%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU264+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 08:38:15 AM UTC 2026
% Result : Theorem 25.89s 6.96s
% Output : Refutation 26.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 309
% Syntax : Number of formulae : 620 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 2530 ( 457 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 7607 ( 261 ~; 24 |; 823 &;5436 @)
% ( 119 <=>; 944 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 2 con; 0-3 aty)
% Number of variables : 1537 ( 0 ^;1437 !; 100 ?;1537 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(cast_to_subset_decl,type,
cast_to_subset: $i > $i ).
thf(well_orders_decl,type,
well_orders: $i > $i > $o ).
thf(is_reflexive_in_decl,type,
is_reflexive_in: $i > $i > $o ).
thf(is_transitive_in_decl,type,
is_transitive_in: $i > $i > $o ).
thf(is_antisymmetric_in_decl,type,
is_antisymmetric_in: $i > $i > $o ).
thf(is_connected_in_decl,type,
is_connected_in: $i > $i > $o ).
thf(is_well_founded_in_decl,type,
is_well_founded_in: $i > $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(function_inverse_decl,type,
function_inverse: $i > $i ).
thf(relation_inverse_decl,type,
relation_inverse: $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(union_of_subsets_decl,type,
union_of_subsets: $i > $i > $i ).
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(succ_decl,type,
succ: $i > $i ).
thf(relation_isomorphism_decl,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(connected_decl,type,
connected: $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(well_founded_relation_decl,type,
well_founded_relation: $i > $o ).
thf(well_ordering_decl,type,
well_ordering: $i > $o ).
thf(being_limit_ordinal_decl,type,
being_limit_ordinal: $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_field_decl,type,
relation_field: $i > $i ).
thf(union_decl,type,
union: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(set_meet_decl,type,
set_meet: $i > $i ).
thf(relation_restriction_decl,type,
relation_restriction: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(relation_inverse_image_decl,type,
relation_inverse_image: $i > $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_restriction: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(ordinal_subset_decl,type,
ordinal_subset: $i > $i > $o ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(fiber_decl,type,
fiber: $i > $i > $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
thf(unordered_triple_decl,type,
unordered_triple: $i > $i > $i > $i ).
thf(are_equipotent_decl,type,
are_equipotent: $i > $i > $o ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
<=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(645,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(1665,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(760,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)],[78]) ).
thf(182,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(1454,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(1105,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(1031,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_rng @ ( B @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(962,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_rng @ ( B @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(11,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(352,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(1315,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(518,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
<=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(2077,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( C @ ( B @ ( A @ unordered_pair ) @ subset ) ) )
& ( ( C @ ( B @ ( A @ unordered_pair ) @ subset ) )
=> ( ( C @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(1924,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( B @ ( A @ relation_rng_restriction ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(2014,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( B @ ( A @ relation_rng_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(215,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(1728,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(38,axiom,
! [A: $i] :
~ ( A @ succ @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(449,plain,
! [A: $i] :
~ ( A @ succ @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2099,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(655,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_intersection2 ) )
= empty_set )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(1692,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)],[212]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(582,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)],[58]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ fiber ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord1) ).
thf(1142,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) )
=> ( C
= ( B @ ( A @ fiber ) ) ) )
& ( ( C
= ( B @ ( A @ fiber ) ) )
=> ! [D: $i] :
( ( ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( A @ ( B @ ( D @ ordered_pair ) @ in ) )
& ( D != B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( B @ ( C @ relation_composition ) @ apply ) )
= ( A @ ( C @ apply ) @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(1269,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( B @ ( C @ relation_composition ) @ apply ) )
= ( A @ ( C @ apply ) @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(2195,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
thf(385,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ succ @ ordinal )
& ( A @ succ @ epsilon_connected )
& ( A @ succ @ epsilon_transitive )
& ~ ( A @ succ @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(51,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(533,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(1275,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)],[155]) ).
thf(42,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(472,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(1327,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(152,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(1260,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(243,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(1919,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(945,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
thf(2146,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(1063,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(340,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(404,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,axiom,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(417,plain,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ transitive )
<=> ( A @ relation_field @ ( A @ is_transitive_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
thf(1475,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_transitive_in ) )
=> ( A @ transitive ) )
& ( ( A @ transitive )
=> ( A @ relation_field @ ( A @ is_transitive_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ being_limit_ordinal )
<=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
thf(1254,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) )
=> ( A @ being_limit_ordinal ) )
& ( ( A @ being_limit_ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( A @ ( B @ in ) )
=> ( A @ ( B @ succ @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(1887,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)],[236]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(320,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(2173,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(1904,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)],[240]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(1518,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field @ ( A @ well_orders ) )
<=> ( A @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
thf(1409,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ well_ordering )
=> ( A @ relation_field @ ( A @ well_orders ) ) )
& ( ( A @ relation_field @ ( A @ well_orders ) )
=> ( A @ well_ordering ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
| ( ( A @ relation_dom )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(934,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
| ( ( A @ relation_dom )
= empty_set ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(1059,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(542,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(1760,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)],[221]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(1660,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(244,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(1922,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(1379,plain,
! [A: $i,B: $i] :
( ( ( A @ relation_empty_yielding )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ relation_empty_yielding )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_image ) )
= ( A @ ( B @ relation_dom @ set_intersection2 ) @ ( B @ relation_image ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(1247,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_image ) )
= ( A @ ( B @ relation_dom @ set_intersection2 ) @ ( B @ relation_image ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ relation_inverse ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(1479,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_inverse ) ) )
& ( ( B
= ( A @ relation_inverse ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
thf(770,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(2024,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(316,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(1319,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= empty_set )
<=> ( ( A @ relation_rng )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(870,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ relation_rng )
= empty_set )
=> ( ( A @ relation_dom )
= empty_set ) )
& ( ( ( A @ relation_dom )
= empty_set )
=> ( ( A @ relation_rng )
= empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(237,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(1890,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(756,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(443,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(172,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(1418,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ~ ( ~ ( A @ ( B @ in ) )
& ( A != B )
& ~ ( B @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(966,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)],[112]) ).
thf(44,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(480,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(1020,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ antisymmetric )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
thf(574,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) )
=> ( A @ antisymmetric ) )
& ( ( A @ antisymmetric )
=> ! [B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
thf(1377,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
& ( A @ well_ordering ) )
=> ( B @ well_ordering ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(239,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(1896,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(956,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ reflexive )
<=> ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
thf(849,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ reflexive ) )
& ( ( A @ reflexive )
=> ! [B: $i] :
( ( A @ relation_field @ ( B @ in ) )
=> ( A @ ( B @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(135,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(1169,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(687,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ epsilon_transitive )
<=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(1943,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) )
=> ( A @ epsilon_transitive ) )
& ( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( A @ ( B @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_ordering )
=> ( A @ ( B @ relation_restriction ) @ well_ordering ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
thf(1201,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_ordering )
=> ( A @ ( B @ relation_restriction ) @ well_ordering ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(452,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ relation_field @ ( A @ in ) )
=> ( ( B @ ( A @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ relation_field @ ( A @ in ) )
=> ( ( B @ ( A @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_connected_in ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
thf(1736,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( A @ is_connected_in ) ) )
& ( ( B @ ( A @ is_connected_in ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( C != D )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ relation )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ ordered_pair ) ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(1868,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)],[233]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_rng @ ( A @ relation_dom @ cartesian_product2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(2061,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_rng @ ( A @ relation_dom @ cartesian_product2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B
= ( A @ ( C @ relation_dom_restriction ) ) )
<=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(1047,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) )
=> ( B
= ( A @ ( C @ relation_dom_restriction ) ) ) )
& ( ( B
= ( A @ ( C @ relation_dom_restriction ) ) )
=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ( ( B @ relation_dom )
= ( A @ ( C @ relation_dom @ set_intersection2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
thf(1730,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_connected_in ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ( A @ relation_field @ ( A @ is_connected_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ reflexive )
<=> ( A @ relation_field @ ( A @ is_reflexive_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
thf(952,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_reflexive_in ) )
=> ( A @ reflexive ) )
& ( ( A @ reflexive )
=> ( A @ relation_field @ ( A @ is_reflexive_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( A @ function_inverse )
= ( A @ relation_inverse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(349,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( A @ function_inverse )
= ( A @ relation_inverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(1174,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)],[137]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(1502,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( A @ ( A @ ordinal_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B
= ( A @ identity_relation ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(693,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) )
=> ( B
= ( A @ identity_relation ) ) )
& ( ( B
= ( A @ identity_relation ) )
=> ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( ( C @ ( B @ apply ) )
= C ) )
& ( ( B @ relation_dom )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(34,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(429,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(2150,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)],[294]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(729,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_inverse_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= ( A @ relation_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ relation_inverse @ relation_dom ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(1423,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_dom )
= ( A @ relation_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ relation_inverse @ relation_dom ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(1602,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ~ ( ( A @ being_limit_ordinal )
& ? [B: $i] :
( ( A
= ( B @ succ ) )
& ( B @ ordinal ) ) )
& ~ ( ! [B: $i] :
( ( B @ ordinal )
=> ( A
!= ( B @ succ ) ) )
& ~ ( A @ being_limit_ordinal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
thf(435,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ~ ( ( A @ being_limit_ordinal )
& ? [B: $i] :
( ( A
= ( B @ succ ) )
& ( B @ ordinal ) ) )
& ~ ( ! [B: $i] :
( ( B @ ordinal )
=> ( A
!= ( B @ succ ) ) )
& ~ ( A @ being_limit_ordinal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ ( B @ relation_dom_restriction ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(1951,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ ( B @ relation_dom_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_antisymmetric_in ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
thf(665,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) )
=> ( B @ ( A @ is_antisymmetric_in ) ) )
& ( ( B @ ( A @ is_antisymmetric_in ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(2181,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( D @ relation_rng @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(2213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( D @ relation_rng @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ transitive )
=> ( A @ ( B @ relation_restriction ) @ transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
thf(1407,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ transitive )
=> ( A @ ( B @ relation_restriction ) @ transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
<=> ( B @ ( A @ cartesian_product2 ) @ ( C @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1910,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)],[241]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(2115,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)],[288]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_founded_relation )
=> ( A @ ( B @ relation_restriction ) @ well_founded_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
thf(1762,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ well_founded_relation )
=> ( A @ ( B @ relation_restriction ) @ well_founded_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ in ) )
<=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(1772,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ unordered_triple ) ) ) )
=> ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ in ) ) )
& ( ( D @ ( E @ in ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(251,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( B @ ( C @ powerset @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(1953,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( B @ ( C @ powerset @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(1096,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(1878,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(356,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
<=> ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(1755,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) )
=> ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_composition ) @ relation_dom @ ( A @ in ) )
=> ( ( B @ relation_dom @ ( A @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(857,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(165,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(1350,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_inverse_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(1936,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)],[247]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ relation_restriction ) )
= ( B @ ( B @ cartesian_product2 ) @ ( A @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
thf(650,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ relation_restriction ) )
= ( B @ ( B @ cartesian_product2 ) @ ( A @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
<=> ( B @ ( A @ succ @ ordinal_subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
thf(948,plain,
! [A: $i] :
( ( A @ ordinal )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( ( B @ ( A @ succ @ ordinal_subset ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( B @ ( A @ succ @ ordinal_subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(1683,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_dom ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(1329,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_dom ) ) )
& ( ( B
= ( A @ relation_dom ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(1028,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(537,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(642,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2053,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(1842,plain,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ relation_rng @ subset ) )
=> ( ( B @ ( A @ relation_composition ) @ relation_dom )
= ( A @ relation_dom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(2108,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ relation_rng @ subset ) )
=> ( ( B @ ( A @ relation_composition ) @ relation_dom )
= ( A @ relation_dom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(180,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(1446,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) )
= ( B @ ( A @ identity_relation @ relation_composition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(1099,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) )
= ( B @ ( A @ identity_relation @ relation_composition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(255,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
thf(1974,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ ( A @ fiber ) @ disjoint ) )
& ( B @ ( C @ in ) ) )
& ( B != empty_set )
& ( A @ relation_field @ ( B @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(1932,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)],[246]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(984,plain,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_transitive_in ) )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(1852,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ is_transitive_in ) ) )
& ( ( B @ ( A @ is_transitive_in ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( E @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( A @ ( E @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(175,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(1429,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_inverse @ function )
& ( A @ relation_inverse @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(371,plain,
! [A: $i] :
( ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_inverse @ function )
& ( A @ relation_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(191,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(1525,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ ordinal )
<=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(921,plain,
! [A: $i] :
( ( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) )
& ( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(1515,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(2189,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)],[303]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(888,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)],[98]) ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(311,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)],[2]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_difference ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(1695,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_difference ) ) ) )
& ( ( C
= ( B @ ( A @ set_difference ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(773,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ transitive )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
thf(586,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ transitive ) )
& ( ( A @ transitive )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) )
=> ( A @ ( D @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_well_founded_in ) )
<=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
thf(2121,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) )
=> ( B @ ( A @ is_well_founded_in ) ) )
& ( ( B @ ( A @ is_well_founded_in ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ ( A @ fiber ) @ disjoint ) )
& ( C @ ( D @ in ) ) )
& ( C != empty_set )
& ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2001,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(223,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(1764,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1680,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(1595,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)],[195]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(819,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)],[87]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(958,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(1965,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(190,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(1520,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(545,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(242,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(1916,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(402,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(382,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)],[22]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(2029,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)],[266]) ).
thf(84,axiom,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(787,plain,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(1092,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(1090,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
<=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) )
=> ( B @ ( C @ relation_restriction ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(293,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(2148,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(391,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(1139,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(406,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(69,axiom,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(681,plain,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1282,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)],[157]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(2084,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(419,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(2097,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)],[281]) ).
thf(14,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(362,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(1722,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ relation_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_reflexive_in ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(880,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) )
=> ( B @ ( A @ is_reflexive_in ) ) )
& ( ( B @ ( A @ is_reflexive_in ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ ( C @ ordered_pair ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ proper_subset ) )
=> ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
thf(1690,plain,
! [A: $i] :
( ( A @ epsilon_transitive )
=> ! [B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ proper_subset ) )
=> ( B @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
<=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) ) )
& ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(377,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(990,plain,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(863,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( A @ ( B @ ordinal_subset ) )
| ( B @ ( A @ ordinal_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) )
& ( B @ relation_field @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
thf(2065,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) )
& ( B @ relation_field @ ( A @ ( B @ relation_restriction ) @ relation_field @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(1667,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(477,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)],[43]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(816,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(1630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) )
=> ( C @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( B
= ( A @ ( C @ apply ) ) )
& ( C @ relation_dom @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(483,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ ( C @ relation_dom_restriction ) @ apply ) )
= ( B @ ( C @ apply ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ connected )
=> ( A @ ( B @ relation_restriction ) @ connected ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
thf(943,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ connected )
=> ( A @ ( B @ relation_restriction ) @ connected ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ well_orders ) )
<=> ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
thf(330,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) )
=> ( B @ ( A @ well_orders ) ) )
& ( ( B @ ( A @ well_orders ) )
=> ( ( B @ ( A @ is_well_founded_in ) )
& ( B @ ( A @ is_connected_in ) )
& ( B @ ( A @ is_antisymmetric_in ) )
& ( B @ ( A @ is_transitive_in ) )
& ( B @ ( A @ is_reflexive_in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ reflexive )
=> ( A @ ( B @ relation_restriction ) @ reflexive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
thf(932,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ reflexive )
=> ( A @ ( B @ relation_restriction ) @ reflexive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(9,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(345,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(367,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(609,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)],[61]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( A @ ( B @ relation_inverse_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(2111,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( A @ ( B @ relation_inverse_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_field @ ( B @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(521,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( C @ relation_field @ ( B @ in ) )
& ( C @ relation_field @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(2075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_composition ) @ relation_rng @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(2171,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( B @ ( A @ relation_composition ) @ relation_rng @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(145,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(1213,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(201,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ relation_dom @ ( B @ in ) )
=> ( ( C
= ( B @ ( A @ apply ) ) )
<=> ( C = empty_set ) ) )
& ( ( A @ relation_dom @ ( B @ in ) )
=> ( ( C
= ( B @ ( A @ apply ) ) )
<=> ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(1643,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ relation_dom @ ( B @ in ) )
=> ( ( ( C = empty_set )
=> ( C
= ( B @ ( A @ apply ) ) ) )
& ( ( C
= ( B @ ( A @ apply ) ) )
=> ( C = empty_set ) ) ) )
& ( ( A @ relation_dom @ ( B @ in ) )
=> ( ( ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C
= ( B @ ( A @ apply ) ) ) )
& ( ( C
= ( B @ ( A @ apply ) ) )
=> ( A @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(177,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(1435,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ ( C @ relation_inverse_image ) @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ ( C @ relation_inverse_image ) @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(149,axiom,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(1250,plain,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(1496,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) )
=> ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_inverse_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( D @ ( A @ ordered_pair ) @ in ) )
& ( C @ relation_rng @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(1102,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(653,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)],[65]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(1805,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)],[226]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(2069,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
<=> ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(1413,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) )
=> ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) ) )
& ( ( A @ ( C @ relation_dom_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( A @ ( B @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(1809,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(204,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ proper_subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(1662,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(426,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(1203,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)],[144]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(795,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(663,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ( B @ relation_field @ ( A @ subset ) )
& ( B @ well_ordering ) )
=> ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_wellord1) ).
thf(2037,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ( B @ relation_field @ ( A @ subset ) )
& ( B @ well_ordering ) )
=> ( ( A @ ( B @ relation_restriction ) @ relation_field )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(257,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ subset ) )
=> ( D @ ( E @ in ) ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(1990,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ~ ( B @ ( C @ are_equipotent ) )
& ( B @ ( C @ subset ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ subset ) )
=> ( D @ ( E @ in ) ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ subset ) )
& ( B @ ( C @ in ) ) )
=> ( B @ ( D @ in ) ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(1181,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( C @ ( B @ relation_composition ) @ apply ) )
= ( A @ ( B @ apply ) @ ( C @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ ( C @ ( B @ relation_composition ) @ apply ) )
= ( A @ ( B @ apply ) @ ( C @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(776,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)],[83]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ being_limit_ordinal )
<=> ( A
= ( A @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(525,plain,
! [A: $i] :
( ( ( A
= ( A @ union ) )
=> ( A @ being_limit_ordinal ) )
& ( ( A @ being_limit_ordinal )
=> ( A
= ( A @ union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(72,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(707,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( B @ ( C @ fiber ) @ ( B @ ( A @ ( C @ relation_restriction ) @ fiber ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( B @ ( C @ fiber ) @ ( B @ ( A @ ( C @ relation_restriction ) @ fiber ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(297,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2175,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_ordering )
<=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
thf(409,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) )
=> ( A @ well_ordering ) )
& ( ( A @ well_ordering )
=> ( ( A @ well_founded_relation )
& ( A @ connected )
& ( A @ antisymmetric )
& ( A @ transitive )
& ( A @ reflexive ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(993,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(1770,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)],[224]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(1605,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)],[197]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(327,plain,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(248,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(1941,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ antisymmetric )
=> ( A @ ( B @ relation_restriction ) @ antisymmetric ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
thf(1252,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ antisymmetric )
=> ( A @ ( B @ relation_restriction ) @ antisymmetric ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(1186,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(121,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1038,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)],[121]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(2219,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(13,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(359,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(147,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(1220,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( C @ function_inverse @ ( A @ ( B @ relation_isomorphism ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_wellord1) ).
thf(470,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( C @ function_inverse @ ( A @ ( B @ relation_isomorphism ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(202,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(1658,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(158,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(1285,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(1218,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)],[146]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_rng @ ( A @ subset ) )
=> ( ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(2056,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_rng @ ( A @ subset ) )
=> ( ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ subset ) )
=> ( A @ ( B @ relation_image ) @ ( B @ relation_inverse_image ) @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(2113,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ relation_dom @ ( A @ subset ) )
=> ( A @ ( B @ relation_image ) @ ( B @ relation_inverse_image ) @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ union @ ordinal )
& ( A @ union @ epsilon_connected )
& ( A @ union @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
thf(1023,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ union @ ordinal )
& ( A @ union @ epsilon_connected )
& ( A @ union @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(727,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(207,axiom,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(1670,plain,
( ( empty_set @ ordinal )
& ( empty_set @ epsilon_connected )
& ( empty_set @ epsilon_transitive )
& ( empty_set @ empty )
& ( empty_set @ one_to_one )
& ( empty_set @ function )
& ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(37,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(446,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(876,plain,
! [A: $i] :
( ( A @ ordinal )
=> ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(1881,plain,
! [A: $i,B: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_dom_restriction ) @ function )
& ( B @ ( A @ relation_dom_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ~ ( ( ( B @ ( A @ complements_of_subsets ) )
= empty_set )
& ( B != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(1272,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)],[154]) ).
thf(173,axiom,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1421,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(53,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(539,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(308,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2215,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(1734,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(1108,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_dom_restriction ) @ relation_rng @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(2187,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_dom_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ antisymmetric )
<=> ( A @ relation_field @ ( A @ is_antisymmetric_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
thf(1189,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_antisymmetric_in ) )
=> ( A @ antisymmetric ) )
& ( ( A @ antisymmetric )
=> ( A @ relation_field @ ( A @ is_antisymmetric_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(1289,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(368,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(1385,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(290,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_rng @ ( A @ relation_dom @ subset ) )
=> ( ( A @ ( B @ relation_composition ) @ relation_rng )
= ( A @ relation_rng ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(2135,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ relation_rng @ ( A @ relation_dom @ subset ) )
=> ( ( A @ ( B @ relation_composition ) @ relation_rng )
= ( A @ relation_rng ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(2026,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_rng_restriction ) @ relation_rng )
= ( A @ ( B @ relation_rng @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(1558,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_rng_restriction ) @ relation_rng )
= ( A @ ( B @ relation_rng @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ( ( A @ ( B @ relation_inverse_image ) )
= empty_set )
& ( B @ relation_rng @ ( A @ subset ) )
& ( A != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2198,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ~ ( ( ( A @ ( B @ relation_inverse_image ) )
= empty_set )
& ( B @ relation_rng @ ( A @ subset ) )
& ( A != empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
<=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(1193,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) )
& ( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( B @ ( A @ ordinal_subset ) )
<=> ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(2183,plain,
! [A: $i,B: $i] :
( ( ( B @ ordinal )
& ( A @ ordinal ) )
=> ( ( ( B @ ( A @ subset ) )
=> ( B @ ( A @ ordinal_subset ) ) )
& ( ( B @ ( A @ ordinal_subset ) )
=> ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_composition ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(1607,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_composition ) ) ) )
& ( ( C
= ( B @ ( A @ relation_composition ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2095,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)],[280]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_composition ) @ relation_rng )
= ( A @ relation_rng @ ( B @ relation_image ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(1893,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ relation_composition ) @ relation_rng )
= ( A @ relation_rng @ ( B @ relation_image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
thf(716,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) )
=> ( A @ connected ) )
& ( ( A @ connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( A @ ( B @ ( C @ ordered_pair ) @ in ) )
& ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
& ( B != C )
& ( A @ relation_field @ ( C @ in ) )
& ( A @ relation_field @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
<=> ( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_wellord1) ).
thf(549,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) )
=> ( C @ ( B @ ( A @ relation_isomorphism ) ) ) )
& ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( C @ apply ) @ ( D @ ( C @ apply ) @ ordered_pair ) @ in ) )
& ( A @ relation_field @ ( E @ in ) )
& ( A @ relation_field @ ( D @ in ) ) ) ) )
& ( C @ one_to_one )
& ( ( C @ relation_rng )
= ( B @ relation_field ) )
& ( ( C @ relation_dom )
= ( A @ relation_field ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(1444,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ( ( B @ ( A @ in ) )
=> ( A @ ordinal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( B @ ( C @ relation_rng @ subset ) )
& ( A @ ( C @ relation_dom @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2102,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( B @ ( C @ relation_rng @ subset ) )
& ( A @ ( C @ relation_dom @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(867,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(865,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) @ relation_dom )
= ( A @ ( B @ relation_dom @ set_intersection2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(854,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_dom_restriction ) @ relation_dom )
= ( A @ ( B @ relation_dom @ set_intersection2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(256,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ordinal ) ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(1986,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ in ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ordinal ) ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(422,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(2050,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(2201,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)],[306]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(1561,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)],[193]) ).
thf(120,axiom,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(1033,plain,
? [A: $i] :
( ( A @ ordinal )
& ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(110,axiom,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(960,plain,
! [A: $i] :
( ( ( A @ epsilon_connected )
& ( A @ epsilon_transitive ) )
=> ( A @ ordinal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
<=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(2040,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ proper_subset ) ) )
& ( ( B @ ( A @ proper_subset ) )
=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(274,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( A @ relation_dom @ ( B @ ( A @ relation_composition ) @ relation_dom @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(2063,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( A @ relation_dom @ ( B @ ( A @ relation_composition ) @ relation_dom @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ well_founded_relation )
<=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
thf(928,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( ( A @ relation_field @ ( A @ is_well_founded_in ) )
=> ( A @ well_founded_relation ) )
& ( ( A @ well_founded_relation )
=> ( A @ relation_field @ ( A @ is_well_founded_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(1172,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)],[136]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(767,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)],[80]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
thf(395,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( B @ ( A @ relation_isomorphism ) ) )
=> ( ( ( A @ well_founded_relation )
=> ( B @ well_founded_relation ) )
& ( ( A @ antisymmetric )
=> ( B @ antisymmetric ) )
& ( ( A @ connected )
=> ( B @ connected ) )
& ( ( A @ transitive )
=> ( B @ transitive ) )
& ( ( A @ reflexive )
=> ( B @ reflexive ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(822,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)],[88]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(1431,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( B @ empty ) ) )
& ( ~ ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( A @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(1505,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)],[187]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ~ ( ! [C: $i] :
( ( C @ ordinal )
=> ~ ( ! [D: $i] :
( ( D @ ordinal )
=> ( ( A @ ( D @ in ) )
=> ( D @ ( C @ ordinal_subset ) ) ) )
& ( A @ ( C @ in ) ) ) )
& ( A != empty_set )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(2138,plain,
! [A: $i,B: $i] :
( ( B @ ordinal )
=> ~ ( ! [C: $i] :
( ( C @ ordinal )
=> ~ ( ! [D: $i] :
( ( D @ ordinal )
=> ( ( A @ ( D @ in ) )
=> ( D @ ( C @ ordinal_subset ) ) ) )
& ( A @ ( C @ in ) ) ) )
& ( A != empty_set )
& ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(5,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(322,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(486,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) )
=> ( A @ one_to_one ) )
& ( ( A @ one_to_one )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
thf(940,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(1962,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(1184,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(262,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ relation_rng @ ( A @ relation_rng @ subset ) )
& ( B @ relation_dom @ ( A @ relation_dom @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(2018,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ relation_rng @ ( A @ relation_rng @ subset ) )
& ( B @ relation_dom @ ( A @ relation_dom @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(284,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(2106,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(592,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)],[60]) ).
thf(15,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(364,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(2177,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(231,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(1848,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(181,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ in ) )
& ( B @ ( D @ in ) ) )
& ( B @ ( C @ in ) ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(1449,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)],[181]) ).
thf(228,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B
= ( A @ function_inverse ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(1812,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) )
=> ( B
= ( A @ function_inverse ) ) )
& ( ( B
= ( A @ function_inverse ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ identity_relation ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(496,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ identity_relation ) ) )
& ( ( B
= ( A @ identity_relation ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ epsilon_connected )
<=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(454,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( A @ epsilon_connected ) )
& ( ( A @ epsilon_connected )
=> ! [B: $i,C: $i] :
~ ( ~ ( B @ ( C @ in ) )
& ( B != C )
& ~ ( C @ ( B @ in ) )
& ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4021,plain,
$false,
inference(e,[status(thm)],[645,1665,760,1454,1105,1031,962,352,1315,518,2077,1924,2014,1728,449,2099,655,1971,1692,582,762,1142,379,1269,2195,385,533,1275,472,1327,1260,1919,945,2146,1063,340,404,417,1475,1254,1887,320,2173,1904,1518,1409,2217,934,1059,542,1760,1660,1922,1379,1247,1479,770,1568,2024,316,1319,870,1890,756,443,1418,966,480,1020,574,1377,1896,956,849,1169,687,1943,1201,452,1311,1736,1868,2061,1047,1730,952,349,1174,1502,693,429,2150,729,1423,1602,435,1951,665,1687,2179,2181,2213,1407,1910,2115,1762,1772,1953,1096,1878,356,1755,857,1350,1936,650,948,1683,1329,1028,537,642,2053,1842,2108,1446,1099,1974,1932,984,1852,1429,371,1525,921,1515,2189,888,311,1695,773,586,2121,1278,1135,2001,1764,1680,1595,375,819,1752,2016,958,1965,1520,545,1916,402,382,2029,787,1092,1090,1638,2148,391,1139,406,681,1282,2084,419,2097,362,1722,880,1690,1439,377,990,863,2065,1667,477,816,1630,483,943,330,932,345,367,609,2111,521,2075,2171,1213,1643,1435,2022,1250,1496,1102,653,1805,2069,1413,1809,1662,426,1203,795,663,2037,1990,1181,1845,776,525,707,2012,2175,409,993,712,1770,1605,327,1941,1252,1186,1038,2219,359,1220,470,1658,1285,1218,2056,2113,1023,727,1670,446,876,1881,1272,1421,539,2215,1734,1108,2187,1189,1289,368,1385,2135,2026,1558,2198,1193,2183,1607,2095,1893,716,549,1444,2102,867,865,854,1986,422,2050,2201,1561,1033,960,2040,2063,928,1172,767,395,822,1431,1505,2138,322,486,940,1962,1184,2018,2106,592,364,2177,1848,2059,1449,1812,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU264+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n006.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 09:01:27 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.95/1.32 % [INFO] Parsing done (342ms).
% 1.95/1.33 % [INFO] Running in sequential loop mode.
% 3.01/1.71 % [INFO] eprover registered as external prover.
% 3.01/1.72 % [INFO] Scanning for conjecture ...
% 3.20/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 330 axioms. Running axiom selection ...
% 3.37/2.03 % [INFO] Axiom selection finished. Selected 308 axioms (removed 22 axioms).
% 4.54/2.35 % [INFO] Problem is first-order (TPTP FOF).
% 4.54/2.38 % [INFO] Type checking passed.
% 4.54/2.39 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 25.89/6.95 % External prover 'e' found a proof!
% 25.89/6.95 % [INFO] Killing All external provers ...
% 25.89/6.95 % Time passed: 6411ms (effective reasoning time: 5615ms)
% 25.89/6.95 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 25.89/6.96 % Axioms used in derivation (308): d1_enumset1, redefinition_m2_relset_1, redefinition_r1_ordinal1, l3_wellord1, fc1_zfmisc_1, d1_tarski, t30_relat_1, t147_funct_1, d4_funct_1, t32_wellord1, t19_xboole_1, t99_relat_1, t17_xboole_1, t90_relat_1, t43_subset_1, t54_wellord1, d5_relat_1, d6_relat_2, l82_funct_1, idempotence_k3_xboole_0, d4_ordinal1, t1_boole, t39_wellord1, t3_xboole_1, l1_wellord1, l2_wellord1, fc1_xboole_0, dt_k2_subset_1, d5_tarski, fc4_relat_1, d12_relat_1, t44_relat_1, fc4_funct_1, t1_subset, t144_relat_1, fc4_subset_1, t22_funct_1, fc3_relat_1, d8_funct_1, t117_relat_1, t2_boole, t32_ordinal1, t47_relat_1, fc9_relat_1, l3_subset_1, t99_zfmisc_1, d1_wellord1, t47_setfam_1, fc1_funct_1, d9_funct_1, rc3_funct_1, t56_relat_1, t37_xboole_1, dt_m2_relset_1, cc1_relat_1, t21_ordinal1, redefinition_k6_setfam_1, commutativity_k3_xboole_0, t55_funct_1, t62_funct_1, d2_tarski, d4_subset_1, involutiveness_k3_subset_1, rc1_funct_1, fc2_xboole_0, d1_xboole_0, t64_relat_1, d6_ordinal1, l50_zfmisc_1, t23_funct_1, t34_funct_1, t118_zfmisc_1, d3_wellord1, t14_relset_1, rc3_relat_1, t6_boole, rc2_subset_1, dt_k6_subset_1, d1_relat_1, d13_relat_1, t46_zfmisc_1, t1_xboole_1, d9_relat_2, t31_ordinal1, t116_relat_1, cc2_ordinal1, commutativity_k2_xboole_0, fc3_subset_1, t5_subset, d4_relat_1, t4_xboole_0, d12_relat_2, existence_m1_relset_1, l25_zfmisc_1, t1_zfmisc_1, t17_wellord1, fc2_subset_1, d8_xboole_0, d5_wellord1, d1_ordinal1, rc4_funct_1, fc2_funct_1, t5_wellord1, t8_funct_1, t33_xboole_1, t166_relat_1, l32_xboole_1, t8_zfmisc_1, t23_wellord1, t2_tarski, t4_boole, t146_funct_1, d13_funct_1, dt_k4_relat_1, t4_subset, fc3_xboole_0, t178_relat_1, d2_xboole_0, dt_k2_funct_1, t20_wellord1, t19_wellord1, fc13_relat_1, d4_tarski, t18_wellord1, d16_relat_2, t9_zfmisc_1, t174_relat_1, redefinition_k5_setfam_1, involutiveness_k4_relat_1, cc1_ordinal1, t7_boole, t21_wellord1, cc1_funct_1, t23_ordinal1, t118_relat_1, d10_relat_1, t143_relat_1, d2_subset_1, t24_wellord1, t48_xboole_1, t3_ordinal1, l4_wellord1, fc1_subset_1, t33_zfmisc_1, fc5_funct_1, fc3_ordinal1, rc2_funct_1, t160_relat_1, d11_relat_1, connectedness_r1_ordinal1, t8_wellord1, fc10_relat_1, rc1_subset_1, cc3_ordinal1, t74_relat_1, rc3_ordinal1, t83_xboole_1, t45_relat_1, l28_zfmisc_1, t140_relat_1, d14_relat_1, d7_xboole_0, fc5_relat_1, cc2_funct_1, t46_setfam_1, d2_wellord1, l4_zfmisc_1, t3_subset, cc1_relset_1, t24_ordinal1, t33_ordinal1, t115_relat_1, existence_m1_subset_1, antisymmetry_r2_xboole_0, dt_k6_setfam_1, d2_zfmisc_1, fc11_relat_1, l3_zfmisc_1, commutativity_k2_tarski, d7_relat_1, rc1_ordinal1, t106_zfmisc_1, t25_wellord1, t145_funct_1, l71_subset_1, dt_k7_relat_1, l2_zfmisc_1, d8_relat_1, t42_ordinal1, t94_relat_1, t48_setfam_1, d4_wellord1, d5_subset_1, t92_zfmisc_1, t146_relat_1, t70_funct_1, t31_wellord1, d1_zfmisc_1, t69_enumset1, t41_ordinal1, d7_wellord1, existence_m2_relset_1, t38_zfmisc_1, l55_zfmisc_1, t10_ordinal1, dt_k8_relat_1, d8_setfam_1, t26_xboole_1, t63_xboole_1, t22_wellord1, rc2_relat_1, t72_funct_1, involutiveness_k7_setfam_1, t8_xboole_1, t37_relat_1, d3_tarski, t39_zfmisc_1, t119_zfmisc_1, rc1_relat_1, t60_relat_1, t54_funct_1, dt_k5_relat_1, reflexivity_r1_tarski, t28_xboole_1, d1_relset_1, t6_zfmisc_1, dt_k6_relat_1, reflexivity_r1_ordinal1, t2_xboole_1, fc6_relat_1, d12_funct_1, d3_ordinal1, t46_relat_1, rc2_ordinal1, d4_xboole_0, d14_relat_2, t35_funct_1, t36_xboole_1, t20_relat_1, dt_k5_setfam_1, t68_funct_1, t54_subset_1, dt_k7_setfam_1, t21_funct_1, dt_k2_wellord1, d1_relat_2, t136_zfmisc_1, fc1_relat_1, d6_wellord1, d6_relat_1, l23_zfmisc_1, t8_boole, rc1_xboole_0, fc3_funct_1, t16_wellord1, t12_xboole_1, d3_relat_1, fc7_relat_1, fc1_ordinal1, t49_wellord1, t86_relat_1, fc8_relat_1, t10_zfmisc_1, t2_subset, t37_zfmisc_1, fc2_relat_1, d2_ordinal1, fc12_relat_1, t65_relat_1, t21_relat_1, d1_setfam_1, symmetry_r1_xboole_0, idempotence_k2_xboole_0, t9_tarski, t145_relat_1, d10_xboole_0, t7_xboole_1, t50_subset_1, fc2_ordinal1, t7_tarski, t60_xboole_1, t57_funct_1, t3_boole, d5_funct_1, redefinition_k6_subset_1, t12_relset_1, d8_relat_2, t25_relat_1, d4_relat_2, t3_xboole_0, l29_wellord1, rc2_xboole_0, t45_xboole_1, fc4_ordinal1, t40_xboole_1, irreflexivity_r2_xboole_0, t53_wellord1, t65_zfmisc_1, d3_xboole_0, d2_relat_1, t39_xboole_1, t71_relat_1, t88_relat_1, t167_relat_1, dt_k3_subset_1, l1_zfmisc_1, t119_relat_1, antisymmetry_r2_hidden
% 25.89/6.96 % No. of inferences in proof: 620
% 25.89/6.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6411 ms resp. 5615 ms w/o parsing
% 26.78/7.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.78/7.13 % [INFO] Killing All external provers ...
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