TSTP Solution File: SET117+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET117+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:52:40 EDT 2023
% Result : Theorem 5.51s 2.27s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 75
% Syntax : Number of formulae : 121 ( 33 unt; 31 typ; 0 def)
% Number of atoms : 266 ( 47 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1010 ( 15 ~; 8 |; 89 &; 819 @)
% ( 19 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 6 con; 0-3 aty)
% Number of variables : 179 ( 0 ^; 167 !; 12 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(first_type,type,
first: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(universal_class_type,type,
universal_class: $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(null_class_type,type,
null_class: $i ).
thf(flip_type,type,
flip: $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A )
=> ( member @ A @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_ordered_pairs_are_sets) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A )
=> ( member @ A @ universal_class ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ! [A: $i] :
( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A )
=> ( member @ A @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) )
<=> ( ( 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/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) )
=> ( ( 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 ) ) )
& ( ( ( 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 ) )
=> ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
thf(97,plain,
! [A: $i] :
( ( inverse @ A )
= ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i] :
( ( A != null_class )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( member @ B @ A )
& ( disjoint @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
thf(124,plain,
! [A: $i] :
( ( A != null_class )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( member @ B @ A )
& ( disjoint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
thf(236,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
<=> ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
thf(112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) )
=> ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) ) )
& ( ( ( member @ C @ universal_class )
& ( member @ D @ ( image @ B @ ( image @ A @ ( singleton @ C ) ) ) ) )
=> ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(45,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
thf(250,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( domain_of @ A ) )
<=> ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( member @ B @ ( domain_of @ A ) )
=> ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) ) )
& ( ( ( member @ B @ universal_class )
& ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class ) )
=> ( member @ B @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [A: $i] :
( ( member @ A @ identity_relation )
<=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
thf(239,plain,
! [A: $i] :
( ( ( member @ A @ identity_relation )
=> ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) ) )
& ( ? [B: $i] :
( ( member @ B @ universal_class )
& ( A
= ( ordered_pair @ B @ B ) ) )
=> ( member @ A @ identity_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( cross_product @ A @ B ) )
=> ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( cross_product @ A @ B ) )
=> ( C
= ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_class @ B ) )
<=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( power_class @ B ) )
=> ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) ) )
& ( ( ( member @ A @ universal_class )
& ( subclass @ A @ B ) )
=> ( member @ A @ ( power_class @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subclass @ A @ B )
& ( subclass @ B @ A ) ) )
& ( ( ( subclass @ A @ B )
& ( subclass @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class ) )
=> ( ( ( first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
thf(211,plain,
! [A: $i,B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(14,axiom,
! [A: $i] :
( ( inductive @ A )
<=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
thf(106,plain,
! [A: $i] :
( ( ( inductive @ A )
=> ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) ) )
& ( ( ( member @ null_class @ A )
& ( subclass @ ( image @ successor_relation @ A ) @ A ) )
=> ( inductive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
<=> ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
=> ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) ) )
& ( ( ( member @ A @ universal_class )
& ( member @ B @ universal_class )
& ( ( successor @ A )
= B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( restrict @ B @ A @ C )
= ( intersection @ B @ ( cross_product @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
<=> ( ( 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/sandbox/benchmark/theBenchmark.p',flip_defn) ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
=> ( ( 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 ) ) )
& ( ( ( 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 ) )
=> ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
thf(53,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(169,plain,
! [A: $i,B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
<=> ( ( member @ A @ C )
& ( member @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
thf(141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
=> ( ( member @ A @ C )
& ( member @ B @ D ) ) )
& ( ( ( member @ A @ C )
& ( member @ B @ D ) )
=> ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ! [C: $i] :
~ ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
thf(73,plain,
! [A: $i] :
( ( range_of @ A )
= ( domain_of @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
thf(237,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
! [A: $i] :
~ ( member @ A @ null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
thf(187,plain,
! [A: $i] :
~ ( member @ A @ null_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum_class @ B ) )
<=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( sum_class @ B ) )
=> ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) ) )
& ( ? [C: $i] :
( ( member @ A @ C )
& ( member @ C @ B ) )
=> ( member @ A @ ( sum_class @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(213,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
<=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( ( member @ ( ordered_pair @ A @ B ) @ element_relation )
=> ( ( member @ B @ universal_class )
& ( member @ A @ B ) ) )
& ( ( ( member @ B @ universal_class )
& ( member @ A @ B ) )
=> ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( image @ B @ A )
= ( range_of @ ( restrict @ B @ A @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( member @ B @ ( complement @ A ) )
<=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( member @ B @ ( complement @ A ) )
=> ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) ) )
& ( ( ( member @ B @ universal_class )
& ~ ( member @ B @ A ) )
=> ( member @ B @ ( complement @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( apply @ A @ B )
= ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
thf(67,plain,
! [A: $i] :
( ( singleton @ A )
= ( unordered_pair @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
thf(182,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
thf(158,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) ) )
& ( ( ( member @ A @ universal_class )
& ( ( A = B )
| ( A = C ) ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( function @ B ) )
=> ( member @ ( image @ B @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
thf(190,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ universal_class )
& ( function @ B ) )
=> ( member @ ( image @ B @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,axiom,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
thf(183,plain,
? [A: $i] :
( ( member @ A @ universal_class )
& ( inductive @ A )
& ! [B: $i] :
( ( inductive @ B )
=> ( subclass @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subclass @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( ( subclass @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subclass @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
thf(215,plain,
! [A: $i] :
( ( member @ A @ universal_class )
=> ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(40,axiom,
? [A: $i] :
( ( function @ A )
& ! [B: $i] :
( ( member @ B @ universal_class )
=> ( ( B = null_class )
| ( member @ ( apply @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
thf(232,plain,
? [A: $i] :
( ( function @ A )
& ! [B: $i] :
( ( member @ B @ universal_class )
=> ( ( B = null_class )
| ( member @ ( apply @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(13,axiom,
! [A: $i] :
( ( function @ A )
<=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
thf(100,plain,
! [A: $i] :
( ( ( function @ A )
=> ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) )
& ( ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
& ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) )
=> ( function @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(252,plain,
$false,
inference(e,[status(thm)],[46,147,97,124,236,112,250,82,239,131,217,247,56,153,211,106,160,70,192,53,169,141,134,73,237,118,204,187,76,213,198,223,226,50,67,182,158,171,190,183,90,215,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET117+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 18:25:02 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.01 % [INFO] Parsing done (156ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.98/1.23 % [INFO] eprover registered as external prover.
% 1.98/1.24 % [INFO] cvc4 registered as external prover.
% 1.98/1.24 % [INFO] Scanning for conjecture ...
% 2.10/1.31 % [INFO] Found a conjecture and 43 axioms. Running axiom selection ...
% 2.29/1.36 % [INFO] Axiom selection finished. Selected 43 axioms (removed 0 axioms).
% 2.36/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.43 % [INFO] Type checking passed.
% 2.58/1.43 % [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 ...
% 5.51/2.26 % External prover 'e' found a proof!
% 5.51/2.26 % [INFO] Killing All external provers ...
% 5.51/2.26 % Time passed: 1731ms (effective reasoning time: 1236ms)
% 5.51/2.26 % 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)>
% 5.51/2.26 % Axioms used in derivation (43): sum_class_defn, image_defn, cross_product_defn, extensionality, infinity, first_second, rotate, null_class_defn, sum_class, restrict_defn, compose_defn1, inductive_defn, unordered_pair, cross_product, flip_defn, function_defn, element_relation_defn, identity_relation, unordered_pair_defn, successor_relation_defn1, power_class_defn, intersection, inverse_defn, replacement, element_relation, singleton_set_defn, subclass_defn, domain_of, power_class, flip, compose_defn2, choice, complement, disjoint_defn, apply_defn, regularity, successor_defn, ordered_pair_defn, class_elements_are_sets, range_of_defn, union_defn, successor_relation_defn2, rotate_defn
% 5.51/2.26 % No. of inferences in proof: 90
% 5.51/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1731 ms resp. 1236 ms w/o parsing
% 5.79/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.79/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------