%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL949_4 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 07:53:26 AM UTC 2026
% Result : Theorem 20.12s 5.46s
% Output : Refutation 20.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 99
% Syntax : Number of formulae : 288 ( 37 unt; 0 typ; 11 def)
% Number of atoms : 2494 ( 74 equ; 0 cnn)
% Maximal formula atoms : 100 ( 8 avg)
% Number of connectives : 8837 ( 359 ~; 297 |; 169 &;6363 @)
% ( 0 <=>;1649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 15 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 13 con; 0-9 aty)
% Number of variables : 1697 ( 36 ^;1638 !; 12 ?;1697 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(universal_class_decl,type,
universal_class: $i ).
thf(identity_relation_decl,type,
identity_relation: $i ).
thf(successor_relation_decl,type,
successor_relation: $i ).
thf(element_relation_decl,type,
element_relation: $i ).
thf(null_class_decl,type,
null_class: $i ).
thf(qmltpeq_decl,type,
qmltpeq: '$ki_world' > $i > $i > $o ).
thf(inductive_decl,type,
inductive: '$ki_world' > $i > $o ).
thf(disjoint_decl,type,
disjoint: '$ki_world' > $i > $i > $o ).
thf(function_decl,type,
function: '$ki_world' > $i > $o ).
thf(member_decl,type,
member: '$ki_world' > $i > $i > $o ).
thf(subclass_decl,type,
subclass: '$ki_world' > $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(rotate_decl,type,
rotate: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(power_class_decl,type,
power_class: $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(restrict_decl,type,
restrict: $i > $i > $i > $i ).
thf(second_decl,type,
second: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(sum_class_decl,type,
sum_class: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(flip_decl,type,
flip: $i > $i ).
thf(first_decl,type,
first: $i > $i ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(sk1_decl,type,
sk1: '$ki_world' ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: '$ki_world' ).
thf(sk4_decl,type,
sk4: '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk5_decl,type,
sk5: '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk6_decl,type,
sk6: '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk33_decl,type,
sk33: '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk112_decl,type,
sk112: $i ).
thf(sk113_decl,type,
sk113: '$ki_world' > $i > '$ki_world' > '$ki_world' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: '$ki_world'] :
~ ( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subclass ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) )
=> ! [B: '$ki_world'] :
( ( B @ ( sk1 @ '$ki_accessible' ) )
=> ( A @ ( A @ ( B @ subclass ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: '$ki_world'] :
~ ( ( A @ ( sk1 @ '$ki_accessible' ) )
=> ( sk2 @ ( sk2 @ ( A @ subclass ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world',D: $i,E: '$ki_world',F: $i,G: '$ki_world',H: $i,I: '$ki_world'] :
@+[J: '$ki_world'] :
~ ( ( J @ ( A @ '$ki_accessible' ) )
=> ( B @ ( D @ cross_product ) @ ( F @ ( H @ ordered_pair ) @ ( J @ member ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world',D: $i,E: '$ki_world',F: $i,G: '$ki_world',H: $i,I: '$ki_world'] :
@+[J: '$ki_world'] :
~ ( ( J @ ( A @ '$ki_accessible' ) )
=> ( D @ ( H @ ( J @ member ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world',D: $i,E: '$ki_world',F: $i,G: '$ki_world',H: $i,I: '$ki_world'] :
@+[J: '$ki_world'] :
~ ( ( J @ ( A @ '$ki_accessible' ) )
=> ( B @ ( F @ ( J @ member ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( universal_class @ ( C @ ( E @ member ) ) ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( C @ ( A @ apply ) @ ( E @ member ) ) ) )
| ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( null_class @ ( C @ ( E @ qmltpeq ) ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ function ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world'] :
@+[D: '$ki_world'] :
~ ( ( D @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ member ) ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world'] :
@+[D: '$ki_world'] :
~ ( ( D @ ( A @ '$ki_accessible' ) )
=> ( null_class @ ( B @ ( D @ member ) ) ) ) ) ) ).
thf(sk112_def,definition,
( sk112
= ( @+[A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( E @ inductive ) ) )
=> ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( A @ ( E @ subclass ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ inductive ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( A @ ( B @ member ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ) ) ) ).
thf(sk113_def,definition,
( sk113
= ( ^ [A: '$ki_world',B: $i,C: '$ki_world'] :
@+[D: '$ki_world'] :
~ ( ( D @ ( A @ '$ki_accessible' ) )
=> ( B @ ( D @ inductive ) ) ) ) ) ).
thf(41,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ apply ) @ ( F @ ( B @ apply ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_1) ).
thf(352,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ apply ) @ ( F @ ( B @ apply ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(54,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( B @ unordered_pair ) @ ( E @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_0) ).
thf(404,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( B @ unordered_pair ) @ ( E @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(12,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ~ ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ~ ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
thf(158,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ~ ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ~ ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subclass ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subclass ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ subclass ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(91,plain,
( ~ ( sk2 @ ( sk2 @ ( sk3 @ subclass ) ) )
& ( sk3 @ ( sk1 @ '$ki_accessible' ) )
& ( sk2 @ ( sk1 @ '$ki_exists_in_world_$i' ) )
& ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
sk1 @ ( '$ki_local_world' @ '$ki_accessible' ),
inference(cnfConj,[status(thm)],[91]) ).
thf(75,axiom,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( E @ inductive ) ) )
=> ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( A @ ( E @ subclass ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ inductive ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( A @ ( B @ member ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
thf(547,plain,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( E @ inductive ) ) )
=> ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( A @ ( E @ subclass ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ inductive ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( A @ ( B @ member ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(548,plain,
! [F: '$ki_world',E: '$ki_world',D: $i,C: '$ki_world',B: '$ki_world',A: '$ki_world'] :
( ( ( D @ ( sk112 @ ( F @ subclass ) ) )
| ~ ( F @ ( E @ '$ki_accessible' ) )
| ~ ( D @ ( C @ ( D @ ( E @ sk113 ) ) @ inductive ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( D @ ( sk112 @ ( F @ subclass ) ) )
| ~ ( F @ ( E @ '$ki_accessible' ) )
| ( C @ ( D @ ( E @ sk113 ) ) @ ( E @ '$ki_accessible' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( sk112 @ ( B @ inductive ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( universal_class @ ( sk112 @ ( A @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( sk112 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(cnf,[status(esa)],[547]) ).
thf(553,plain,
! [A: '$ki_world'] :
( ( universal_class @ ( sk112 @ ( A @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[548]) ).
thf(975,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( universal_class @ ( sk112 @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,553]) ).
thf(976,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( universal_class @ ( sk112 @ ( A @ member ) ) ) ),
inference(simp,[status(thm)],[975]) ).
thf(977,plain,
universal_class @ ( sk112 @ ( sk1 @ member ) ),
inference(pattern_uni,[status(thm)],[976:[bind(A,$thf( sk1 ))]]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ disjoint ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ disjoint ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_2) ).
thf(120,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ disjoint ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ disjoint ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(202,plain,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(72,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ union ) @ ( B @ ( F @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(523,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ union ) @ ( B @ ( F @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(10,axiom,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( universal_class @ ( C @ ( E @ member ) ) ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( C @ ( A @ apply ) @ ( E @ member ) ) ) )
| ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( null_class @ ( C @ ( E @ qmltpeq ) ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ function ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
thf(134,plain,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$ki_exists_in_world_$i' ) )
=> ! [D: '$ki_world'] :
( ( D @ ( B @ '$ki_accessible' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( universal_class @ ( C @ ( E @ member ) ) ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( C @ ( C @ ( A @ apply ) @ ( E @ member ) ) ) )
| ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( null_class @ ( C @ ( E @ qmltpeq ) ) ) ) ) ) ) ) )
& ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ function ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(135,plain,
! [F: '$ki_world',E: '$ki_world',D: '$ki_world',C: $i,B: '$ki_world',A: '$ki_world'] :
( ( ( C @ ( C @ ( sk12 @ apply ) @ ( F @ member ) ) )
| ~ ( F @ ( D @ '$ki_accessible' ) )
| ( null_class @ ( C @ ( E @ qmltpeq ) ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ~ ( universal_class @ ( C @ ( B @ ( C @ ( D @ sk13 ) ) @ member ) ) )
| ~ ( D @ ( B @ '$ki_accessible' ) )
| ~ ( C @ ( B @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( C @ ( C @ ( sk12 @ apply ) @ ( F @ member ) ) )
| ~ ( F @ ( D @ '$ki_accessible' ) )
| ( null_class @ ( C @ ( E @ qmltpeq ) ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ( B @ ( C @ ( D @ sk13 ) ) @ ( D @ '$ki_accessible' ) )
| ~ ( D @ ( B @ '$ki_accessible' ) )
| ~ ( C @ ( B @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( sk12 @ ( A @ function ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( sk12 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(137,plain,
! [A: '$ki_world'] :
( ( sk12 @ ( A @ function ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[135]) ).
thf(760,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( A @ function ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,137]) ).
thf(761,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( A @ function ) ) ),
inference(simp,[status(thm)],[760]) ).
thf(762,plain,
sk12 @ ( sk1 @ function ),
inference(pattern_uni,[status(thm)],[761:[bind(A,$thf( sk1 ))]]) ).
thf(47,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ inverse @ domain_of @ ( B @ range_of @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
thf(384,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ inverse @ domain_of @ ( B @ range_of @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(11,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( B @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ flip @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ flip @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( B @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_defn) ).
thf(142,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( B @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ flip @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ flip @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( B @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( F @ ( D @ ( B @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( F @ ( B @ unordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(184,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( F @ ( B @ unordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,plain,
sk3 @ ( sk1 @ '$ki_accessible' ),
inference(cnfConj,[status(thm)],[91]) ).
thf(93,plain,
sk2 @ ( sk1 @ '$ki_exists_in_world_$i' ),
inference(cnfConj,[status(thm)],[91]) ).
thf(21,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ~ ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( null_class @ ( B @ ( D @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
thf(210,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ~ ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( null_class @ ( B @ ( D @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(211,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( A @ ( B @ ( C @ sk33 ) ) @ ( C @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[210]) ).
thf(213,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[211]) ).
thf(668,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk2 @ ( sk1 @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[93,213]) ).
thf(669,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk2 @ ( sk1 @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[668]) ).
thf(670,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(691,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(696,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[691,92]) ).
thf(697,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[696]) ).
thf(700,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,697]) ).
thf(701,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[700]) ).
thf(702,plain,
~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[701:[bind(A,$thf( sk3 ))]]) ).
thf(77,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( null_class @ ( universal_class @ ( D @ singleton @ ( B @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ domain_of @ ( D @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ domain_of @ ( D @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( null_class @ ( universal_class @ ( D @ singleton @ ( B @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_0) ).
thf(559,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( null_class @ ( universal_class @ ( D @ singleton @ ( B @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ domain_of @ ( D @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ domain_of @ ( D @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( null_class @ ( universal_class @ ( D @ singleton @ ( B @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(84,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ flip @ ( C @ subclass ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_0) ).
thf(638,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ flip @ ( C @ subclass ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(61,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ cross_product ) @ ( F @ ( B @ cross_product ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_1) ).
thf(453,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ cross_product ) @ ( F @ ( B @ cross_product ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ intersection ) @ ( B @ ( F @ intersection ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(116,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ intersection ) @ ( B @ ( F @ intersection ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ image ) @ ( B @ ( F @ image ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_2) ).
thf(527,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ image ) @ ( B @ ( F @ image ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(46,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ first @ ( B @ first @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_substitution_1) ).
thf(380,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ first @ ( B @ first @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(33,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ? [F: $i] :
( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ ( G @ member ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ ( G @ member ) ) ) )
& ( F @ ( E @ '$ki_exists_in_world_$i' ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ ( F @ member ) ) ) )
=> ? [F: $i] :
( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ ( G @ member ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ ( G @ member ) ) ) )
& ( F @ ( E @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).
thf(270,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ? [F: $i] :
( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ ( G @ member ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ ( G @ member ) ) ) )
& ( F @ ( E @ '$ki_exists_in_world_$i' ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ ( F @ member ) ) ) )
=> ? [F: $i] :
( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ ( G @ member ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ ( G @ member ) ) ) )
& ( F @ ( E @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(550,plain,
sk112 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ),
inference(cnfConj,[status(thm)],[548]) ).
thf(692,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk112 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[550,213]) ).
thf(693,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk112 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(694,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ ( '$ki_local_world' @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( sk112 ))]]) ).
thf(695,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ ( '$ki_local_world' @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[694]) ).
thf(76,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(557,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(558,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(cnf,[status(esa)],[557]) ).
thf(821,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[695,558]) ).
thf(822,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[821]) ).
thf(823,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,822]) ).
thf(824,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[823]) ).
thf(825,plain,
~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[824:[bind(A,$thf( sk1 ))]]) ).
thf(30,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ unordered_pair ) @ ( B @ ( F @ unordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(260,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ unordered_pair ) @ ( B @ ( F @ unordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ image ) @ sum_class @ ( D @ ( B @ apply ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
thf(392,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ image ) @ sum_class @ ( D @ ( B @ apply ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(192,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(59,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ intersection ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ intersection ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_0) ).
thf(435,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ intersection ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ intersection ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(828,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( B @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,822]) ).
thf(829,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( B @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[828]) ).
thf(830,plain,
~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( '$ki_local_world' @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(551,plain,
! [A: '$ki_world'] :
( ( sk112 @ ( A @ inductive ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[548]) ).
thf(554,plain,
! [A: '$ki_world'] :
( ( sk112 @ ( A @ inductive ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(836,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( A @ inductive ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,554]) ).
thf(837,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( A @ inductive ) ) ),
inference(simp,[status(thm)],[836]) ).
thf(841,plain,
! [A: '$ki_world'] :
( ( sk3 != A )
| ( sk1 != '$ki_local_world' )
| ( sk112 @ ( A @ inductive ) ) ),
inference(simp,[status(thm)],[837]) ).
thf(842,plain,
( ( sk1 != '$ki_local_world' )
| ( sk112 @ ( sk3 @ inductive ) ) ),
inference(simp,[status(thm)],[841]) ).
thf(24,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( successor_relation @ ( A @ subclass ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(224,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( successor_relation @ ( A @ subclass ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(71,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ cross_product ) @ ( B @ ( F @ cross_product ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_2) ).
thf(519,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ cross_product ) @ ( B @ ( F @ cross_product ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(16,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ image ) @ ( F @ ( B @ image ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_1) ).
thf(188,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ image ) @ ( F @ ( B @ image ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ member ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ sum_class @ ( D @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_0) ).
thf(388,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ member ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ sum_class @ ( D @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( C @ subclass ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(356,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( C @ subclass ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ power_class @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_substitution_1) ).
thf(256,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ power_class @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(973,plain,
! [A: '$ki_world'] :
( ( ( universal_class @ ( sk112 @ ( A @ member ) ) )
!= ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ member ) ) ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[553,825]) ).
thf(974,plain,
! [A: '$ki_world'] :
( ( ( universal_class @ ( sk112 @ ( A @ member ) ) )
!= ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ member ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[973]) ).
thf(996,plain,
! [A: '$ki_world'] :
( ( null_class != universal_class )
| ( sk112 != sk112 )
| ( A
!= ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[974]) ).
thf(1009,plain,
( ( null_class != universal_class )
| ~ ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[996]) ).
thf(1021,plain,
( ( ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( null_class != universal_class )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,1009]) ).
thf(1022,plain,
( ( ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1026,plain,
( ( ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) )
!= sk1 )
| ( '$ki_local_world' != '$ki_local_world' )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1028,plain,
( ( ( '$ki_local_world' @ ( sk112 @ ( sk1 @ sk33 ) ) )
!= sk1 )
| ( null_class != universal_class ) ),
inference(simp,[status(thm)],[1026]) ).
thf(86,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(642,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ union ) @ ( F @ ( H @ member ) ) ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(3,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ unordered_pair ) @ ( B @ singleton @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(96,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ unordered_pair ) @ ( B @ singleton @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( B @ ( successor_relation @ image ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( null_class @ ( D @ member ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ inductive ) ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ inductive ) ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( B @ ( successor_relation @ image ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( null_class @ ( D @ member ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
thf(622,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( B @ ( successor_relation @ image ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( null_class @ ( D @ member ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ inductive ) ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ inductive ) ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( B @ ( successor_relation @ image ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( null_class @ ( D @ member ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(87,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ intersection ) @ ( F @ ( B @ intersection ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(654,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ intersection ) @ ( F @ ( B @ intersection ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(62,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ function ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ function ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_substitution_1) ).
thf(457,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ function ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ function ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(763,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( B @ function ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,137]) ).
thf(764,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( B @ function ) ) ),
inference(simp,[status(thm)],[763]) ).
thf(765,plain,
sk12 @ ( '$ki_local_world' @ function ),
inference(pattern_uni,[status(thm)],[764:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(52,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) @ ( D @ ( B @ ordered_pair ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(398,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) @ ( D @ ( B @ ordered_pair ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ rotate @ ( C @ subclass ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_0) ).
thf(412,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( B @ rotate @ ( C @ subclass ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(82,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ member ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ power_class @ ( D @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_0) ).
thf(618,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ member ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ power_class @ ( D @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(31,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(264,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(743,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( B @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,697]) ).
thf(744,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( sk1 @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( B @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[743]) ).
thf(745,plain,
~ ( null_class @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[744:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(14,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( D @ restrict ) ) @ ( H @ ( F @ ( B @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_1) ).
thf(180,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ ( D @ restrict ) ) @ ( H @ ( F @ ( B @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( H @ ( F @ restrict ) ) @ ( B @ ( H @ ( F @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_3) ).
thf(176,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( H @ ( F @ restrict ) ) @ ( B @ ( H @ ( F @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ complement @ ( B @ complement @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_substitution_1) ).
thf(286,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ complement @ ( B @ complement @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(204,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ qmltpeq ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(70,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ successor @ ( F @ qmltpeq ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( successor_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( successor_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ successor @ ( F @ qmltpeq ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(498,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ successor @ ( F @ qmltpeq ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( successor_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( successor_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ successor @ ( F @ qmltpeq ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(27,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ordered_pair ) @ ( F @ ( B @ ordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_1) ).
thf(236,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ordered_pair ) @ ( F @ ( B @ ordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(350,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ ( B @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(55,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(406,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ member ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(44,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( element_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( element_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).
thf(362,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( element_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( element_relation @ ( D @ ( B @ ordered_pair ) @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ member ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(451,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ compose ) @ ( E @ subclass ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
thf(98,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ compose ) @ ( E @ subclass ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(81,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ restrict ) ) @ range_of @ ( B @ ( D @ image ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
thf(616,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ restrict ) ) @ range_of @ ( B @ ( D @ image ) @ ( E @ qmltpeq ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(67,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ function ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ image ) @ ( F @ member ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(477,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ function ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( D @ image ) @ ( F @ member ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(79,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ disjoint ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ disjoint ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_1) ).
thf(594,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ disjoint ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ disjoint ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(68,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( F @ restrict ) ) @ ( H @ ( B @ ( F @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_2) ).
thf(483,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( D @ ( B @ ( J @ qmltpeq ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( F @ restrict ) ) @ ( H @ ( B @ ( F @ restrict ) ) @ ( J @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(28,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ singleton @ ( D @ image ) @ ( D @ image ) @ ( H @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( F @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ compose ) @ ( H @ ( F @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ compose ) @ ( H @ ( F @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ singleton @ ( D @ image ) @ ( D @ image ) @ ( H @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( F @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).
thf(240,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ singleton @ ( D @ image ) @ ( D @ image ) @ ( H @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( F @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ compose ) @ ( H @ ( F @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ compose ) @ ( H @ ( F @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ singleton @ ( D @ image ) @ ( D @ image ) @ ( H @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( F @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(766,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( A @ function ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,137]) ).
thf(767,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk12 @ ( A @ function ) ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
! [A: '$ki_world'] :
( ( sk3 != A )
| ( sk1 != '$ki_local_world' )
| ( sk12 @ ( A @ function ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
( ( sk1 != '$ki_local_world' )
| ( sk12 @ ( sk3 @ function ) ) ),
inference(simp,[status(thm)],[768]) ).
thf(18,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ sum_class @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_substitution_1) ).
thf(198,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ sum_class @ ( B @ sum_class @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ apply ) @ ( B @ ( F @ apply ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_2) ).
thf(130,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ apply ) @ ( B @ ( F @ apply ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ inductive ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ inductive ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_substitution_1) ).
thf(226,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ inductive ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( F @ inductive ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ range_of @ ( B @ range_of @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_substitution_1) ).
thf(431,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ range_of @ ( B @ range_of @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(88,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ subclass ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_2) ).
thf(658,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( B @ ( F @ ( H @ subclass ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ( H @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(51,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ union ) @ ( F @ ( B @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(394,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ union ) @ ( F @ ( B @ union ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(36,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
thf(306,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ power_class @ ( B @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(66,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ rotate @ ( B @ rotate @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_substitution_1) ).
thf(473,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ rotate @ ( B @ rotate @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(74,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( identity_relation @ ( B @ inverse @ ( B @ compose ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ subclass ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ function ) ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ function ) ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( identity_relation @ ( B @ inverse @ ( B @ compose ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ subclass ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).
thf(531,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( identity_relation @ ( B @ inverse @ ( B @ compose ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ subclass ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ function ) ) ) ) )
& ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ function ) ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( identity_relation @ ( B @ inverse @ ( B @ compose ) @ ( D @ subclass ) ) ) )
& ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ subclass ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(69,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ~ ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( null_class @ ( B @ ( E @ qmltpeq ) ) ) ) )
=> ? [D: $i] :
( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ ( E @ disjoint ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ ( E @ member ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( E @ member ) ) ) )
& ( D @ ( C @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
thf(487,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ! [D: '$ki_world'] :
( ( D @ ( C @ '$ki_accessible' ) )
=> ~ ! [E: '$ki_world'] :
( ( E @ ( D @ '$ki_accessible' ) )
=> ( null_class @ ( B @ ( E @ qmltpeq ) ) ) ) )
=> ? [D: $i] :
( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ ( E @ disjoint ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( B @ ( D @ ( E @ member ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( E @ member ) ) ) )
& ( D @ ( C @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(136,plain,
sk12 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ),
inference(cnfConj,[status(thm)],[135]) ).
thf(677,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk12 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[136,213]) ).
thf(678,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( sk12 @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
!= ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
| ~ ( null_class @ ( B @ ( A @ ( B @ ( C @ sk33 ) ) @ member ) ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ ( '$ki_local_world' @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( sk12 ))]]) ).
thf(688,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ ( '$ki_local_world' @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(748,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[688,558]) ).
thf(749,plain,
! [A: '$ki_world'] :
( ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[748]) ).
thf(38,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ cross_product ) @ ( F @ ( H @ member ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ second @ ( F @ first @ ordered_pair ) @ ( F @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_0) ).
thf(342,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ cross_product ) @ ( F @ ( H @ member ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ second @ ( F @ first @ ordered_pair ) @ ( F @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ cross_product ) @ ( D @ intersection ) @ ( F @ ( B @ ( D @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
thf(640,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( F @ ( B @ cross_product ) @ ( D @ intersection ) @ ( F @ ( B @ ( D @ restrict ) ) @ ( G @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(57,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ member ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ complement @ ( D @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ complement @ ( D @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ member ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_0) ).
thf(414,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ member ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ complement @ ( D @ ( F @ member ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ complement @ ( D @ ( F @ member ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ member ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( universal_class @ ( D @ ( F @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(95,plain,
~ ( sk2 @ ( sk2 @ ( sk3 @ subclass ) ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(838,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( B @ inductive ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,554]) ).
thf(839,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( B @ inductive ) ) ),
inference(simp,[status(thm)],[838]) ).
thf(840,plain,
sk112 @ ( '$ki_local_world' @ inductive ),
inference(pattern_uni,[status(thm)],[839:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(63,axiom,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(463,plain,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(78,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
thf(576,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ! [H: '$ki_world'] :
( ( H @ ( F @ '$ki_accessible' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( B @ ( G @ ( I @ member ) ) ) )
=> ! [I: '$ki_world'] :
( ( I @ ( H @ '$ki_accessible' ) )
=> ( D @ ( G @ ( I @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(80,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ ( H @ ( F @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ rotate @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ rotate @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ ( H @ ( F @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_defn) ).
thf(600,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ ( H @ ( F @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ rotate @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ rotate @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( B @ ( D @ ( H @ ( F @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ ( universal_class @ cross_product ) @ cross_product ) @ ( H @ ( F @ ( D @ ordered_pair ) @ ordered_pair ) @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(48,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ singleton @ ( B @ union ) @ ( B @ successor @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).
thf(386,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( B @ singleton @ ( B @ union ) @ ( B @ successor @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(64,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ domain_of @ ( B @ domain_of @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_substitution_1) ).
thf(465,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ domain_of @ ( B @ domain_of @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(756,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,749]) ).
thf(757,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[756]) ).
thf(758,plain,
! [A: '$ki_world'] :
( ( sk3 != A )
| ( sk1 != '$ki_local_world' )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( sk3 @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[758]) ).
thf(23,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ subclass ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_1) ).
thf(218,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ subclass ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ ( H @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ ( B @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ ( B @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
thf(100,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ! [H: $i] :
( ( H @ ( G @ '$ki_exists_in_world_$i' ) )
=> ( ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ ( B @ ( J @ member ) ) ) ) )
=> ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( J @ member ) ) ) ) ) )
& ! [I: '$ki_world'] :
( ( I @ ( G @ '$ki_accessible' ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( J @ member ) ) ) )
=> ( ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( H @ ( D @ ( J @ member ) ) ) )
& ! [J: '$ki_world'] :
( ( J @ ( I @ '$ki_accessible' ) )
=> ( F @ ( B @ ( J @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(101,plain,
! [M: '$ki_world',L: '$ki_world',K: '$ki_world',J: '$ki_world',I: '$ki_world',H: $i,G: '$ki_world',F: $i,E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( M @ member ) ) )
| ~ ( M @ ( L @ '$ki_accessible' ) )
| ~ ( H @ ( D @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk6 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( F @ ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk5 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( L @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( M @ member ) ) )
| ~ ( M @ ( L @ '$ki_accessible' ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk6 ) ) ) ) ) ) ) ) @ ( L @ '$ki_accessible' ) )
| ~ ( F @ ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk5 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( L @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( M @ member ) ) )
| ~ ( M @ ( L @ '$ki_accessible' ) )
| ~ ( H @ ( D @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk6 ) ) ) ) ) ) ) ) @ member ) ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk5 ) ) ) ) ) ) ) ) @ ( L @ '$ki_accessible' ) )
| ~ ( L @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( M @ member ) ) )
| ~ ( M @ ( L @ '$ki_accessible' ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk6 ) ) ) ) ) ) ) ) @ ( L @ '$ki_accessible' ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( L @ sk5 ) ) ) ) ) ) ) ) @ ( L @ '$ki_accessible' ) )
| ~ ( L @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ ( D @ ( K @ member ) ) )
| ~ ( K @ ( I @ '$ki_accessible' ) )
| ~ ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( F @ ( B @ ( J @ member ) ) )
| ~ ( J @ ( I @ '$ki_accessible' ) )
| ~ ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( H @ ( D @ ( K @ member ) ) )
| ~ ( K @ ( I @ '$ki_accessible' ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ ( I @ '$ki_accessible' ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( F @ ( B @ ( J @ member ) ) )
| ~ ( J @ ( I @ '$ki_accessible' ) )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ ( I @ '$ki_accessible' ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(103,plain,
! [J: '$ki_world',I: '$ki_world',H: $i,G: '$ki_world',F: $i,E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( F @ ( B @ ( J @ member ) ) )
| ~ ( J @ ( I @ '$ki_accessible' ) )
| ~ ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( H @ ( G @ '$ki_exists_in_world_$i' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( F @ ( E @ '$ki_exists_in_world_$i' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[101]) ).
thf(464,plain,
! [B: $i,A: '$ki_world'] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(cnf,[status(esa)],[463]) ).
thf(843,plain,
! [J: '$ki_world',I: '$ki_world',H: $i,G: '$ki_world',F: $i,E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( F @ ( B @ ( J @ member ) ) )
| ~ ( J @ ( I @ '$ki_accessible' ) )
| ~ ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ $true
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ $true
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ $true
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[103,464]) ).
thf(844,plain,
! [J: '$ki_world',I: '$ki_world',H: $i,G: '$ki_world',F: $i,E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( F @ ( B @ ( J @ member ) ) )
| ~ ( J @ ( I @ '$ki_accessible' ) )
| ~ ( H @ ( F @ cross_product ) @ ( D @ ( B @ ordered_pair ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ sk4 ) ) ) ) ) ) ) ) @ member ) ) )
| ~ ( I @ ( G @ '$ki_accessible' ) )
| ~ ( G @ ( E @ '$ki_accessible' ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[843]) ).
thf(99,plain,
! [E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ compose ) @ ( E @ subclass ) ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( D @ ( C @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(770,plain,
! [E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ compose ) @ ( E @ subclass ) ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ $true
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[99,464]) ).
thf(771,plain,
! [E: '$ki_world',D: $i,C: '$ki_world',B: $i,A: '$ki_world'] :
( ( universal_class @ ( universal_class @ cross_product ) @ ( B @ ( D @ compose ) @ ( E @ subclass ) ) )
| ~ ( E @ ( C @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(826,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,822]) ).
thf(827,plain,
! [A: '$ki_world'] :
( ( ( sk3 @ ( sk1 @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[826]) ).
thf(831,plain,
! [A: '$ki_world'] :
( ( sk3 != A )
| ( sk1 != '$ki_local_world' )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[827]) ).
thf(832,plain,
( ( sk1 != '$ki_local_world' )
| ~ ( null_class @ ( sk112 @ ( '$ki_local_world' @ ( sk112 @ ( sk3 @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[831]) ).
thf(39,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ second @ ( B @ second @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_substitution_1) ).
thf(346,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ second @ ( B @ second @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ordered_pair ) @ ( B @ ( F @ ordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_2) ).
thf(214,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ ordered_pair ) @ ( B @ ( F @ ordered_pair ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(35,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
thf(290,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ subclass ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ subclass ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ cross_product ) @ flip @ domain_of @ ( B @ inverse @ ( C @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
thf(378,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ cross_product ) @ flip @ domain_of @ ( B @ inverse @ ( C @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(750,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,749]) ).
thf(751,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( A @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(752,plain,
~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( sk1 @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[751:[bind(A,$thf( sk1 ))]]) ).
thf(833,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( A @ inductive ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,554]) ).
thf(834,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( sk112 @ ( A @ inductive ) ) ),
inference(simp,[status(thm)],[833]) ).
thf(835,plain,
sk112 @ ( sk1 @ inductive ),
inference(pattern_uni,[status(thm)],[834:[bind(A,$thf( sk1 ))]]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ inverse @ ( B @ inverse @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution_1) ).
thf(126,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ inverse @ ( B @ inverse @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( element_relation @ ( A @ subclass ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_0) ).
thf(268,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( universal_class @ ( universal_class @ cross_product ) @ ( element_relation @ ( A @ subclass ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ successor @ ( B @ successor @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution_1) ).
thf(358,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ successor @ ( B @ successor @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(89,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ flip @ ( B @ flip @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_substitution_1) ).
thf(664,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ flip @ ( B @ flip @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ singleton @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(400,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ qmltpeq ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ singleton @ ( B @ singleton @ ( F @ qmltpeq ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( B @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( B @ ( H @ member ) ) ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(322,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ( ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( H @ member ) ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( B @ ( H @ member ) ) ) ) ) )
& ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ unordered_pair ) @ ( B @ ( H @ member ) ) ) )
=> ( ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( B @ ( H @ qmltpeq ) ) ) )
| ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) ) )
& ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( universal_class @ ( B @ ( H @ member ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(65,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ compose ) @ ( B @ ( F @ compose ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_2) ).
thf(469,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( F @ compose ) @ ( B @ ( F @ compose ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(753,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( B @ sk33 ) ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,749]) ).
thf(754,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( B @ sk33 ) ) @ member ) ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(755,plain,
~ ( null_class @ ( sk12 @ ( '$ki_local_world' @ ( sk12 @ ( '$ki_local_world' @ sk33 ) ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[754:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(26,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ compose ) @ ( F @ ( B @ compose ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_1) ).
thf(232,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ! [F: $i] :
( ( F @ ( E @ '$ki_exists_in_world_$i' ) )
=> ! [G: '$ki_world'] :
( ( G @ ( E @ '$ki_accessible' ) )
=> ( ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( D @ ( B @ ( H @ qmltpeq ) ) ) )
=> ! [H: '$ki_world'] :
( ( H @ ( G @ '$ki_accessible' ) )
=> ( F @ ( D @ compose ) @ ( F @ ( B @ compose ) @ ( H @ qmltpeq ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1748,plain,
$false,
inference(e,[status(thm)],[352,404,158,977,120,202,523,762,384,142,184,702,559,638,453,116,527,380,270,825,260,392,192,137,92,435,830,842,224,519,697,188,388,356,256,1028,554,642,547,96,622,654,457,134,765,398,558,412,618,264,745,180,176,286,204,498,236,350,406,362,451,98,616,477,594,483,240,769,198,130,226,431,658,394,306,473,531,487,749,342,553,557,640,414,95,840,463,576,600,386,465,759,218,844,771,832,346,214,290,378,752,835,210,126,268,358,664,400,94,464,822,90,322,469,1009,755,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL949_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n003.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 23:53:23 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.00/1.39 % [INFO] Parsing done (423ms).
% 2.50/1.41 % [INFO] Running in sequential loop mode.
% 3.23/1.79 % [INFO] eprover registered as external prover.
% 3.46/1.80 % [INFO] Scanning for conjecture ...
% 3.66/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 87 axioms. Running axiom selection ...
% 3.93/2.08 % [INFO] Axiom selection finished. Selected 87 axioms (removed 0 axioms).
% 5.00/2.43 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.00/2.47 % [INFO] Type checking passed.
% 5.00/2.47 % [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 ...
% 20.12/5.46 % External prover 'e' found a proof!
% 20.12/5.46 % [INFO] Killing All external provers ...
% 20.12/5.46 % Time passed: 4913ms (effective reasoning time: 4044ms)
% 20.12/5.46 % 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)>
% 20.12/5.46 % Axioms used in derivation (87): sum_class_defn, compose_defn1, member_substitution_1, image_defn, $ki_exists_in_world_$i_nonempty, flip_defn, function_defn, domain_of_substitution_1, compose_substitution_2, element_relation_defn, range_of_substitution_1, restrict_substitution_3, unordered_pair_defn, successor_substitution_1, successor_relation_defn1, power_class_defn, cross_product_substitution_2, first_substitution_1, inverse_defn, disjoint_substitution_2, replacement, apply_substitution_2, singleton_set_defn, element_relation_0, intersection_substitution_1, flip_substitution_1, cross_product_defn, rotate_0, function_substitution_1, mrel_reflexive, complement_0, sum_class_substitution_1, extensionality, cross_product_0, domain_of_0, unordered_pair_substitution_2, intersection_0, infinity, intersection_substitution_2, image_substitution_1, ordered_pair_substitution_1, power_class_substitution_1, disjoint_substitution_1, sum_class_0, union_substitution_2, subclass_substitution_1, reflexivity, inductive_substitution_1, restrict_substitution_2, null_class_defn, unordered_pair_substitution_1, complement_substitution_1, subclass_defn, rotate_substitution_1, image_substitution_2, subclass_substitution_2, power_class_0, compose_defn2, restrict_defn, flip_0, union_substitution_1, mrel_transitive, ordered_pair_substitution_2, choice, disjoint_defn, compose_substitution_1, unordered_pair_0, apply_defn, regularity, restrict_substitution_1, second_substitution_1, successor_defn, ordered_pair_defn, class_elements_are_sets, $ki_exists_in_world_$i_const, range_of_defn, transitivity, union_defn, successor_relation_defn2, cross_product_substitution_1, rotate_defn, member_substitution_2, inductive_defn, inverse_substitution_1, apply_substitution_1, singleton_substitution_1, symmetry
% 20.12/5.46 % No. of inferences in proof: 277
% 20.12/5.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4913 ms resp. 4044 ms w/o parsing
% 20.11/5.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.11/5.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------