TSTP Solution File: SET057-7 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET057-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:52:14 EDT 2023
% Result : Unsatisfiable 4.75s 2.18s
% Output : Refutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 149
% Syntax : Number of formulae : 250 ( 67 unt; 49 typ; 0 def)
% Number of atoms : 393 ( 80 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1810 ( 184 ~; 192 |; 0 &;1434 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 11 con; 0-3 aty)
% Number of variables : 392 ( 0 ^; 392 !; 0 ?; 392 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(not_subclass_element_type,type,
not_subclass_element: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(subset_relation_type,type,
subset_relation: $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(subclass_type,type,
subclass: $i > $i > $o ).
thf(flip_type,type,
flip: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(universal_class_type,type,
universal_class: $i ).
thf(rotate_type,type,
rotate: $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(element_relation_type,type,
element_relation: $i ).
thf(power_class_type,type,
power_class: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(single_valued_class_type,type,
single_valued_class: $i > $o ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(restrict_type,type,
restrict: $i > $i > $i > $i ).
thf(compatible_type,type,
compatible: $i > $i > $i > $o ).
thf(homomorphism_type,type,
homomorphism: $i > $i > $i > $o ).
thf(operation_type,type,
operation: $i > $o ).
thf(sum_class_type,type,
sum_class: $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(inductive_type,type,
inductive: $i > $o ).
thf(successor_relation_type,type,
successor_relation: $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(diagonalise_type,type,
diagonalise: $i > $i ).
thf(cantor_type,type,
cantor: $i > $i ).
thf(null_class_type,type,
null_class: $i ).
thf(regular_type,type,
regular: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(omega_type,type,
omega: $i ).
thf(not_homomorphism1_type,type,
not_homomorphism1: $i > $i > $i > $i ).
thf(not_homomorphism2_type,type,
not_homomorphism2: $i > $i > $i > $i ).
thf(choice_type,type,
choice: $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(first_type,type,
first: $i > $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
thf(211,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) )
= ( union @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
thf(144,plain,
! [A: $i] :
( ~ ( function @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
thf(175,plain,
! [A: $i] :
( ~ ( 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)],[37]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,negated_conjecture,
member @ ( not_subclass_element @ x @ y ) @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality2_1) ).
thf(101,plain,
member @ ( not_subclass_element @ x @ y ) @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( unordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(34,axiom,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
thf(170,plain,
subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(100,axiom,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
thf(308,plain,
! [A: $i] :
( ( A = null_class )
| ( member @ ( regular @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
thf(120,plain,
! [A: $i] :
( ( complement @ ( image @ element_relation @ ( complement @ A ) ) )
= ( power_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,axiom,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
thf(202,plain,
! [A: $i] :
( ( union @ A @ ( singleton @ A ) )
= ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
thf(142,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
thf(153,plain,
! [A: $i] :
( ~ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation )
| ( single_valued_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
thf(184,plain,
! [A: $i] :
( ( A = null_class )
| ( ( intersection @ A @ ( regular @ A ) )
= null_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( range_of @ ( restrict @ A @ B @ universal_class ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
thf(280,plain,
! [A: $i] :
( ~ ( member @ null_class @ A )
| ~ ( subclass @ ( image @ successor_relation @ A ) @ A )
| ( inductive @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( ( domain_of @ ( domain_of @ B ) )
= ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( compatible @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( ( successor @ A )
!= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( ( successor @ A )
!= B )
| ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
thf(117,plain,
! [B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(49,axiom,
function @ choice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
thf(201,plain,
function @ choice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality2_2) ).
thf(102,plain,
x != y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
thf(302,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( sum_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) @ ( domain_of @ A ) )
| ( homomorphism @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( member @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) @ ( domain_of @ A ) )
| ( homomorphism @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( function @ A )
| ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( function @ A )
| ( ( domain_of @ ( domain_of @ B ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ C ) ) )
| ( compatible @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
thf(192,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ omega @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ C )
| ( subclass @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( subclass @ B @ C )
| ( subclass @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( second @ ( not_subclass_element @ ( restrict @ A @ ( singleton @ B ) @ C ) @ null_class ) )
= ( range @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( second @ ( not_subclass_element @ ( restrict @ A @ ( singleton @ B ) @ C ) @ null_class ) )
= ( range @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [A: $i] : ( subclass @ A @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
thf(169,plain,
! [A: $i] : ( subclass @ A @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
thf(124,plain,
! [A: $i] :
( ~ ( single_valued_class @ A )
| ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
thf(109,plain,
( ( intersection @ ( inverse @ subset_relation ) @ subset_relation )
= identity_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subclass @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( rotate @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ C @ A ) @ B ) @ ( rotate @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
thf(266,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ ( power_class @ A ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) )
= ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( flip @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ D )
| ~ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ ( flip @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
thf(148,plain,
! [A: $i] :
( ~ ( function @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
!= ( domain_of @ A ) )
| ~ ( subclass @ ( range_of @ A ) @ ( domain_of @ ( domain_of @ A ) ) )
| ( operation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ B @ ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(39,axiom,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagonalisation) ).
thf(180,plain,
! [A: $i] :
( ( complement @ ( domain_of @ ( intersection @ A @ identity_relation ) ) )
= ( diagonalise @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
thf(191,plain,
subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
thf(286,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( not_subclass_element @ A @ B ) @ B )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
thf(204,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( sum_class @ ( image @ A @ ( singleton @ B ) ) )
= ( apply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subclass @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
thf(274,plain,
! [B: $i,A: $i] :
( ~ ( function @ A )
| ~ ( member @ B @ universal_class )
| ( member @ ( image @ A @ B ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(53,axiom,
inductive @ omega,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
thf(208,plain,
inductive @ omega,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3,negated_conjecture,
~ ( member @ ( not_subclass_element @ y @ x ) @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality2_3) ).
thf(103,plain,
~ ( member @ ( not_subclass_element @ y @ x ) @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
thf(213,plain,
! [A: $i] :
( ~ ( one_to_one @ A )
| ( function @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ ( image @ C @ ( singleton @ D ) ) ) )
| ~ ( member @ ( ordered_pair @ D @ A ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ D @ A ) @ ( compose @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ ( image @ C @ ( singleton @ D ) ) ) )
| ~ ( member @ ( ordered_pair @ D @ A ) @ ( cross_product @ universal_class @ universal_class ) )
| ( member @ ( ordered_pair @ D @ A ) @ ( compose @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(27,axiom,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
thf(155,plain,
! [B: $i,A: $i] : ( subclass @ ( compose @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( ( apply @ B @ ( ordered_pair @ ( apply @ C @ ( not_homomorphism1 @ C @ A @ B ) ) @ ( apply @ C @ ( not_homomorphism2 @ C @ A @ B ) ) ) )
!= ( apply @ C @ ( apply @ A @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) ) ) )
| ( homomorphism @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( operation @ A )
| ~ ( operation @ B )
| ~ ( compatible @ C @ A @ B )
| ( ( apply @ B @ ( ordered_pair @ ( apply @ C @ ( not_homomorphism1 @ C @ A @ B ) ) @ ( apply @ C @ ( not_homomorphism2 @ C @ A @ B ) ) ) )
!= ( apply @ C @ ( apply @ A @ ( ordered_pair @ ( not_homomorphism1 @ C @ A @ B ) @ ( not_homomorphism2 @ C @ A @ B ) ) ) ) )
| ( homomorphism @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(15,axiom,
! [A: $i] : ( subclass @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
thf(130,plain,
! [A: $i] : ( subclass @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ element_relation )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
thf(226,plain,
! [A: $i] :
( ~ ( member @ A @ universal_class )
| ( A = null_class )
| ( member @ ( apply @ choice @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
thf(167,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( cross_product @ B @ C ) )
= ( restrict @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( cross_product @ B @ C ) )
= ( restrict @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
thf(112,plain,
! [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ( operation @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ( member @ A @ ( domain_of @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( ( restrict @ B @ ( singleton @ A ) @ universal_class )
= null_class )
| ( member @ A @ ( domain_of @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( member @ ( not_subclass_element @ A @ B ) @ A )
| ( subclass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( operation @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
= ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
thf(177,plain,
! [A: $i] :
( ~ ( operation @ A )
| ( ( cross_product @ ( domain_of @ ( domain_of @ A ) ) @ ( domain_of @ ( domain_of @ A ) ) )
= ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(40,axiom,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cantor_class) ).
thf(182,plain,
! [A: $i] :
( ( intersection @ ( domain_of @ A ) @ ( diagonalise @ ( compose @ ( inverse @ element_relation ) @ A ) ) )
= ( cantor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ A ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( rotate @ D ) )
| ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(98,axiom,
member @ omega @ universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
thf(304,plain,
member @ omega @ universal_class,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( complement @ B ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(35,axiom,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
= subset_relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
thf(171,plain,
( ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( intersection @ ( cross_product @ universal_class @ universal_class ) @ ( complement @ ( compose @ ( complement @ element_relation ) @ ( inverse @ element_relation ) ) ) ) )
= subset_relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
thf(290,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( member @ null_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( ( restrict @ A @ ( singleton @ B ) @ universal_class )
!= null_class )
| ~ ( member @ B @ ( domain_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
thf(272,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ universal_class )
| ( member @ A @ ( unordered_pair @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) )
= ( symmetric_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( intersection @ ( complement @ ( intersection @ A @ B ) ) @ ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) )
= ( symmetric_difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ( member @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ D )
| ( member @ ( ordered_pair @ A @ C ) @ ( cross_product @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
thf(262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ C @ D )
| ( member @ ( ordered_pair @ A @ C ) @ ( cross_product @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(23,axiom,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
thf(146,plain,
! [A: $i] :
( ( domain_of @ ( restrict @ element_relation @ universal_class @ A ) )
= ( sum_class @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
thf(305,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ successor_relation )
| ( ( successor @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(4,axiom,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
thf(107,plain,
! [A: $i] :
( ( domain_of @ ( inverse @ A ) )
= ( range_of @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
thf(268,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(67,axiom,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
thf(239,plain,
! [B: $i,A: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
thf(242,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ universal_class @ universal_class ) )
| ~ ( member @ A @ B )
| ( member @ ( ordered_pair @ A @ B ) @ element_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
thf(126,plain,
! [A: $i] :
( ~ ( function @ ( inverse @ A ) )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(136,plain,
! [A: $i] :
( ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) )
= ( inverse @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ A @ B ) @ C )
= ( restrict @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( cross_product @ A @ B ) @ C )
= ( restrict @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
thf(163,plain,
! [A: $i] :
( ~ ( inductive @ A )
| ( subclass @ ( image @ successor_relation @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
thf(111,plain,
! [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( first @ ( not_subclass_element @ ( restrict @ A @ B @ ( singleton @ C ) ) @ null_class ) )
= ( domain @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( first @ ( not_subclass_element @ ( restrict @ A @ B @ ( singleton @ C ) ) @ null_class ) )
= ( domain @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(11,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
thf(122,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ~ ( member @ ( ordered_pair @ D @ E ) @ ( domain_of @ B ) )
| ( ( apply @ C @ ( ordered_pair @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) )
= ( apply @ A @ ( apply @ B @ ( ordered_pair @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
thf(215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C )
| ~ ( member @ ( ordered_pair @ D @ E ) @ ( domain_of @ B ) )
| ( ( apply @ C @ ( ordered_pair @ ( apply @ A @ D ) @ ( apply @ A @ E ) ) )
= ( apply @ A @ ( apply @ B @ ( ordered_pair @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose @ C @ D ) )
| ( member @ B @ ( image @ C @ ( image @ D @ ( singleton @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ A @ B ) @ ( compose @ C @ D ) )
| ( member @ B @ ( image @ C @ ( image @ D @ ( singleton @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(311,plain,
$false,
inference(e,[status(thm)],[288,211,173,144,175,138,101,249,170,276,308,120,202,142,153,184,196,189,284,280,133,206,292,233,117,270,201,220,102,302,260,160,192,165,229,252,224,156,169,124,109,256,244,266,128,237,298,148,264,180,191,286,204,187,113,274,208,103,140,213,240,155,198,130,278,226,167,209,112,194,295,282,177,182,231,218,304,258,171,290,246,272,151,300,262,146,305,107,268,239,242,126,136,131,163,111,254,122,215,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET057-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.05/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n006.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 19:08:37 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.84/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/0.98 % [INFO] Parsing done (182ms).
% 1.40/0.99 % [INFO] Running in sequential loop mode.
% 1.84/1.24 % [INFO] eprover registered as external prover.
% 1.84/1.24 % [INFO] cvc4 registered as external prover.
% 1.84/1.24 % [INFO] Scanning for conjecture ...
% 1.92/1.31 % [INFO] Found a conjecture and 97 axioms. Running axiom selection ...
% 2.21/1.38 % [INFO] Axiom selection finished. Selected 97 axioms (removed 0 axioms).
% 2.45/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.45/1.45 % [INFO] Type checking passed.
% 2.45/1.45 % [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 ...
% 4.75/2.18 % External prover 'e' found a proof!
% 4.75/2.18 % [INFO] Killing All external provers ...
% 4.75/2.18 % Time passed: 1718ms (effective reasoning time: 1180ms)
% 4.75/2.18 % 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)>
% 4.75/2.18 % Axioms used in derivation (97): operation4, flip2, inverse, range, domain1, operation3, equal_implies_subclass1, complement1, one_to_one2, omega_is_inductive1, cartesian_product4, rotate2, homomorphism4, range_of, function3, regularity1, singleton_set, identity_relation, union, flip3, element_relation2, unordered_pairs_in_universal, compose2, homomorphism3, compatible3, symmetric_difference, cartesian_product1, not_subclass_members1, image, replacement, successor, ordered_pair, successor_relation1, domain, homomorphism1, one_to_one3, single_valued_class1, compose3, omega_is_inductive2, rotate1, choice1, power_class2, regularity2, equal_implies_subclass2, element_relation3, homomorphism6, intersection1, sum_class_definition, inductive2, inductive1, compatible2, sum_class2, subclass_members, cartesian_product2, not_subclass_members2, successor_relation3, domain2, function1, compatible4, intersection3, single_valued_class2, unordered_pair_member, apply, element_relation1, transitivity_of_subclass, operation1, restriction1, cartesian_product3, flip1, homomorphism5, compatible1, unordered_pair2, complement2, operation2, rotate3, one_to_one1, subclass_implies_equal, function2, cantor_class, successor_relation2, corollary_1_to_cartesian_product, restriction2, omega_in_universal, class_elements_are_sets, diagonalisation, intersection2, inductive3, corollary_2_to_unordered_pair, corollary_1_to_unordered_pair, subclass_is_reflexive, homomorphism2, power_class_definition, corollary_2_to_cartesian_product, choice2, unordered_pair3, subset_relation, compose1
% 4.75/2.18 % No. of inferences in proof: 201
% 4.75/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1718 ms resp. 1180 ms w/o parsing
% 4.75/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.75/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------