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(755,plain,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( ( B @ empty )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( B @ empty ) ) ) )
& ( ~ ( A @ empty )
=> ( ( ( A @ ( B @ in ) )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( A @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(946,plain,
$false,
inference(e,[status(thm)],[809,518,555,666,352,333,249,741,878,730,217,384,797,829,320,702,460,448,316,687,734,866,507,678,661,297,693,815,862,349,847,435,522,682,551,710,842,285,697,403,783,857,884,193,637,837,515,654,457,605,792,805,765,558,674,888,773,794,750,161,689,601,513,430,402,732,413,445,144,419,737,318,811,140,799,626,769,668,330,700,520,827,868,608,135,680,342,823,855,739,705,282,744,336,656,864,386,314,876,859,450,203,671,524,844,813,748,304,390,786,568,346,549,832,684,432,835,564,210,801,437,767,635,839,728,528,163,850,691,871,803,755,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU306+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n019.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 09:09:48 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.97/1.37 % [INFO] Parsing done (381ms).
% 1.97/1.38 % [INFO] Running in sequential loop mode.
% 3.35/1.77 % [INFO] eprover registered as external prover.
% 3.35/1.78 % [INFO] Scanning for conjecture ...
% 4.00/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 473 axioms. Running axiom selection ...
% 4.36/2.13 % [INFO] Axiom selection finished. Selected 132 axioms (removed 341 axioms).
% 5.53/2.36 % [INFO] Problem is first-order (TPTP FOF).
% 5.53/2.38 % [INFO] Type checking passed.
% 5.53/2.38 % [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 ...
% 13.14/4.42 % External prover 'e' found a proof!
% 13.14/4.42 % [INFO] Killing All external provers ...
% 13.14/4.42 % Time passed: 3866ms (effective reasoning time: 3031ms)
% 13.14/4.42 % 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)>
% 13.14/4.42 % Axioms used in derivation (132): redefinition_k5_setfam_1, s1_funct_1__e10_24__wellord2__1, d1_lattices, redefinition_m2_relset_1, t43_subset_1, cc2_finset_1, fc1_zfmisc_1, dt_k5_relset_1, t3_xboole_1, dt_k4_relset_1, fc1_xboole_0, dt_k2_subset_1, existence_l1_lattices, t1_subset, t26_lattices, fc4_relat_1, fc4_subset_1, existence_l3_lattices, l3_subset_1, t99_zfmisc_1, rc2_partfun1, t47_setfam_1, s1_tarski__e10_24__wellord2__2, t56_relat_1, cc1_relat_1, redefinition_k6_setfam_1, dt_m2_relset_1, t18_finset_1, d3_pre_topc, dt_k2_binop_1, d4_subset_1, involutiveness_k3_subset_1, rc1_funct_1, d1_xboole_0, l50_zfmisc_1, dt_l1_lattices, t118_zfmisc_1, t16_relset_1, t6_boole, rc2_subset_1, existence_l2_lattices, dt_k6_subset_1, d1_relat_1, t1_xboole_1, t5_subset, existence_m1_relset_1, dt_l3_lattices, dt_l2_lattices, t2_tarski, d3_lattices, t4_subset, d4_tarski, t7_boole, cc1_funct_1, s1_tarski__e10_24__wellord2__1, rc3_struct_0, t13_finset_1, t3_ordinal1, d2_subset_1, commutativity_k4_lattices, fc1_subset_1, t33_zfmisc_1, rc2_funct_1, t9_funct_2, rc1_subset_1, rc1_funct_2, t46_setfam_1, t3_subset, cc1_relset_1, t22_relset_1, dt_k6_setfam_1, dt_u1_lattices, d2_zfmisc_1, existence_m1_subset_1, t106_zfmisc_1, t48_setfam_1, l71_subset_1, t92_zfmisc_1, d1_zfmisc_1, d8_setfam_1, t63_xboole_1, rc2_relat_1, existence_m2_relset_1, l55_zfmisc_1, redefinition_k2_binop_1, involutiveness_k7_setfam_1, d1_relset_1, d3_tarski, fc1_struct_0, redefinition_k3_lattices, t119_zfmisc_1, s1_xboole_0__e10_24__wellord2__1, rc1_relat_1, dt_k4_lattices, reflexivity_r1_tarski, t2_xboole_1, d2_lattices, d1_funct_2, dt_k1_lattices, dt_k5_setfam_1, rc3_finset_1, dt_k7_setfam_1, cc1_finset_1, t54_subset_1, rc1_finset_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, d3_relat_1, d1_setfam_1, symmetry_r1_xboole_0, d8_lattices, d1_funct_1, t50_subset_1, commutativity_k3_lattices, d10_xboole_0, existence_l1_struct_0, t7_tarski, dt_u2_lattices, dt_k2_lattices, t3_xboole_0, cc16_membered, rc2_xboole_0, dt_k3_subset_1, d2_relat_1, t23_lattices, dt_k3_lattices, antisymmetry_r2_hidden, t23_relset_1, redefinition_k4_lattices, dt_k2_pre_topc
% 13.14/4.42 % No. of inferences in proof: 268
% 13.14/4.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3866 ms resp. 3031 ms w/o parsing
% 14.08/4.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.08/4.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------