%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL949^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 : Wed Sep 30 08:14:19 AM UTC 2026
% Result : Theorem 33.90s 8.79s
% Output : Refutation 35.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 94
% Syntax : Number of formulae : 182 ( 11 unt; 0 typ; 8 def)
% Number of atoms : 2021 ( 8 equ; 0 cnn)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 4774 ( 11 ~; 6 |; 70 &;4068 @)
% ( 0 <=>; 619 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 16 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 7 con; 0-3 aty)
% Number of variables : 955 ( 217 ^; 732 !; 6 ?; 955 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_decl,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $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: $i > $i > mworld > $o ).
thf(inductive_decl,type,
inductive: $i > mworld > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > mworld > $o ).
thf(function_decl,type,
function: $i > mworld > $o ).
thf(member_decl,type,
member: $i > $i > mworld > $o ).
thf(subclass_decl,type,
subclass: $i > $i > mworld > $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(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(47,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mand @ ( mbox @ ( member @ A @ universal_class ) )
@ ( mand @ ( mbox @ ( inductive @ A ) )
@ ( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( inductive @ B ) ) @ ( mbox @ ( subclass @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
thf(408,plain,
? [A: $i] :
( ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( member @ A @ universal_class @ B ) )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( inductive @ A @ B ) )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ! [C: $i,D: mworld] :
( ( mrel @ B @ D )
=> ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( inductive @ C @ E ) )
=> ! [E: mworld] :
( ( mrel @ D @ E )
=> ( subclass @ A @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mand
@ ( mbox
@ ( mimplies @ ( mbox @ ( disjoint @ A @ B ) )
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) )
@ ( mbox @ ( disjoint @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(446,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( disjoint @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i,H: mworld] :
( ( mrel @ F @ H )
=> ~ ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
& ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i,H: mworld] :
( ( mrel @ F @ H )
=> ~ ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
& ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( disjoint @ B @ D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(38,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_substitution_1) ).
thf(346,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( image @ B @ F ) @ ( image @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(84,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mand
@ ( mbox
@ ( mimplies @ ( mbox @ ( subclass @ A @ B ) )
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) )
@ ( mbox @ ( subclass @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(645,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i,H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ! [G: $i,H: mworld] :
( ( mrel @ F @ H )
=> ( ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ B @ I ) )
=> ! [I: mworld] :
( ( mrel @ H @ I )
=> ( member @ G @ D @ I ) ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(80,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ C ) ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(629,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ D @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ F @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(62,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_0) ).
thf(518,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( subclass @ ( flip @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1,conjecture,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subclass @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subclass) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subclass @ A @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(88,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( subclass @ B @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(385,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( unordered_pair @ F @ B ) @ ( unordered_pair @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(61,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ B @ ( complement @ A ) ) ) @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ B @ A ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ B @ A ) ) ) ) ) @ ( mbox @ ( member @ B @ ( complement @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_0) ).
thf(500,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ ( complement @ B ) @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( member @ D @ B @ G ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( member @ D @ B @ G ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ ( complement @ B ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(10,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( function @ A ) ) ) @ ( mbox @ ( function @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_substitution_1) ).
thf(153,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( function @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( function @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) ) @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_defn) ).
thf(417,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i] :
( ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ D ) @ F ) @ ( flip @ H ) @ J ) )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ D ) @ F ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ B ) @ F ) @ H @ J ) ) ) ) )
& ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ D ) @ F ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ B ) @ F ) @ H @ J ) ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ D ) @ F ) @ ( flip @ H ) @ J ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution_1) ).
thf(257,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( successor @ B ) @ ( successor @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ) @ ( mand @ ( mbox @ ( member @ C @ universal_class ) ) @ ( mbox @ ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ C @ universal_class ) ) @ ( mbox @ ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
thf(389,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i] :
( ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ F @ H ) @ ( compose @ D @ B ) @ J ) )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ F @ universal_class @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ H @ ( image @ D @ ( image @ D @ ( singleton @ F ) ) ) @ J ) ) ) ) )
& ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ F @ universal_class @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ H @ ( image @ D @ ( image @ D @ ( singleton @ F ) ) ) @ J ) ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ F @ H ) @ ( compose @ D @ B ) @ J ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(77,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mbox @ ( member @ ( power_class @ A ) @ universal_class ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_0) ).
thf(619,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ B @ universal_class @ D ) )
=> ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ ( power_class @ B ) @ universal_class @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(18,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_substitution_2) ).
thf(196,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i,I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ B @ D @ J ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ ( restrict @ F @ B @ H ) @ ( restrict @ F @ D @ H ) @ J ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(93,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_substitution_2) ).
thf(261,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( image @ F @ B ) @ ( image @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(78,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( range_of @ A ) @ ( domain_of @ ( inverse @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
thf(623,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ ( range_of @ B ) @ ( domain_of @ ( inverse @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(70,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(574,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ D @ B @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ) @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( member @ A @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( member @ A @ B ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
thf(602,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ ( ordered_pair @ B @ D ) @ element_relation @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ D @ F ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ D @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ ( ordered_pair @ B @ D ) @ element_relation @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(29,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( image @ B @ A ) @ ( range_of @ ( restrict @ B @ A @ universal_class ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
thf(265,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( qmltpeq @ ( image @ D @ B ) @ ( range_of @ ( restrict @ D @ B @ universal_class ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_substitution_1) ).
thf(381,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( ordered_pair @ B @ F ) @ ( ordered_pair @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(67,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( function @ A ) ) @ ( mand @ ( mbox @ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ) @ ( mbox @ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ) @ ( mbox @ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ) @ ( mbox @ ( function @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
thf(534,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ! [C: mworld] :
( ( mrel @ A @ C )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( function @ B @ D ) )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ B @ ( cross_product @ universal_class @ universal_class ) @ D ) )
& ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ ( compose @ B @ ( inverse @ B ) ) @ identity_relation @ D ) ) ) ) )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ B @ ( cross_product @ universal_class @ universal_class ) @ D ) )
& ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ ( compose @ B @ ( inverse @ B ) ) @ identity_relation @ D ) ) )
=> ! [D: mworld] :
( ( mrel @ C @ D )
=> ( function @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(55,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) ) @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
thf(467,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i] :
( ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ F ) @ H ) @ ( rotate @ B ) @ J ) )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ F ) @ H ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ F @ H ) @ D ) @ B @ J ) ) ) ) )
& ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ F ) @ H ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ F @ H ) @ D ) @ B @ J ) ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ ( ordered_pair @ D @ F ) @ H ) @ ( rotate @ B ) @ J ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(56,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(484,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ B @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(79,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_substitution_1) ).
thf(625,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( domain_of @ B ) @ ( domain_of @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(37,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ ( intersection @ A @ B ) ) ) @ ( mand @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) @ ( mbox @ ( member @ C @ ( intersection @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_0) ).
thf(329,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( intersection @ B @ D ) @ H ) )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) ) ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( intersection @ B @ D ) @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(68,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( disjoint @ A @ C ) ) ) @ ( mbox @ ( disjoint @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_substitution_1) ).
thf(551,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( disjoint @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( disjoint @ D @ F @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ A @ ( unordered_pair @ B @ C ) ) ) @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) @ ( mbox @ ( member @ A @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(285,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ ( unordered_pair @ D @ F ) @ H ) )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ universal_class @ H ) )
& ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ F @ H ) ) ) ) ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ universal_class @ H ) )
& ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ F @ H ) ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ ( unordered_pair @ D @ F ) @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(71,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subclass @ C @ A ) ) ) @ ( mbox @ ( subclass @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_substitution_2) ).
thf(578,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subclass @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subclass @ F @ D @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( ordered_pair @ A @ B ) @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(188,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( qmltpeq @ ( ordered_pair @ B @ D ) @ ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ ( singleton @ D ) ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ A @ ( power_class @ B ) ) ) @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mbox @ ( subclass @ A @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mbox @ ( subclass @ A @ B ) ) ) @ ( mbox @ ( member @ A @ ( power_class @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
thf(356,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ ( power_class @ D ) @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ ( power_class @ D ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(58,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( singleton @ A ) @ ( unordered_pair @ A @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(488,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ ( singleton @ B ) @ ( unordered_pair @ B @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(22,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mbox @ ( function @ B ) ) ) @ ( mbox @ ( member @ ( image @ B @ A ) @ universal_class ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(212,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( function @ D @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ ( image @ D @ B ) @ universal_class @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(244,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(66,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_substitution_2) ).
thf(530,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( compose @ F @ B ) @ ( compose @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(85,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( member @ ( unordered_pair @ A @ B ) @ universal_class ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_0) ).
thf(662,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( member @ ( unordered_pair @ B @ D ) @ universal_class @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(13,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( apply @ A @ B ) @ ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
thf(180,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( qmltpeq @ ( apply @ B @ D ) @ ( sum_class @ ( image @ B @ ( singleton @ D ) ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( successor @ A ) @ ( union @ A @ ( singleton @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
thf(444,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ ( successor @ B ) @ ( union @ B @ ( singleton @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(72,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_substitution_2) ).
thf(584,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( apply @ F @ B ) @ ( apply @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(12,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( first @ A ) @ ( first @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_substitution_1) ).
thf(176,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( first @ B ) @ ( first @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_substitution_1) ).
thf(281,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( compose @ B @ F ) @ ( compose @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_substitution_1) ).
thf(204,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( range_of @ B ) @ ( range_of @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(39,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( disjoint @ C @ A ) ) ) @ ( mbox @ ( disjoint @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_substitution_2) ).
thf(350,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( disjoint @ F @ B @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( disjoint @ F @ D @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(11,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mand @ ( mbox @ ( subclass @ A @ B ) ) @ ( mbox @ ( subclass @ B @ A ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subclass @ A @ B ) ) @ ( mbox @ ( subclass @ B @ A ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
thf(159,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ D @ B @ F ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( subclass @ D @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_0) ).
thf(406,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( subclass @ ( rotate @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(377,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( unordered_pair @ B @ F ) @ ( unordered_pair @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_substitution_2) ).
thf(434,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( cross_product @ F @ B ) @ ( cross_product @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ A @ null_class ) ) ) )
@ ( mexists_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ B @ A ) ) @ ( mbox @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
thf(271,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ~ ! [E: mworld] :
( ( mrel @ D @ E )
=> ( qmltpeq @ B @ null_class @ E ) ) )
=> ? [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( member @ D @ universal_class @ E ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( member @ D @ B @ E ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( disjoint @ D @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_substitution_1) ).
thf(208,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( cross_product @ B @ F ) @ ( cross_product @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(63,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_substitution_1) ).
thf(520,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( apply @ B @ F ) @ ( apply @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(668,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( intersection @ F @ B ) @ ( intersection @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(34,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_1) ).
thf(306,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( union @ B @ F ) @ ( union @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ B @ ( domain_of @ A ) ) ) @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class ) ) ) ) ) @ ( mbox @ ( member @ B @ ( domain_of @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_0) ).
thf(135,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ ( domain_of @ B ) @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( qmltpeq @ ( restrict @ B @ ( singleton @ D ) @ universal_class ) @ null_class @ G ) ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ~ ! [G: mworld] :
( ( mrel @ F @ G )
=> ( qmltpeq @ ( restrict @ B @ ( singleton @ D ) @ universal_class ) @ null_class @ G ) ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ ( domain_of @ B ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_substitution_1) ).
thf(267,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( flip @ B ) @ ( flip @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(438,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( singleton @ B ) @ ( singleton @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(59,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( inductive @ A ) ) ) @ ( mbox @ ( inductive @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_substitution_1) ).
thf(490,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( inductive @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( inductive @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(6,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(112,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( qmltpeq @ ( restrict @ B @ A @ C ) @ ( intersection @ B @ ( cross_product @ A @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
thf(194,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( qmltpeq @ ( restrict @ D @ B @ F ) @ ( intersection @ D @ ( cross_product @ B @ F ) ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( inductive @ A ) ) @ ( mand @ ( mbox @ ( member @ null_class @ A ) ) @ ( mbox @ ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ null_class @ A ) ) @ ( mbox @ ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ) @ ( mbox @ ( inductive @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
thf(557,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ! [C: mworld] :
( ( mrel @ A @ C )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( inductive @ B @ D ) )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ null_class @ B @ D ) )
& ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ ( image @ successor_relation @ B ) @ B @ D ) ) ) ) )
& ! [C: mworld] :
( ( mrel @ A @ C )
=> ( ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ null_class @ B @ D ) )
& ! [D: mworld] :
( ( mrel @ C @ D )
=> ( subclass @ ( image @ successor_relation @ B ) @ B @ D ) ) )
=> ! [D: mworld] :
( ( mrel @ C @ D )
=> ( inductive @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(4,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_substitution_2) ).
thf(95,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( ordered_pair @ F @ B ) @ ( ordered_pair @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
thf(327,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( subclass @ ( compose @ D @ B ) @ ( cross_product @ universal_class @ universal_class ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(35,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mand
@ ( mbox
@ ( mimplies @ ( mbox @ ( member @ A @ ( sum_class @ B ) ) )
@ ( mexists_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( member @ A @ C ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( member @ A @ C ) ) @ ( mbox @ ( member @ C @ B ) ) ) )
@ ( mbox @ ( member @ A @ ( sum_class @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(310,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ ( sum_class @ D ) @ F ) )
=> ? [F: $i] :
( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( member @ B @ F @ G ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( member @ F @ D @ G ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ? [F: $i] :
( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( member @ B @ F @ G ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( member @ F @ D @ G ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ ( sum_class @ D ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subclass @ A @ C ) ) ) @ ( mbox @ ( subclass @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_substitution_1) ).
thf(182,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subclass @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( subclass @ D @ F @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(54,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ ( cross_product @ A @ B ) ) ) @ ( mbox @ ( qmltpeq @ C @ ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_0) ).
thf(463,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( cross_product @ B @ D ) @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ F @ ( ordered_pair @ ( first @ F ) @ ( second @ F ) ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(83,axiom,
mlocal @ ( mbox @ ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(643,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(26,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mand @ ( mbox @ ( function @ A ) )
@ ( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ B @ null_class ) ) @ ( mbox @ ( member @ ( apply @ A @ B ) @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
thf(250,plain,
? [A: $i] :
( ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ( function @ A @ B ) )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ! [C: $i,D: mworld] :
( ( mrel @ B @ D )
=> ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( member @ C @ universal_class @ E ) )
=> ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( qmltpeq @ C @ null_class @ E ) )
| ! [E: mworld] :
( ( mrel @ D @ E )
=> ( member @ ( apply @ A @ C ) @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ C @ ( union @ A @ B ) ) ) @ ( mor @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ ( member @ C @ A ) ) @ ( mbox @ ( member @ C @ B ) ) ) @ ( mbox @ ( member @ C @ ( union @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(99,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( union @ B @ D ) @ H ) )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) ) ) )
& ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ B @ H ) )
| ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ D @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ F @ ( union @ B @ D ) @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(64,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_substitution_1) ).
thf(524,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( sum_class @ B ) @ ( sum_class @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(23,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_substitution_1) ).
thf(218,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( power_class @ B ) @ ( power_class @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_substitution_1) ).
thf(588,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( rotate @ B ) @ ( rotate @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(7,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) @ ( mand @ ( mbox @ ( member @ A @ C ) ) @ ( mbox @ ( member @ B @ D ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ A @ C ) ) @ ( mbox @ ( member @ B @ D ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
thf(114,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i] :
( ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ B @ D ) @ ( cross_product @ F @ H ) @ J ) )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ B @ F @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ D @ H @ J ) ) ) ) )
& ! [I: mworld] :
( ( mrel @ G @ I )
=> ( ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ B @ F @ J ) )
& ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ D @ H @ J ) ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( member @ ( ordered_pair @ B @ D ) @ ( cross_product @ F @ H ) @ J ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(190,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( intersection @ B @ F ) @ ( intersection @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( second @ A ) @ ( second @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_substitution_1) ).
thf(373,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( second @ B ) @ ( second @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(86,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_substitution_1) ).
thf(664,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( inverse @ B ) @ ( inverse @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_substitution_2) ).
thf(635,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( union @ F @ B ) @ ( union @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(75,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ A @ C ) ) ) @ ( mbox @ ( member @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(596,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ B @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( member @ D @ F @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(65,axiom,
mlocal @ ( mbox @ ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_0) ).
thf(528,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_substitution_3) ).
thf(131,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i,I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ B @ D @ J ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ ( restrict @ F @ H @ B ) @ ( restrict @ F @ H @ D ) @ J ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] :
( mbox
@ ( mforall_di
@ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_substitution_1) ).
thf(200,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ! [H: $i,I: mworld] :
( ( mrel @ G @ I )
=> ( ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ B @ D @ J ) )
=> ! [J: mworld] :
( ( mrel @ I @ J )
=> ( qmltpeq @ ( restrict @ B @ F @ H ) @ ( restrict @ D @ F @ H ) @ J ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(51,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( subclass @ A @ universal_class ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(442,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( subclass @ B @ universal_class @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(57,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ ( inverse @ A ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
thf(486,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ ( inverse @ B ) @ ( domain_of @ ( flip @ ( cross_product @ B @ universal_class ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(82,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( mnot @ ( mbox @ ( member @ A @ null_class ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(639,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ~ ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ B @ null_class @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(24,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ) @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( qmltpeq @ ( successor @ A ) @ B ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ B @ universal_class ) ) @ ( mbox @ ( qmltpeq @ ( successor @ A ) @ B ) ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(222,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ ( ordered_pair @ B @ D ) @ successor_relation @ F ) )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( successor @ B ) @ D @ F ) ) ) ) )
& ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ B @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ D @ universal_class @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( successor @ B ) @ D @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( member @ ( ordered_pair @ B @ D ) @ successor_relation @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(74,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_substitution_1) ).
thf(592,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( complement @ B ) @ ( complement @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(60,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ A @ universal_class ) ) @ ( mbox @ ( member @ ( sum_class @ A ) @ universal_class ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_0) ).
thf(496,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ B @ universal_class @ D ) )
=> ! [D: mworld] :
( ( mrel @ C @ D )
=> ( member @ ( sum_class @ B ) @ universal_class @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4114,plain,
$false,
inference(e,[status(thm)],[408,446,346,645,629,518,88,385,500,153,417,257,389,619,196,93,261,623,574,602,265,381,534,467,484,625,329,551,285,578,188,356,488,212,244,530,662,180,444,584,176,281,204,350,159,406,377,434,271,208,520,668,306,135,267,438,490,112,194,557,95,327,310,182,463,643,250,99,524,218,588,114,190,373,664,635,596,528,131,200,442,486,639,222,592,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL949^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 10:47:10 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.01/1.13 % [INFO] Parsing done (360ms).
% 2.01/1.15 % [INFO] Running in sequential loop mode.
% 2.66/1.52 % [INFO] eprover registered as external prover.
% 2.66/1.53 % [INFO] Scanning for conjecture ...
% 3.09/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 85 axioms. Running axiom selection ...
% 3.40/1.83 % [INFO] Axiom selection finished. Selected 85 axioms (removed 0 axioms).
% 3.67/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 3.67/1.99 % [INFO] Type checking passed.
% 3.67/2.00 % [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 ...
% 33.90/8.78 % External prover 'e' found a proof!
% 33.90/8.79 % [INFO] Killing All external provers ...
% 33.90/8.79 % Time passed: 8448ms (effective reasoning time: 7634ms)
% 33.90/8.79 % 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)>
% 33.90/8.79 % Axioms used in derivation (85): sum_class_defn, flip_defn, compose_defn1, member_substitution_1, image_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, 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
% 33.90/8.79 % No. of inferences in proof: 174
% 33.90/8.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8448 ms resp. 7634 ms w/o parsing
% 35.56/9.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.56/9.15 % [INFO] Killing All external provers ...
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