%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:22:53 AM UTC 2026
% Result : Theorem 6.62s 2.05s
% Output : Refutation 7.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 93
% Syntax : Number of formulae : 180 ( 13 unt; 0 typ; 8 def)
% Number of atoms : 996 ( 27 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 2612 ( 8 ~; 4 |; 38 &;2320 @)
% ( 0 <=>; 242 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 7 con; 0-3 aty)
% Number of variables : 416 ( 215 ^; 194 !; 7 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
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(mequiv_decl,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(eiw_di_decl,type,
eiw_di: $i > 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(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(71,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ C @ A ) ) @ ( disjoint @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_2) ).
thf(249,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( disjoint @ C @ A @ mactual ) )
=> ( disjoint @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(24,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( range_of @ A ) @ ( domain_of @ ( inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
thf(142,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ ( range_of @ A ) @ ( domain_of @ ( inverse @ A ) ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(75,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_2) ).
thf(257,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(22,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ B @ ( domain_of @ A ) ) @ ( mand @ ( member @ B @ universal_class ) @ ( mnot @ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_0) ).
thf(137,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ B @ ( domain_of @ A ) @ mactual )
= ( ( member @ B @ universal_class @ mactual )
& ~ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(37,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_substitution_1) ).
thf(173,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) @ ( mand @ ( member @ A @ C ) @ ( member @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
thf(95,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) @ mactual )
= ( ( member @ A @ C @ mactual )
& ( member @ B @ D @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ ( cross_product @ A @ B ) ) @ ( qmltpeq @ C @ ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_0) ).
thf(199,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ ( cross_product @ A @ B ) @ mactual )
=> ( qmltpeq @ C @ ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(14,axiom,
mlocal @ ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_0) ).
thf(115,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) @ mactual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(70,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(247,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(56,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_defn) ).
thf(217,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) @ mactual )
= ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual )
& ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(84,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) @ ( mand @ ( member @ A @ universal_class ) @ ( mand @ ( member @ B @ universal_class ) @ ( qmltpeq @ ( successor @ A ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(276,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ ( ordered_pair @ A @ B ) @ successor_relation @ mactual )
= ( ( member @ A @ universal_class @ mactual )
& ( member @ B @ universal_class @ mactual )
& ( qmltpeq @ ( successor @ A ) @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(19,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ B @ ( complement @ A ) ) @ ( mand @ ( member @ B @ universal_class ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_0) ).
thf(125,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ B @ ( complement @ A ) @ mactual )
= ( ( member @ B @ universal_class @ mactual )
& ~ ( member @ B @ A @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_1) ).
thf(157,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( second @ A ) @ ( second @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_substitution_1) ).
thf(189,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( second @ A ) @ ( second @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(93,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_2) ).
thf(121,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ A @ C ) ) @ ( disjoint @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_1) ).
thf(211,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( disjoint @ A @ C @ mactual ) )
=> ( disjoint @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(73,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( qmltpeq @ ( restrict @ B @ A @ C ) @ ( intersection @ B @ ( cross_product @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
thf(253,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( qmltpeq @ ( restrict @ B @ A @ C ) @ ( intersection @ B @ ( cross_product @ A @ C ) ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(15,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( disjoint @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mnot @ ( mand @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
thf(116,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( disjoint @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ~ ( ( member @ C @ A @ mactual )
& ( member @ C @ B @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_substitution_1) ).
thf(243,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( inverse @ A ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
thf(233,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ ( inverse @ A ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(81,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_substitution_1) ).
thf(270,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(48,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(201,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(57,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subclass @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
thf(220,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( subclass @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ C ) ) @ ( qmltpeq @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(102,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( qmltpeq @ B @ C @ mactual ) )
=> ( qmltpeq @ A @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_substitution_1) ).
thf(229,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(46,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(197,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ C @ A @ mactual ) )
=> ( member @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_2) ).
thf(109,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_1) ).
thf(225,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(44,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( first @ A ) @ ( first @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_substitution_1) ).
thf(193,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( first @ A ) @ ( first @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(79,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_2) ).
thf(266,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(50,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_0) ).
thf(205,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ A @ ( power_class @ B ) ) @ ( mand @ ( member @ A @ universal_class ) @ ( subclass @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
thf(128,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( power_class @ B ) @ mactual )
= ( ( member @ A @ universal_class @ mactual )
& ( subclass @ A @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_2) ).
thf(237,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(34,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mnot @ ( member @ A @ null_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
thf(166,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ~ ( member @ A @ null_class @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mequiv @ ( function @ A ) @ ( mand @ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) @ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).
thf(148,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ( function @ A @ mactual )
= ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) @ mactual )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(78,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_1) ).
thf(264,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_substitution_1) ).
thf(161,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(85,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( member @ A @ universal_class ) @ ( function @ B ) ) @ ( member @ ( image @ B @ A ) @ universal_class ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(279,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( member @ A @ universal_class @ mactual )
& ( function @ B @ mactual ) )
=> ( member @ ( image @ B @ A ) @ universal_class @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(43,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(191,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(86,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mand @ ( function @ A )
@ ( mforall_di
@ ^ [B: $i] : ( mimplies @ ( member @ B @ universal_class ) @ ( mor @ ( qmltpeq @ B @ null_class ) @ ( member @ ( apply @ A @ B ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
thf(281,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ( function @ A @ mactual )
& ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ B @ universal_class @ mactual )
=> ( ( qmltpeq @ B @ null_class @ mactual )
| ( member @ ( apply @ A @ B ) @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(76,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mequiv @ ( inductive @ A ) @ ( mand @ ( member @ null_class @ A ) @ ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
thf(259,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ( inductive @ A @ mactual )
= ( ( member @ null_class @ A @ mactual )
& ( subclass @ ( image @ successor_relation @ A ) @ A @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(25,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( subclass @ A @ universal_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(144,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( subclass @ A @ universal_class @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(181,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ A @ C @ mactual ) )
=> ( member @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(31,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_2) ).
thf(159,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(83,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
thf(274,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(69,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( qmltpeq @ ( ordered_pair @ A @ B ) @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(245,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( qmltpeq @ ( ordered_pair @ A @ B ) @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_0) ).
thf(98,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( member @ ( unordered_pair @ A @ B ) @ universal_class @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution_1) ).
thf(140,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(54,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_substitution_1) ).
thf(213,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mimplies @ ( member @ A @ universal_class ) @ ( member @ ( power_class @ A ) @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_0) ).
thf(91,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ( member @ A @ universal_class @ mactual )
=> ( member @ ( power_class @ A ) @ universal_class @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( successor @ A ) @ ( union @ A @ ( singleton @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).
thf(251,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ ( successor @ A ) @ ( union @ A @ ( singleton @ A ) ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(58,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_1) ).
thf(223,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(67,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(241,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ A @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(74,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(255,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ B @ A @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(52,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(209,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) @ ( mand @ ( member @ C @ universal_class ) @ ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).
thf(112,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) @ mactual )
= ( ( member @ C @ universal_class @ mactual )
& ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ C @ A ) ) @ ( subclass @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_2) ).
thf(123,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( subclass @ C @ A @ mactual ) )
=> ( subclass @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ element_relation ) @ ( mand @ ( member @ B @ universal_class ) @ ( member @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).
thf(154,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ ( ordered_pair @ A @ B ) @ element_relation @ mactual )
= ( ( member @ B @ universal_class @ mactual )
& ( member @ A @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mand @ ( member @ A @ universal_class )
@ ( mand @ ( inductive @ A )
@ ( mforall_di
@ ^ [B: $i] : ( mimplies @ ( inductive @ B ) @ ( subclass @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
thf(175,plain,
? [A: $i] :
( ( eiw_di @ A @ mactual )
& ( member @ A @ universal_class @ mactual )
& ( inductive @ A @ mactual )
& ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( inductive @ B @ mactual )
=> ( subclass @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(62,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( qmltpeq @ ( image @ B @ A ) @ ( range_of @ ( restrict @ B @ A @ universal_class ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
thf(231,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( qmltpeq @ ( image @ B @ A ) @ ( range_of @ ( restrict @ B @ A @ universal_class ) ) @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_0) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ A @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution_1) ).
thf(203,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ A @ B ) @ ( mand @ ( subclass @ A @ B ) @ ( subclass @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
thf(104,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
= ( ( subclass @ A @ B @ mactual )
& ( subclass @ B @ A @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( member @ A @ ( sum_class @ B ) )
@ ( mexists_di
@ ^ [C: $i] : ( mand @ ( member @ A @ C ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).
thf(186,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( sum_class @ B ) @ mactual )
= ( ? [C: $i] :
( ( eiw_di @ C @ mactual )
& ( member @ A @ C @ mactual )
& ( member @ C @ B @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(171,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( function @ A ) ) @ ( function @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_substitution_1) ).
thf(119,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( function @ A @ mactual ) )
=> ( function @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(235,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(51,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_0) ).
thf(207,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mimplies @ ( member @ A @ universal_class ) @ ( member @ ( sum_class @ A ) @ universal_class ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_0) ).
thf(272,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ( member @ A @ universal_class @ mactual )
=> ( member @ ( sum_class @ A ) @ universal_class @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(28,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_defn) ).
thf(151,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) @ mactual )
= ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual )
& ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(26,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( qmltpeq @ ( apply @ A @ B ) @ ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
thf(146,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( qmltpeq @ ( apply @ A @ B ) @ ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ C @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_0) ).
thf(183,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ ( intersection @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
& ( member @ C @ B @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(35,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ C @ ( union @ A @ B ) ) @ ( mor @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(168,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ ( union @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
| ( member @ C @ B @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_3) ).
thf(262,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mforall_di
@ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_1) ).
thf(107,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ! [D: $i] :
( ( eiw_di @ D @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(66,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ A @ C ) ) @ ( subclass @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_1) ).
thf(239,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( subclass @ A @ C @ mactual ) )
=> ( subclass @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(80,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( singleton @ A ) @ ( unordered_pair @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(268,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ ( singleton @ A ) @ ( unordered_pair @ A @ A ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(45,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( inductive @ A ) ) @ ( inductive @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_substitution_1) ).
thf(195,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( inductive @ A @ mactual ) )
=> ( inductive @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(21,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mimplies @ ( mnot @ ( qmltpeq @ A @ null_class ) )
@ ( mexists_di
@ ^ [B: $i] : ( mand @ ( member @ B @ universal_class ) @ ( mand @ ( member @ B @ A ) @ ( disjoint @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
thf(131,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( ~ ( qmltpeq @ A @ null_class @ mactual )
=> ? [B: $i] :
( ( eiw_di @ B @ mactual )
& ( member @ B @ universal_class @ mactual )
& ( member @ B @ A @ mactual )
& ( disjoint @ B @ A @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(33,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ A @ ( unordered_pair @ B @ C ) ) @ ( mand @ ( member @ A @ universal_class ) @ ( mor @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(163,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ A @ ( unordered_pair @ B @ C ) @ mactual )
= ( ( member @ A @ universal_class @ mactual )
& ( ( qmltpeq @ A @ B @ mactual )
| ( qmltpeq @ A @ C @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
mlocal @ ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(111,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) @ mactual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_substitution_1) ).
thf(227,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(55,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_1) ).
thf(215,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(100,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(295,plain,
$false,
inference(e,[status(thm)],[249,142,257,137,173,95,199,115,247,217,276,125,157,189,93,121,211,253,116,243,233,270,201,220,102,229,197,109,225,193,266,205,128,237,166,148,264,161,279,191,281,259,144,181,159,274,245,98,140,213,91,251,223,241,255,209,112,123,154,175,231,87,203,104,186,171,119,235,207,272,151,146,183,168,262,107,239,268,195,131,163,111,227,215,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % 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
% 0.10/0.22 % Computer : n019.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:36:47 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.64/0.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/0.71 % [INFO] Parsing done (187ms).
% 1.34/0.72 % [INFO] Running in sequential loop mode.
% 2.01/0.94 % [INFO] eprover registered as external prover.
% 2.01/0.94 % [INFO] Scanning for conjecture ...
% 2.01/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 85 axioms. Running axiom selection ...
% 2.42/1.10 % [INFO] Axiom selection finished. Selected 84 axioms (removed 1 axioms).
% 2.84/1.17 % [INFO] Problem is higher-order (TPTP THF).
% 2.84/1.18 % [INFO] Type checking passed.
% 2.84/1.18 % [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 ...
% 6.62/2.04 % External prover 'e' found a proof!
% 6.62/2.05 % [INFO] Killing All external provers ...
% 6.62/2.05 % Time passed: 1738ms (effective reasoning time: 1322ms)
% 6.62/2.05 % 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)>
% 6.62/2.05 % Axioms used in derivation (84): 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, 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, eiw_di_nonempty, subclass_substitution_2, power_class_0, compose_defn2, restrict_defn, flip_0, union_substitution_1, 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
% 6.62/2.05 % No. of inferences in proof: 172
% 6.62/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1738 ms resp. 1322 ms w/o parsing
% 7.40/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.40/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------