TSTP Solution File: SET763+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:54:15 EDT 2023
% Result : Theorem 29.69s 5.93s
% Output : Refutation 29.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 68
% Syntax : Number of formulae : 193 ( 48 unt; 39 typ; 0 def)
% Number of atoms : 617 ( 92 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 2169 ( 101 ~; 55 |; 205 &;1637 @)
% ( 30 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 6 con; 0-6 aty)
% Number of variables : 561 ( 0 ^; 531 !; 30 ?; 561 :)
% Comments :
%------------------------------------------------------------------------------
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(equal_set_type,type,
equal_set: $i > $i > $o ).
thf(image2_type,type,
image2: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $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(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(injective_type,type,
injective: $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(inverse_image3_type,type,
inverse_image3: $i > $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(inverse_image2_type,type,
inverse_image2: $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(power_set_type,type,
power_set: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i > $i > $i ).
thf(sk32_type,type,
sk32: $i > $i > $i ).
thf(sk40_type,type,
sk40: $i > $i > $i ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
thf(211,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)],[19]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',compose_predicate) ).
thf(132,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)],[13]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ B )
& ( equal_set @ ( image2 @ A @ D ) @ empty_set ) )
=> ( equal_set @ D @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa13) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ B )
& ( equal_set @ ( image2 @ A @ D ) @ empty_set ) )
=> ( equal_set @ D @ empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( maps @ A @ B @ C )
& ( subset @ D @ B )
& ( equal_set @ ( image2 @ A @ D ) @ empty_set ) )
=> ( equal_set @ D @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
equal_set @ ( image2 @ sk1 @ sk4 ) @ empty_set,
inference(cnf,[status(esa)],[31]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
<=> ( ( A = B )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(99,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)],[8]) ).
thf(100,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( unordered_pair @ B @ C ) )
=> ( ( A = B )
| ( A = C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( A = C ) )
=> ( member @ A @ ( unordered_pair @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[99]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(107,plain,
! [B: $i,A: $i] : ( member @ B @ ( unordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[106]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
<=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(205,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)],[18]) ).
thf(206,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( difference @ C @ B ) )
=> ( ( member @ A @ C )
& ~ ( member @ A @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ C )
& ~ ( member @ A @ B ) )
=> ( member @ A @ ( difference @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[205]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( difference @ C @ B ) )
| ~ ( member @ A @ B ) ),
inference(cnf,[status(esa)],[206]) ).
thf(347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ E @ D ) )
| ( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[107,209]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ C @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( unordered_pair @ F @ G ))]]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ C @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(32,plain,
~ ( equal_set @ sk4 @ empty_set ),
inference(cnf,[status(esa)],[31]) ).
thf(321,plain,
( ( equal_set @ ( image2 @ sk1 @ sk4 ) @ empty_set )
!= ( equal_set @ sk4 @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[33,32]) ).
thf(322,plain,
( ( ( image2 @ sk1 @ sk4 )
!= sk4 )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
( ( image2 @ sk1 @ sk4 )
!= sk4 ),
inference(simp,[status(thm)],[322]) ).
thf(35,plain,
maps @ sk1 @ sk2 @ sk3,
inference(cnf,[status(esa)],[31]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(310,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(10,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(112,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)],[10]) ).
thf(113,plain,
( ! [A: $i,B: $i] :
( ( member @ A @ ( singleton @ B ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( member @ A @ ( singleton @ B ) ) ) ),
inference(miniscope,[status(thm)],[112]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( singleton @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[113]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( member @ A @ ( singleton @ B ) ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(493,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( singleton @ B ) )
| ( A != sk4 )
| ( B
!= ( image2 @ sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[118,323]) ).
thf(494,plain,
! [A: $i] :
( ~ ( member @ A @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( A )),bind(B,$thf( image2 @ sk1 @ sk4 ))]]) ).
thf(730,plain,
~ ( member @ sk4 @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( identity @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(217,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)],[20]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(276,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(114,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( singleton @ B ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( singleton @ B ) ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(117,plain,
! [A: $i] : ( member @ A @ ( singleton @ A ) ),
inference(simp,[status(thm)],[116]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ B @ ( difference @ D @ C ) )
| ( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[117,209]) ).
thf(338,plain,
! [B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( singleton @ B ) ) ),
inference(pattern_uni,[status(thm)],[337:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( singleton @ E ))]]) ).
thf(357,plain,
! [B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( singleton @ B ) ) ),
inference(simp,[status(thm)],[338]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ C @ ( difference @ B @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,357]) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( singleton @ A )
!= ( difference @ B @ ( singleton @ C ) ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( difference @ A @ ( singleton @ B ) )
!= ( singleton @ B ) ),
inference(simp,[status(thm)],[368]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( product @ B ) )
<=> ! [C: $i] :
( ( member @ C @ B )
=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(125,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)],[12]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( singleton @ B ) )
| ( B != sk4 )
| ( A
!= ( image2 @ sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[118,323]) ).
thf(488,plain,
! [A: $i] :
( ~ ( member @ ( image2 @ sk1 @ sk4 ) @ ( singleton @ A ) )
| ( A != sk4 ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( image2 @ sk1 @ sk4 )),bind(B,$thf( B ))]]) ).
thf(727,plain,
~ ( member @ ( image2 @ sk1 @ sk4 ) @ ( singleton @ sk4 ) ),
inference(simp,[status(thm)],[488]) ).
thf(761,plain,
! [A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ ( image2 @ sk1 @ sk4 ) @ ( singleton @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[117,727]) ).
thf(790,plain,
! [A: $i] :
( ( A
!= ( image2 @ sk1 @ sk4 ) )
| ( ( singleton @ A )
!= ( singleton @ sk4 ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(800,plain,
( ( singleton @ ( image2 @ sk1 @ sk4 ) )
!= ( singleton @ sk4 ) ),
inference(simp,[status(thm)],[790]) ).
thf(854,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( singleton @ B ) )
| ( B
!= ( singleton @ sk4 ) )
| ( A
!= ( singleton @ ( image2 @ sk1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,800]) ).
thf(855,plain,
! [A: $i] :
( ~ ( member @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( singleton @ ( image2 @ sk1 @ sk4 ) )),bind(B,$thf( B ))]]) ).
thf(870,plain,
~ ( member @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) @ ( singleton @ ( singleton @ sk4 ) ) ),
inference(simp,[status(thm)],[855]) ).
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/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
thf(36,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(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 ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ! [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(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( apply @ B @ ( sk5 @ D @ C @ B @ A ) @ ( sk7 @ D @ C @ B @ A ) )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[37]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( apply @ B @ ( sk5 @ D @ C @ B @ A ) @ ( sk7 @ D @ C @ B @ A ) )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(simp,[status(thm)],[38]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( power_set @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(316,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(28,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(307,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( image2 @ A @ B ) )
<=> ? [D: $i] :
( ( member @ D @ B )
& ( apply @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
thf(270,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)],[25]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(cnf,[status(esa)],[100]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( member @ A @ ( unordered_pair @ B @ C ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(105,plain,
! [B: $i,A: $i] : ( member @ A @ ( unordered_pair @ A @ B ) ),
inference(simp,[status(thm)],[104]) ).
thf(308,plain,
~ ? [A: $i] : ( member @ A @ empty_set ),
inference(miniscope,[status(thm)],[307]) ).
thf(309,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(cnf,[status(esa)],[308]) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[105,309]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( unordered_pair @ A @ B )
!= empty_set ) ),
inference(simp,[status(thm)],[327]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ B @ A )
!= empty_set ),
inference(simp,[status(thm)],[328]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( union @ B @ C ) )
<=> ( ( member @ A @ B )
| ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(224,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)],[21]) ).
thf(862,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( singleton @ B ) )
| ( A
!= ( singleton @ sk4 ) )
| ( B
!= ( singleton @ ( image2 @ sk1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[118,800]) ).
thf(863,plain,
! [A: $i] :
( ~ ( member @ A @ ( singleton @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) ) )
| ( A
!= ( singleton @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( A )),bind(B,$thf( singleton @ ( image2 @ sk1 @ sk4 ) ))]]) ).
thf(874,plain,
~ ( member @ ( singleton @ sk4 ) @ ( singleton @ ( singleton @ ( image2 @ sk1 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[863]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',injective) ).
thf(188,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)],[17]) ).
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/sandbox2/benchmark/theBenchmark.p',compose_function) ).
thf(53,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(9,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/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
thf(109,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)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
<=> ( ( member @ A @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(77,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)],[6]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',image3) ).
thf(237,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)],[23]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',isomorphism) ).
thf(244,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)],[24]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( sk6 @ D @ C @ B @ A ) @ D )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[37]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( sk6 @ D @ C @ B @ A ) @ D )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(simp,[status(thm)],[42]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,357]) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( singleton @ D ) ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ A @ C )
!= ( difference @ B @ ( singleton @ C ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(34,plain,
subset @ sk4 @ sk2,
inference(cnf,[status(esa)],[31]) ).
thf(277,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[276]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( member @ ( sk40 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[277]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( member @ ( sk40 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[278]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ B @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[107,309]) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( unordered_pair @ A @ B )
!= empty_set ) ),
inference(simp,[status(thm)],[333]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[334]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',inverse_image3) ).
thf(181,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)],[16]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',decreasing_function) ).
thf(162,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)],[15]) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ E @ D ) )
| ( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[105,209]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( unordered_pair @ F @ G ))]]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
~ ( member @ B @ ( difference @ A @ ( unordered_pair @ B @ C ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(154,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)],[14]) ).
thf(218,plain,
( ! [A: $i,B: $i] :
( ( identity @ A @ B )
=> ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
=> ( identity @ A @ B ) ) ),
inference(miniscope,[status(thm)],[217]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( member @ ( sk32 @ B @ A ) @ B )
| ( identity @ A @ B ) ),
inference(cnf,[status(esa)],[218]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( member @ ( sk32 @ B @ A ) @ B )
| ( identity @ A @ B ) ),
inference(simp,[status(thm)],[219]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( identity @ A @ B )
| ( ( member @ ( sk32 @ B @ A ) @ B )
!= ( member @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[222,309]) ).
thf(382,plain,
! [A: $i] : ( identity @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( E )),bind(B,$thf( empty_set )),bind(C,$thf( sk32 @ empty_set @ E ))]]) ).
thf(386,plain,
! [A: $i] : ( identity @ A @ empty_set ),
inference(simp,[status(thm)],[382]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( member @ A @ ( sum @ B ) )
<=> ? [C: $i] :
( ( member @ C @ B )
& ( member @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(231,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)],[22]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( one_to_one @ A @ B @ C )
<=> ( ( injective @ A @ B @ C )
& ( surjective @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
thf(119,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)],[11]) ).
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/sandbox2/benchmark/theBenchmark.p',increasing_function) ).
thf(58,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(425,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( member @ ( sk40 @ B @ A ) @ A )
!= ( member @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[281,309]) ).
thf(426,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( sk40 @ D @ empty_set ))]]) ).
thf(432,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(simp,[status(thm)],[426]) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( unordered_pair @ A @ B ) )
!= ( member @ D @ ( difference @ C @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,357]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( unordered_pair @ A @ B )
!= ( difference @ C @ ( singleton @ D ) ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ C @ A )
!= ( difference @ B @ ( singleton @ C ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ C @ ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,359]) ).
thf(395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( singleton @ A )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( unordered_pair @ B @ C ) )
!= ( singleton @ B ) ),
inference(simp,[status(thm)],[395]) ).
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/sandbox2/benchmark/theBenchmark.p',maps) ).
thf(283,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(403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ D @ ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[117,362]) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( singleton @ A )
!= ( difference @ B @ ( unordered_pair @ C @ D ) ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( unordered_pair @ B @ C ) )
!= ( singleton @ C ) ),
inference(simp,[status(thm)],[410]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( singleton @ A ) )
!= ( member @ B @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[117,309]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( singleton @ A )
!= empty_set ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[325]) ).
thf(330,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( equal_maps @ A @ B @ C @ D )
| ( ( member @ ( sk6 @ D @ C @ B @ A ) @ D )
!= ( member @ E @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[45,309]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] : ( equal_maps @ C @ B @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( empty_set )),bind(E,$thf( sk6 @ empty_set @ G @ H @ I ))]]) ).
thf(332,plain,
! [C: $i,B: $i,A: $i] : ( equal_maps @ C @ B @ A @ empty_set ),
inference(simp,[status(thm)],[331]) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( sk7 @ D @ C @ B @ A ) @ D )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[37]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ ( sk7 @ D @ C @ B @ A ) @ D )
| ( equal_maps @ A @ B @ C @ D ) ),
inference(simp,[status(thm)],[41]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',inverse_predicate) ).
thf(83,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)],[7]) ).
thf(5399,plain,
$false,
inference(e,[status(thm)],[211,132,33,362,323,35,310,730,217,276,372,125,357,870,46,316,307,117,270,329,224,874,188,53,109,77,237,205,105,244,45,375,32,34,118,281,335,181,162,209,112,359,31,154,727,386,231,99,800,119,58,432,36,373,400,283,415,326,107,332,47,83,309,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.04/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 18:53:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.83/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/0.97 % [INFO] Parsing done (143ms).
% 1.30/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.20 % [INFO] eprover registered as external prover.
% 1.71/1.20 % [INFO] cvc4 registered as external prover.
% 1.71/1.21 % [INFO] Scanning for conjecture ...
% 1.86/1.27 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.08/1.32 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.27/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.40 % [INFO] Type checking passed.
% 2.27/1.40 % [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 ...
% 29.69/5.91 % External prover 'e' found a proof!
% 29.69/5.91 % [INFO] Killing All external provers ...
% 29.69/5.92 % Time passed: 5435ms (effective reasoning time: 4939ms)
% 29.69/5.92 % 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)>
% 29.69/5.93 % 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
% 29.69/5.93 % No. of inferences in proof: 154
% 29.69/5.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5435 ms resp. 4939 ms w/o parsing
% 29.71/5.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.71/5.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------