%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU230+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 : n026.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 08:38:08 AM UTC 2026
% Result : Theorem 19.02s 11.57s
% Output : Refutation 20.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 235
% Syntax : Number of formulae : 472 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 1774 ( 403 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 5446 ( 176 ~; 22 |; 542 &;3968 @)
% ( 87 <=>; 651 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 2 con; 0-3 aty)
% Number of variables : 1167 ( 0 ^;1079 !; 88 ?;1167 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
thf(cast_to_subset_decl,type,
cast_to_subset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
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(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_inverse_image_decl,type,
relation_inverse_image: $i > $i > $i ).
thf(union_of_subsets_decl,type,
union_of_subsets: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(union_decl,type,
union: $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_restriction: $i > $i > $i ).
thf(meet_of_subsets_decl,type,
meet_of_subsets: $i > $i > $i ).
thf(complements_of_subsets_decl,type,
complements_of_subsets: $i > $i > $i ).
thf(relation_field_decl,type,
relation_field: $i > $i ).
thf(set_meet_decl,type,
set_meet: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(are_equipotent_decl,type,
are_equipotent: $i > $i > $o ).
thf(unordered_triple_decl,type,
unordered_triple: $i > $i > $i > $i ).
thf(231,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(1633,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)],[231]) ).
thf(66,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(479,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)],[66]) ).
thf(112,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(645,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(169,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(892,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)],[169]) ).
thf(185,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(1083,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)],[185]) ).
thf(62,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(468,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)],[62]) ).
thf(126,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(683,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(228,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(1618,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)],[228]) ).
thf(164,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(873,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(247,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(189,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(1142,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)],[189]) ).
thf(103,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(614,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_union2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(124,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(677,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(233,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(1671,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)],[233]) ).
thf(39,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(385,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(500,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(160,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(814,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)],[160]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(698,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(206,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(1354,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)],[206]) ).
thf(121,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(670,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)],[121]) ).
thf(217,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(1497,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)],[217]) ).
thf(235,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(1705,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)],[235]) ).
thf(156,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(782,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)],[156]) ).
thf(198,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(1228,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)],[198]) ).
thf(230,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(1623,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)],[230]) ).
thf(93,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(570,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)],[93]) ).
thf(212,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(1430,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)],[212]) ).
thf(201,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(1298,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)],[201]) ).
thf(36,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(372,plain,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(99,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(587,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(32,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(357,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(88,axiom,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(559,plain,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(638,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(219,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(1514,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)],[219]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(606,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)],[102]) ).
thf(47,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(416,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(55,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(448,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(216,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(1489,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)],[216]) ).
thf(100,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(591,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)],[100]) ).
thf(30,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(353,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(190,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(1169,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)],[190]) ).
thf(208,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(1377,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)],[208]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(265,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(602,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(176,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(981,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)],[176]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(766,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(452,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(37,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(380,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)],[37]) ).
thf(77,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(512,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)],[77]) ).
thf(80,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(529,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)],[80]) ).
thf(118,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(661,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(83,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(546,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(366,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(138,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(714,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)],[138]) ).
thf(209,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(1387,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)],[209]) ).
thf(89,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(561,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)],[89]) ).
thf(12,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(275,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(142,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(729,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)],[142]) ).
thf(45,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(407,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)],[45]) ).
thf(130,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(693,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(107,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(630,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(211,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(1423,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)],[211]) ).
thf(91,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(566,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_rng @ ( A @ relation_dom @ cartesian_product2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(166,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(879,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)],[166]) ).
thf(213,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(1457,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)],[213]) ).
thf(71,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(493,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(757,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)],[151]) ).
thf(85,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(551,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)],[85]) ).
thf(136,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(710,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(224,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(1573,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)],[224]) ).
thf(15,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(285,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,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(519,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)],[79]) ).
thf(114,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(650,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_dom @ ( A @ ( B @ relation_inverse_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(204,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(1328,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)],[204]) ).
thf(187,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1121,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)],[187]) ).
thf(141,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(725,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(40,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(388,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)],[40]) ).
thf(31,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(356,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(49,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(420,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(63,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(471,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)],[63]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(884,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(69,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(488,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(339,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)],[28]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(554,plain,
! [A: $i] :
( ( A @ relation )
=> ( A @ relation_inverse @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(65,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(476,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(175,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(970,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)],[175]) ).
thf(179,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(1016,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ in ) )
& ( C @ ( B @ in ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(193,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(1207,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)],[193]) ).
thf(105,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(622,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)],[105]) ).
thf(113,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(647,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)],[113]) ).
thf(133,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(701,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(116,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(654,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(503,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(205,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(1333,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)],[205]) ).
thf(1,conjecture,
! [A: $i] : ( A @ succ @ ( A @ in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( A @ succ @ ( A @ in ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(237,plain,
~ ! [A: $i] : ( A @ succ @ ( A @ in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(244,plain,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,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(398,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)],[43]) ).
thf(215,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(1466,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)],[215]) ).
thf(232,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(1663,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)],[232]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(906,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(174,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(965,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)],[174]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(425,plain,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(234,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(1698,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)],[234]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(1219,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)],[196]) ).
thf(13,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(279,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(94,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(573,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)],[94]) ).
thf(98,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(584,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)],[98]) ).
thf(161,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(819,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)],[161]) ).
thf(143,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(732,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_field )
= ( A @ relation_rng @ ( A @ relation_dom @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(1615,plain,
! [A: $i] :
( ( A @ succ )
= ( A @ singleton @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(155,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(772,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)],[155]) ).
thf(147,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(743,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)],[147]) ).
thf(96,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(577,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)],[96]) ).
thf(220,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(1535,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)],[220]) ).
thf(8,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(259,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)],[8]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(413,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_inverse @ relation_inverse )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(111,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(641,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(41,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(391,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)],[41]) ).
thf(38,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(382,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)],[38]) ).
thf(22,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(313,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)],[22]) ).
thf(182,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(1058,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)],[182]) ).
thf(157,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(804,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(214,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(1464,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)],[214]) ).
thf(200,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(1271,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)],[200]) ).
thf(207,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(1371,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)],[207]) ).
thf(194,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(1209,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)],[194]) ).
thf(125,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(681,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)],[125]) ).
thf(33,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(362,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)],[33]) ).
thf(145,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(737,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)],[145]) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(1571,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(509,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(434,plain,
! [A: $i] :
( ( A @ powerset @ union )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(104,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(616,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)],[104]) ).
thf(19,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(303,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)],[19]) ).
thf(159,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(811,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)],[159]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(323,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(67,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(483,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)],[67]) ).
thf(154,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(769,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)],[154]) ).
thf(191,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(1177,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(26,axiom,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(330,plain,
( ( ( empty_set @ relation_rng )
= empty_set )
& ( ( empty_set @ relation_dom )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,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(251,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)],[7]) ).
thf(203,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(1325,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(127,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(685,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)],[127]) ).
thf(58,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(455,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(299,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(199,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(1250,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)],[199]) ).
thf(10,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(267,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)],[10]) ).
thf(52,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(431,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(109,axiom,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(636,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(131,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(695,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(394,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_inverse @ relation )
& ( A @ relation_inverse @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(306,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,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(473,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(140,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(722,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(173,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(944,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)],[173]) ).
thf(84,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(548,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)],[84]) ).
thf(210,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(1420,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(148,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(749,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)],[148]) ).
thf(78,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(516,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(150,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(754,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(490,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(675,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(59,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(458,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(162,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(823,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)],[162]) ).
thf(137,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(712,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)],[137]) ).
thf(97,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(580,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)],[97]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(690,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(17,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(295,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)],[17]) ).
thf(14,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(282,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(197,axiom,
! [A: $i] :
~ ( A @ succ @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(1225,plain,
! [A: $i] :
~ ( A @ succ @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(327,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,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(310,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)],[21]) ).
thf(122,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(673,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,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(370,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ ( B @ relation_dom_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(163,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(840,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)],[163]) ).
thf(221,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(1538,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)],[221]) ).
thf(188,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(1130,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)],[188]) ).
thf(82,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(544,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)],[82]) ).
thf(27,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(336,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(134,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(703,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(117,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(656,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(1052,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)],[181]) ).
thf(186,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(1094,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)],[186]) ).
thf(177,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(1008,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)],[177]) ).
thf(165,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(876,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(56,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(450,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( B @ ( A @ relation_rng_restriction ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(192,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(1180,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)],[192]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(556,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(81,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(539,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(128,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(688,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(195,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(1216,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)],[195]) ).
thf(183,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(1062,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)],[183]) ).
thf(108,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(632,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)],[108]) ).
thf(44,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(401,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)],[44]) ).
thf(48,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(418,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(115,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(652,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)],[115]) ).
thf(29,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(351,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)],[29]) ).
thf(92,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(568,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)],[92]) ).
thf(120,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(667,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)],[120]) ).
thf(16,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(287,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)],[16]) ).
thf(152,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(763,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)],[152]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(272,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(149,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(752,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)],[149]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(23,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(315,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)],[23]) ).
thf(50,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(422,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(144,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(735,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ relation_rng @ ( A @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(90,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(564,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(75,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(506,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(158,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(807,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)],[158]) ).
thf(54,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(437,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)],[54]) ).
thf(119,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(664,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)],[119]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(1710,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(184,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(1065,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)],[184]) ).
thf(139,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(720,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)],[139]) ).
thf(226,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(1610,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)],[226]) ).
thf(168,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(886,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)],[168]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ proper_subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(239,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,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(242,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(106,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(624,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)],[106]) ).
thf(146,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(740,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(464,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(575,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(180,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(1019,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)],[180]) ).
thf(171,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(908,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)],[171]) ).
thf(229,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(1621,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)],[229]) ).
thf(225,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(1606,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)],[225]) ).
thf(68,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(486,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)],[68]) ).
thf(202,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(1320,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)],[202]) ).
thf(172,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(935,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)],[172]) ).
thf(222,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(1565,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)],[222]) ).
thf(72,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(496,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)],[72]) ).
thf(135,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(708,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)],[135]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1014,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(2470,plain,
$false,
inference(e,[status(thm)],[1633,479,645,892,1083,468,683,1618,873,247,1142,614,677,1671,385,500,814,698,1354,670,1497,1705,782,1228,1623,570,1430,1298,372,587,357,559,638,1514,606,416,448,1489,591,353,1169,1377,265,602,981,766,452,380,512,529,661,546,366,714,1387,561,275,729,407,693,630,1423,566,879,1457,493,757,551,710,1573,285,519,650,1328,1121,725,388,356,420,471,884,488,339,554,476,970,1016,1207,622,647,701,654,503,1333,237,244,398,1466,1663,906,965,425,1698,1219,279,573,584,819,732,1615,772,743,577,1535,259,413,641,391,382,313,1058,804,1464,1271,1371,1209,681,362,737,1571,509,434,616,303,811,323,483,769,1177,330,462,251,1325,685,455,299,1250,267,431,636,695,394,306,473,722,944,548,1420,749,516,754,490,675,458,823,712,580,690,295,282,1225,327,310,673,370,840,1538,1130,544,336,703,656,1052,1094,1008,876,450,1180,556,539,688,1216,1062,632,401,418,652,351,568,667,287,763,272,752,1512,315,422,735,564,506,807,437,664,1710,1065,720,1610,886,239,242,624,740,464,575,1019,908,1621,1606,486,1320,935,1565,496,708,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.21/5.49 % Computer : n026.cluster.edu
% 0.21/5.49 % Model : x86_64 x86_64
% 0.21/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.49 % Memory : 8046.5625MB
% 0.21/5.49 % OS : Linux 6.8.0-71-generic
% 0.21/5.49 % CPULimit : 300
% 0.21/5.49 % WCLimit : 300
% 0.21/5.49 % DateTime : Sat Sep 26 08:58:01 UTC 2026
% 0.21/5.49 % CPUTime :
% 0.21/5.49 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
% 1.42/6.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.76/6.87 % [INFO] Parsing done (504ms).
% 2.76/6.89 % [INFO] Running in sequential loop mode.
% 4.07/7.50 % [INFO] eprover registered as external prover.
% 4.30/7.51 % [INFO] Scanning for conjecture ...
% 4.69/7.72 % [INFO] Found a conjecture (or negated_conjecture) and 254 axioms. Running axiom selection ...
% 5.19/7.94 % [INFO] Axiom selection finished. Selected 234 axioms (removed 20 axioms).
% 6.42/8.31 % [INFO] Problem is first-order (TPTP FOF).
% 6.42/8.35 % [INFO] Type checking passed.
% 6.42/8.36 % [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 ...
% 19.02/11.56 % External prover 'e' found a proof!
% 19.02/11.56 % [INFO] Killing All external provers ...
% 19.02/11.56 % Time passed: 5857ms (effective reasoning time: 4664ms)
% 19.02/11.56 % 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)>
% 19.02/11.57 % Axioms used in derivation (234): d1_enumset1, t43_subset_1, fc1_zfmisc_1, d1_tarski, t30_relat_1, t147_funct_1, d4_funct_1, t19_xboole_1, t99_relat_1, t17_xboole_1, t90_relat_1, d5_relat_1, l82_funct_1, idempotence_k3_xboole_0, t1_boole, t3_xboole_1, 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, d8_funct_1, t117_relat_1, t2_boole, t47_relat_1, fc9_relat_1, l3_subset_1, t99_zfmisc_1, t47_setfam_1, fc1_funct_1, d9_funct_1, rc3_funct_1, t56_relat_1, t37_xboole_1, cc1_relat_1, 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, l50_zfmisc_1, t23_funct_1, t34_funct_1, t118_zfmisc_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, t116_relat_1, commutativity_k2_xboole_0, fc3_subset_1, t5_subset, d4_relat_1, t4_xboole_0, l25_zfmisc_1, t1_zfmisc_1, fc2_subset_1, d8_xboole_0, d1_ordinal1, rc4_funct_1, fc2_funct_1, t8_funct_1, t2_tarski, t33_xboole_1, t166_relat_1, l32_xboole_1, t8_zfmisc_1, fc13_relat_1, 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, d4_tarski, t9_zfmisc_1, t174_relat_1, redefinition_k5_setfam_1, involutiveness_k4_relat_1, t7_boole, cc1_funct_1, t118_relat_1, d10_relat_1, t143_relat_1, d2_subset_1, t48_xboole_1, t3_ordinal1, fc1_subset_1, t33_zfmisc_1, rc2_funct_1, t160_relat_1, d11_relat_1, t74_relat_1, fc10_relat_1, rc1_subset_1, 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, l4_zfmisc_1, t3_subset, t115_relat_1, existence_m1_subset_1, d7_relat_1, antisymmetry_r2_xboole_0, dt_k6_setfam_1, d2_zfmisc_1, fc11_relat_1, l3_zfmisc_1, commutativity_k2_tarski, t106_zfmisc_1, d8_relat_1, t145_funct_1, l71_subset_1, d5_subset_1, dt_k7_relat_1, l2_zfmisc_1, t94_relat_1, t48_setfam_1, t92_zfmisc_1, t146_relat_1, t70_funct_1, d1_zfmisc_1, t69_enumset1, rc2_relat_1, t38_zfmisc_1, l55_zfmisc_1, dt_k8_relat_1, d8_setfam_1, t26_xboole_1, t63_xboole_1, t72_funct_1, involutiveness_k7_setfam_1, t8_xboole_1, t37_relat_1, t28_xboole_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, t6_zfmisc_1, dt_k6_relat_1, t2_xboole_1, d12_funct_1, fc6_relat_1, t46_relat_1, d4_xboole_0, 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, t136_zfmisc_1, fc1_relat_1, d6_relat_1, fc3_funct_1, l23_zfmisc_1, t8_boole, rc1_xboole_0, t12_xboole_1, d3_relat_1, fc7_relat_1, fc1_ordinal1, t86_relat_1, fc8_relat_1, t10_zfmisc_1, t2_subset, t37_zfmisc_1, fc2_relat_1, 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, t50_subset_1, d10_xboole_0, t7_xboole_1, t7_tarski, t60_xboole_1, t57_funct_1, t3_xboole_0, t3_boole, d5_funct_1, redefinition_k6_subset_1, t25_relat_1, rc2_xboole_0, t45_xboole_1, t40_xboole_1, irreflexivity_r2_xboole_0, 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
% 19.02/11.57 % No. of inferences in proof: 472
% 19.02/11.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5857 ms resp. 4664 ms w/o parsing
% 20.92/11.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.92/11.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------