TSTP Solution File: SET755+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 11:54:14 EDT 2023
% Result : Theorem 5.62s 2.37s
% Output : Refutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 59
% Syntax : Number of formulae : 90 ( 3 unt; 30 typ; 0 def)
% Number of atoms : 411 ( 18 equ; 0 cnn)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 1441 ( 7 ~; 6 |; 194 &;1083 @)
% ( 30 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 2 con; 0-6 aty)
% Number of variables : 322 ( 0 ^; 293 !; 29 ?; 322 :)
% Comments :
%------------------------------------------------------------------------------
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(inverse_image2_type,type,
inverse_image2: $i > $i > $i ).
thf(equal_maps_type,type,
equal_maps: $i > $i > $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i > $o ).
thf(compose_function_type,type,
compose_function: $i > $i > $i > $i > $i > $i ).
thf(increasing_type,type,
increasing: $i > $i > $i > $i > $i > $o ).
thf(injective_type,type,
injective: $i > $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(inverse_predicate_type,type,
inverse_predicate: $i > $i > $i > $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(inverse_function_type,type,
inverse_function: $i > $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(one_to_one_type,type,
one_to_one: $i > $i > $i > $o ).
thf(surjective_type,type,
surjective: $i > $i > $i > $o ).
thf(product_type,type,
product: $i > $i ).
thf(compose_predicate_type,type,
compose_predicate: $i > $i > $i > $i > $i > $i > $o ).
thf(decreasing_type,type,
decreasing: $i > $i > $i > $i > $i > $o ).
thf(image2_type,type,
image2: $i > $i > $i ).
thf(inverse_image3_type,type,
inverse_image3: $i > $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(identity_type,type,
identity: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(image3_type,type,
image3: $i > $i > $i > $i ).
thf(isomorphism_type,type,
isomorphism: $i > $i > $i > $i > $i > $o ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( compose_predicate @ A @ B @ C @ D @ E @ F )
<=> ! [G: $i,H: $i] :
( ( ( member @ G @ D )
& ( member @ H @ F ) )
=> ( ( apply @ A @ G @ H )
<=> ? [I: $i] :
( ( member @ I @ E )
& ( apply @ C @ G @ I )
& ( apply @ B @ I @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_predicate) ).
thf(153,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( compose_predicate @ A @ B @ C @ D @ E @ F )
=> ! [G: $i,H: $i] :
( ( ( member @ G @ D )
& ( member @ H @ F ) )
=> ( ( ( apply @ A @ G @ H )
=> ? [I: $i] :
( ( member @ I @ E )
& ( apply @ C @ G @ I )
& ( apply @ B @ I @ H ) ) )
& ( ? [I: $i] :
( ( member @ I @ E )
& ( apply @ C @ G @ I )
& ( apply @ B @ I @ H ) )
=> ( apply @ A @ G @ H ) ) ) ) )
& ( ! [G: $i,H: $i] :
( ( ( member @ G @ D )
& ( member @ H @ F ) )
=> ( ( ( apply @ A @ G @ H )
=> ? [I: $i] :
( ( member @ I @ E )
& ( apply @ C @ G @ I )
& ( apply @ B @ I @ H ) ) )
& ( ? [I: $i] :
( ( member @ I @ E )
& ( apply @ C @ G @ I )
& ( apply @ B @ I @ H ) )
=> ( apply @ A @ G @ H ) ) ) )
=> ( compose_predicate @ A @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( equal_maps @ A @ B @ C @ D )
<=> ! [E: $i,F: $i,G: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D )
& ( member @ G @ D ) )
=> ( ( ( apply @ A @ E @ F )
& ( apply @ B @ E @ G ) )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_maps) ).
thf(37,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( equal_maps @ A @ B @ C @ D )
=> ! [E: $i,F: $i,G: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D )
& ( member @ G @ D ) )
=> ( ( ( apply @ A @ E @ F )
& ( apply @ B @ E @ G ) )
=> ( F = G ) ) ) )
& ( ! [E: $i,F: $i,G: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D )
& ( member @ G @ D ) )
=> ( ( ( apply @ A @ E @ F )
& ( apply @ B @ E @ G ) )
=> ( F = G ) ) )
=> ( equal_maps @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( isomorphism @ A @ B @ C @ D @ E )
<=> ( ( maps @ A @ B @ D )
& ( one_to_one @ A @ B @ D )
& ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( ( apply @ C @ F @ H )
<=> ( apply @ E @ G @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isomorphism) ).
thf(248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( isomorphism @ A @ B @ C @ D @ E )
=> ( ( maps @ A @ B @ D )
& ( one_to_one @ A @ B @ D )
& ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( ( ( apply @ C @ F @ H )
=> ( apply @ E @ G @ I ) )
& ( ( apply @ E @ G @ I )
=> ( apply @ C @ F @ H ) ) ) ) ) )
& ( ( ( maps @ A @ B @ D )
& ( one_to_one @ A @ B @ D )
& ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( ( ( apply @ C @ F @ H )
=> ( apply @ E @ G @ I ) )
& ( ( apply @ E @ G @ I )
=> ( apply @ C @ F @ H ) ) ) ) )
=> ( isomorphism @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(317,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( power_set @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( member @ A @ ( power_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(311,plain,
! [A: $i,B: $i] :
( ( ( equal_set @ A @ B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( equal_set @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( member @ F @ C )
& ( member @ G @ E ) )
=> ( ( apply @ ( compose_function @ A @ B @ C @ D @ E ) @ F @ G )
<=> ? [H: $i] :
( ( member @ H @ D )
& ( apply @ B @ F @ H )
& ( apply @ A @ H @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_function) ).
thf(54,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( member @ F @ C )
& ( member @ G @ E ) )
=> ( ( ( apply @ ( compose_function @ A @ B @ C @ D @ E ) @ F @ G )
=> ? [H: $i] :
( ( member @ H @ D )
& ( apply @ B @ F @ H )
& ( apply @ A @ H @ G ) ) )
& ( ? [H: $i] :
( ( member @ H @ D )
& ( apply @ B @ F @ H )
& ( apply @ A @ H @ G ) )
=> ( apply @ ( compose_function @ A @ B @ C @ D @ E ) @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( one_to_one @ A @ B @ C )
<=> ( ( injective @ A @ B @ C )
& ( surjective @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one) ).
thf(140,plain,
! [A: $i,B: $i,C: $i] :
( ( ( one_to_one @ A @ B @ C )
=> ( ( injective @ A @ B @ C )
& ( surjective @ A @ B @ C ) ) )
& ( ( ( injective @ A @ B @ C )
& ( surjective @ A @ B @ C ) )
=> ( one_to_one @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(95,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ C )
& ( subset @ E @ C )
& ( subset @ D @ E ) )
=> ( subset @ ( inverse_image2 @ A @ D ) @ ( inverse_image2 @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa05) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ C )
& ( subset @ E @ C )
& ( subset @ D @ E ) )
=> ( subset @ ( inverse_image2 @ A @ D ) @ ( inverse_image2 @ A @ E ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ C )
& ( subset @ E @ C )
& ( subset @ D @ E ) )
=> ( subset @ ( inverse_image2 @ A @ D ) @ ( inverse_image2 @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( surjective @ A @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ C )
=> ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjective) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( surjective @ A @ B @ C )
=> ! [D: $i] :
( ( member @ D @ C )
=> ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) ) )
& ( ! [D: $i] :
( ( member @ D @ C )
=> ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) )
=> ( surjective @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( inverse_predicate @ A @ B @ C @ D )
<=> ! [E: $i,F: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D ) )
=> ( ( apply @ B @ E @ F )
<=> ( apply @ A @ F @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_predicate) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( inverse_predicate @ A @ B @ C @ D )
=> ! [E: $i,F: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D ) )
=> ( ( ( apply @ B @ E @ F )
=> ( apply @ A @ F @ E ) )
& ( ( apply @ A @ F @ E )
=> ( apply @ B @ E @ F ) ) ) ) )
& ( ! [E: $i,F: $i] :
( ( ( member @ E @ C )
& ( member @ F @ D ) )
=> ( ( ( apply @ B @ E @ F )
=> ( apply @ A @ F @ E ) )
& ( ( apply @ A @ F @ E )
=> ( apply @ B @ E @ F ) ) ) )
=> ( inverse_predicate @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum @ B ) )
<=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(235,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( sum @ B ) )
=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) )
& ( ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( sum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( inverse_image2 @ A @ B ) )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( inverse_image2 @ A @ B ) )
=> ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ C @ D ) ) )
& ( ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( member @ C @ ( inverse_image2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
<=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( difference @ C @ B ) )
=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) )
& ( ( ( member @ A @ C )
& ~ ( member @ A @ B ) )
=> ( member @ A @ ( difference @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( A = B )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(120,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( A = B )
| ( A = C ) ) )
& ( ( ( A = B )
| ( A = C ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( image2 @ A @ B ) )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
thf(202,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( image2 @ A @ B ) )
=> ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ D @ C ) ) )
& ( ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ D @ C ) )
=> ( member @ C @ ( image2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( union @ B @ C ) )
<=> ( ( member @ A @ B )
| ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(228,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( union @ B @ C ) )
=> ( ( member @ A @ B )
| ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
| ( member @ A @ C ) )
=> ( member @ A @ ( union @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( injective @ A @ B @ C )
<=> ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ F )
& ( apply @ A @ E @ F ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injective) ).
thf(78,plain,
! [A: $i,B: $i,C: $i] :
( ( ( injective @ A @ B @ C )
=> ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ F )
& ( apply @ A @ E @ F ) )
=> ( D = E ) ) ) )
& ( ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ B )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ F )
& ( apply @ A @ E @ F ) )
=> ( D = E ) ) )
=> ( injective @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( identity @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( ( identity @ A @ B )
=> ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) ) )
& ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
=> ( identity @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( singleton @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( member @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( increasing @ A @ B @ C @ D @ E )
<=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ G @ I ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',increasing_function) ).
thf(59,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( increasing @ A @ B @ C @ D @ E )
=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ G @ I ) ) )
& ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ G @ I ) )
=> ( increasing @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( maps @ A @ B @ C )
<=> ( ! [D: $i] :
( ( member @ D @ B )
=> ? [E: $i] :
( ( member @ E @ C )
& ( apply @ A @ D @ E ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ C )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ E )
& ( apply @ A @ D @ F ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
thf(281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( maps @ A @ B @ C )
=> ( ! [D: $i] :
( ( member @ D @ B )
=> ? [E: $i] :
( ( member @ E @ C )
& ( apply @ A @ D @ E ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ C )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ E )
& ( apply @ A @ D @ F ) )
=> ( E = F ) ) ) ) )
& ( ( ! [D: $i] :
( ( member @ D @ B )
=> ? [E: $i] :
( ( member @ E @ C )
& ( apply @ A @ D @ E ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( member @ D @ B )
& ( member @ E @ C )
& ( member @ F @ C ) )
=> ( ( ( apply @ A @ D @ E )
& ( apply @ A @ D @ F ) )
=> ( E = F ) ) ) )
=> ( maps @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(274,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
<=> ( ( member @ A @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( intersection @ B @ C ) )
=> ( ( member @ A @ B )
& ( member @ A @ C ) ) )
& ( ( ( member @ A @ B )
& ( member @ A @ C ) )
=> ( member @ A @ ( intersection @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ D @ ( inverse_image3 @ A @ B @ C ) )
<=> ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image3) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ D @ ( inverse_image3 @ A @ B @ C ) )
=> ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ D @ E ) ) ) )
& ( ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ D @ E ) ) )
=> ( member @ D @ ( inverse_image3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ C ) )
=> ( ( apply @ A @ D @ E )
<=> ( apply @ ( inverse_function @ A @ B @ C ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_function) ).
thf(130,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( member @ D @ B )
& ( member @ E @ C ) )
=> ( ( ( apply @ A @ D @ E )
=> ( apply @ ( inverse_function @ A @ B @ C ) @ E @ D ) )
& ( ( apply @ ( inverse_function @ A @ B @ C ) @ E @ D )
=> ( apply @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( member @ D @ ( image3 @ A @ B @ C ) )
<=> ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image3) ).
thf(241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( member @ D @ ( image3 @ A @ B @ C ) )
=> ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) ) )
& ( ( ( member @ D @ C )
& ? [E: $i] :
( ( member @ E @ B )
& ( apply @ A @ E @ D ) ) )
=> ( member @ D @ ( image3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( product @ B ) )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( ( member @ A @ ( product @ B ) )
=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) )
& ( ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) )
=> ( member @ A @ ( product @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( decreasing @ A @ B @ C @ D @ E )
<=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ I @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decreasing_function) ).
thf(183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( decreasing @ A @ B @ C @ D @ E )
=> ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ I @ G ) ) )
& ( ! [F: $i,G: $i,H: $i,I: $i] :
( ( ( member @ F @ B )
& ( member @ G @ D )
& ( member @ H @ B )
& ( member @ I @ D )
& ( apply @ C @ F @ H )
& ( apply @ A @ F @ G )
& ( apply @ A @ H @ I ) )
=> ( apply @ E @ I @ G ) )
=> ( decreasing @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(328,plain,
$false,
inference(cvc4,[status(thm)],[153,37,248,317,311,54,140,95,31,175,104,235,305,215,120,202,228,78,221,133,59,281,274,98,208,130,241,146,183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 18:21:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.96 % [INFO] Parsing done (137ms).
% 1.23/0.97 % [INFO] Running in sequential loop mode.
% 1.67/1.17 % [INFO] eprover registered as external prover.
% 1.67/1.17 % [INFO] cvc4 registered as external prover.
% 1.67/1.18 % [INFO] Scanning for conjecture ...
% 2.05/1.24 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.05/1.29 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.38/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.36 % [INFO] Type checking passed.
% 2.38/1.36 % [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 ...
% 5.62/2.36 % External prover 'cvc4' found a proof!
% 5.62/2.36 % [INFO] Killing All external provers ...
% 5.62/2.36 % Time passed: 1856ms (effective reasoning time: 1390ms)
% 5.62/2.36 % 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)>
% 5.62/2.37 % Axioms used in derivation (28): power_set, unordered_pair, inverse_image3, union, intersection, one_to_one, surjective, injective, increasing_function, image2, identity, difference, sum, product, empty_set, inverse_predicate, isomorphism, decreasing_function, image3, subset, equal_maps, inverse_function, equal_set, compose_function, inverse_image2, singleton, maps, compose_predicate
% 5.62/2.37 % No. of inferences in proof: 60
% 5.62/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1856 ms resp. 1390 ms w/o parsing
% 5.99/2.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.99/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------