TSTP Solution File: SEU053+1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V2H0Afbpa0 true
% Computer : n007.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 : Thu Aug 31 19:10:20 EDT 2023
% Result : Theorem 8.41s 1.80s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 30
% Syntax : Number of formulae : 142 ( 46 unt; 17 typ; 0 def)
% Number of atoms : 276 ( 108 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1070 ( 115 ~; 106 |; 9 &; 804 @)
% ( 3 <=>; 13 =>; 20 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 ^; 126 !; 1 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__2_type,type,
sk__2: $i > $i ).
thf(relation_image_type,type,
relation_image: $i > $i > $i ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(sk__9_type,type,
sk__9: $i ).
thf(function_type,type,
function: $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(sk__1_type,type,
sk__1: $i > $i ).
thf(disjoint_nonempty_type,type,
disjoint_nonempty: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk__14_type,type,
sk__14: $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(relation_type,type,
relation: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(t122_funct_1,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i,C: $i] :
( ( relation_image @ A @ ( set_intersection2 @ B @ C ) )
= ( set_intersection2 @ ( relation_image @ A @ B ) @ ( relation_image @ A @ C ) ) )
=> ( one_to_one @ A ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i,C: $i] :
( ( relation_image @ A @ ( set_intersection2 @ B @ C ) )
= ( set_intersection2 @ ( relation_image @ A @ B ) @ ( relation_image @ A @ C ) ) )
=> ( one_to_one @ A ) ) ),
inference('cnf.neg',[status(esa)],[t122_funct_1]) ).
thf(zip_derived_cl61,plain,
~ ( one_to_one @ sk__14 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(d8_funct_1,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i] :
( ( in @ ( sk__2 @ X0 ) @ ( relation_dom @ X0 ) )
| ( one_to_one @ X0 )
| ~ ( function @ X0 )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[d8_funct_1]) ).
thf(idempotence_k3_xboole_0,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) ).
thf(zip_derived_cl31,plain,
! [X0: $i] :
( ( set_intersection2 @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[idempotence_k3_xboole_0]) ).
thf(t17_zfmisc_1,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( disjoint @ ( singleton @ A ) @ ( singleton @ B ) ) ) ).
thf(zip_derived_cl64,plain,
! [X0: $i,X1: $i] :
( ( disjoint @ ( singleton @ X0 ) @ ( singleton @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf,[status(esa)],[t17_zfmisc_1]) ).
thf(d7_xboole_0,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i] :
( ( ( set_intersection2 @ X0 @ X1 )
= empty_set )
| ~ ( disjoint @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[d7_xboole_0]) ).
thf(zip_derived_cl182,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( ( set_intersection2 @ ( singleton @ X1 ) @ ( singleton @ X0 ) )
= empty_set ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl11]) ).
thf(zip_derived_cl62,plain,
! [X0: $i,X1: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ X1 ) )
= ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i] :
( ( disjoint @ X0 @ X1 )
| ( ( set_intersection2 @ X0 @ X1 )
!= empty_set ) ),
inference(cnf,[status(esa)],[d7_xboole_0]) ).
thf(symmetry_r1_xboole_0,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i] :
( ( disjoint @ X0 @ X1 )
| ~ ( disjoint @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[symmetry_r1_xboole_0]) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: $i] :
( ( ( set_intersection2 @ X1 @ X0 )
!= empty_set )
| ( disjoint @ X0 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl57]) ).
thf(zip_derived_cl11_001,plain,
! [X0: $i,X1: $i] :
( ( ( set_intersection2 @ X0 @ X1 )
= empty_set )
| ~ ( disjoint @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[d7_xboole_0]) ).
thf(zip_derived_cl173,plain,
! [X0: $i,X1: $i] :
( ( ( set_intersection2 @ X0 @ X1 )
!= empty_set )
| ( ( set_intersection2 @ X1 @ X0 )
= empty_set ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl170,zip_derived_cl11]) ).
thf(zip_derived_cl256,plain,
! [X0: $i,X1: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ X1 @ X0 ) )
!= empty_set )
| ( ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) )
= empty_set ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl173]) ).
thf(zip_derived_cl62_002,plain,
! [X0: $i,X1: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ X1 ) )
= ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl403,plain,
! [X0: $i,X1: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ X1 ) )
!= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X1 @ X0 ) )
= empty_set ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl256,zip_derived_cl62]) ).
thf(zip_derived_cl428,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( ( relation_image @ sk__14 @ empty_set )
!= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ X0 ) @ ( singleton @ X1 ) ) )
= empty_set ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl182,zip_derived_cl403]) ).
thf(t149_relat_1,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ empty_set )
= empty_set ) ) ).
thf(zip_derived_cl63,plain,
! [X0: $i] :
( ( ( relation_image @ X0 @ empty_set )
= empty_set )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[t149_relat_1]) ).
thf(zip_derived_cl62_003,plain,
! [X0: $i,X1: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ X1 ) )
= ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl259,plain,
! [X0: $i] :
( ~ ( relation @ sk__14 )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ empty_set ) )
= ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ empty_set ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl63,zip_derived_cl62]) ).
thf(zip_derived_cl59,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(t2_boole,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) ).
thf(zip_derived_cl66,plain,
! [X0: $i] :
( ( set_intersection2 @ X0 @ empty_set )
= empty_set ),
inference(cnf,[status(esa)],[t2_boole]) ).
thf(zip_derived_cl66_004,plain,
! [X0: $i] :
( ( set_intersection2 @ X0 @ empty_set )
= empty_set ),
inference(cnf,[status(esa)],[t2_boole]) ).
thf(zip_derived_cl261,plain,
( ( relation_image @ sk__14 @ empty_set )
= empty_set ),
inference(demod,[status(thm)],[zip_derived_cl259,zip_derived_cl59,zip_derived_cl66,zip_derived_cl66]) ).
thf(zip_derived_cl435,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( empty_set != empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ X0 ) @ ( singleton @ X1 ) ) )
= empty_set ) ),
inference(demod,[status(thm)],[zip_derived_cl428,zip_derived_cl261]) ).
thf(zip_derived_cl436,plain,
! [X0: $i,X1: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ X0 ) @ ( singleton @ X1 ) ) )
= empty_set )
| ( X1 = X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl435]) ).
thf(zip_derived_cl14,plain,
! [X0: $i] :
( ( ( apply @ X0 @ ( sk__1 @ X0 ) )
= ( apply @ X0 @ ( sk__2 @ X0 ) ) )
| ( one_to_one @ X0 )
| ~ ( function @ X0 )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[d8_funct_1]) ).
thf(t117_funct_1,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( relation_image @ B @ ( singleton @ A ) )
= ( singleton @ ( apply @ B @ A ) ) ) ) ) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( relation_dom @ X1 ) )
| ( ( relation_image @ X1 @ ( singleton @ X0 ) )
= ( singleton @ ( apply @ X1 @ X0 ) ) )
| ~ ( function @ X1 )
| ~ ( relation @ X1 ) ),
inference(cnf,[status(esa)],[t117_funct_1]) ).
thf(zip_derived_cl62_005,plain,
! [X0: $i,X1: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ X1 ) )
= ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl357,plain,
! [X0: $i,X1: $i] :
( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ~ ( in @ X0 @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ X0 ) @ X1 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ X0 ) ) @ ( relation_image @ sk__14 @ X1 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl62]) ).
thf(zip_derived_cl59_006,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl361,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ X0 ) @ X1 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ X0 ) ) @ ( relation_image @ sk__14 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl1067,plain,
! [X0: $i] :
( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ( one_to_one @ sk__14 )
| ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl361]) ).
thf(zip_derived_cl59_007,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_008,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl61_009,plain,
~ ( one_to_one @ sk__14 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1078,plain,
! [X0: $i] :
( ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1067,zip_derived_cl59,zip_derived_cl60,zip_derived_cl61]) ).
thf(zip_derived_cl7874,plain,
( ! [X0: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) )
<= ! [X0: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl1078]) ).
thf(zip_derived_cl58_010,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( relation_dom @ X1 ) )
| ( ( relation_image @ X1 @ ( singleton @ X0 ) )
= ( singleton @ ( apply @ X1 @ X0 ) ) )
| ~ ( function @ X1 )
| ~ ( relation @ X1 ) ),
inference(cnf,[status(esa)],[t117_funct_1]) ).
thf(zip_derived_cl256_011,plain,
! [X0: $i,X1: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ X1 @ X0 ) )
!= empty_set )
| ( ( set_intersection2 @ ( relation_image @ sk__14 @ X0 ) @ ( relation_image @ sk__14 @ X1 ) )
= empty_set ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl173]) ).
thf(zip_derived_cl408,plain,
! [X0: $i,X1: $i] :
( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ~ ( in @ X0 @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X1 @ ( singleton @ X0 ) ) )
!= empty_set )
| ( ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ X0 ) ) @ ( relation_image @ sk__14 @ X1 ) )
= empty_set ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl256]) ).
thf(zip_derived_cl59_012,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_013,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl416,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X1 @ ( singleton @ X0 ) ) )
!= empty_set )
| ( ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ X0 ) ) @ ( relation_image @ sk__14 @ X1 ) )
= empty_set ) ),
inference(demod,[status(thm)],[zip_derived_cl408,zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl7915,plain,
( ! [X0: $i] :
( ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set ) )
<= ! [X0: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7874,zip_derived_cl416]) ).
thf(zip_derived_cl15_014,plain,
! [X0: $i] :
( ( in @ ( sk__2 @ X0 ) @ ( relation_dom @ X0 ) )
| ( one_to_one @ X0 )
| ~ ( function @ X0 )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[d8_funct_1]) ).
thf(zip_derived_cl7875,plain,
( ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
<= ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl1078]) ).
thf(zip_derived_cl8009,plain,
( ( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ( one_to_one @ sk__14 ) )
<= ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl7875]) ).
thf(zip_derived_cl59_015,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_016,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8011,plain,
( ( one_to_one @ sk__14 )
<= ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8009,zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl61_017,plain,
~ ( one_to_one @ sk__14 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('0',plain,
in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ),
inference('s_sup-',[status(thm)],[zip_derived_cl8011,zip_derived_cl61]) ).
thf('1',plain,
( ! [X0: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) )
| ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl1078]) ).
thf('2',plain,
! [X0: $i] :
( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= ( set_intersection2 @ ( singleton @ ( apply @ sk__14 @ ( sk__1 @ sk__14 ) ) ) @ ( relation_image @ sk__14 @ X0 ) ) ),
inference('sat_resolution*',[status(thm)],['0','1']) ).
thf(zip_derived_cl8015,plain,
! [X0: $i] :
( ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl7915,'2']) ).
thf(zip_derived_cl8016,plain,
( ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) )
<= ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) ) ),
inference(split,[status(esa)],[zip_derived_cl8015]) ).
thf(zip_derived_cl8019,plain,
( ! [X0: $i] :
( ( ( sk__1 @ sk__14 )
= X0 )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ ( singleton @ X0 ) ) )
= empty_set )
| ( empty_set != empty_set ) )
<= ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl436,zip_derived_cl8016]) ).
thf(zip_derived_cl8035,plain,
( ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ ( singleton @ X0 ) ) )
= empty_set )
| ( ( sk__1 @ sk__14 )
= X0 ) )
<= ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl8019]) ).
thf(zip_derived_cl16,plain,
! [X0: $i] :
( ( in @ ( sk__1 @ X0 ) @ ( relation_dom @ X0 ) )
| ( one_to_one @ X0 )
| ~ ( function @ X0 )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[d8_funct_1]) ).
thf(zip_derived_cl8017,plain,
( ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
<= ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl8015]) ).
thf(zip_derived_cl8052,plain,
( ( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ( one_to_one @ sk__14 ) )
<= ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl8017]) ).
thf(zip_derived_cl59_018,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_019,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8054,plain,
( ( one_to_one @ sk__14 )
<= ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8052,zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl61_020,plain,
~ ( one_to_one @ sk__14 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('3',plain,
in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ),
inference('s_sup-',[status(thm)],[zip_derived_cl8054,zip_derived_cl61]) ).
thf('4',plain,
( ! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) )
| ~ ( in @ ( sk__1 @ sk__14 ) @ ( relation_dom @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl8015]) ).
thf('5',plain,
! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ X0 ) )
= empty_set )
| ( ( relation_image @ sk__14 @ ( set_intersection2 @ X0 @ ( singleton @ ( sk__1 @ sk__14 ) ) ) )
!= empty_set ) ),
inference('sat_resolution*',[status(thm)],['3','4']) ).
thf(zip_derived_cl8195,plain,
! [X0: $i] :
( ( ( relation_image @ sk__14 @ ( set_intersection2 @ ( singleton @ ( sk__2 @ sk__14 ) ) @ ( singleton @ X0 ) ) )
= empty_set )
| ( ( sk__1 @ sk__14 )
= X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl8035,'5']) ).
thf(zip_derived_cl8250,plain,
( ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set )
| ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl31,zip_derived_cl8195]) ).
thf(zip_derived_cl8321,plain,
( ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set )
<= ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set ) ),
inference(split,[status(esa)],[zip_derived_cl8250]) ).
thf(zip_derived_cl58_021,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( relation_dom @ X1 ) )
| ( ( relation_image @ X1 @ ( singleton @ X0 ) )
= ( singleton @ ( apply @ X1 @ X0 ) ) )
| ~ ( function @ X1 )
| ~ ( relation @ X1 ) ),
inference(cnf,[status(esa)],[t117_funct_1]) ).
thf(zip_derived_cl8323,plain,
( ( ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( empty_set
= ( singleton @ ( apply @ sk__14 @ ( sk__2 @ sk__14 ) ) ) )
| ~ ( function @ sk__14 )
| ~ ( relation @ sk__14 ) )
<= ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8321,zip_derived_cl58]) ).
thf(zip_derived_cl60_022,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl59_023,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8355,plain,
( ( ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
| ( empty_set
= ( singleton @ ( apply @ sk__14 @ ( sk__2 @ sk__14 ) ) ) ) )
<= ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set ) ),
inference(demod,[status(thm)],[zip_derived_cl8323,zip_derived_cl60,zip_derived_cl59]) ).
thf(zip_derived_cl12_024,plain,
! [X0: $i,X1: $i] :
( ( disjoint @ X0 @ X1 )
| ( ( set_intersection2 @ X0 @ X1 )
!= empty_set ) ),
inference(cnf,[status(esa)],[d7_xboole_0]) ).
thf(irreflexivity_r1_subset_1,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( disjoint_nonempty @ A @ A ) ) ).
thf(zip_derived_cl32,plain,
! [X0: $i,X1: $i] :
( ~ ( disjoint_nonempty @ X0 @ X0 )
| ( empty @ X0 )
| ( empty @ X1 ) ),
inference(cnf,[status(esa)],[irreflexivity_r1_subset_1]) ).
thf(zip_derived_cl76,plain,
( ! [X0: $i] :
( ( empty @ X0 )
| ~ ( disjoint_nonempty @ X0 @ X0 ) )
<= ! [X0: $i] :
( ( empty @ X0 )
| ~ ( disjoint_nonempty @ X0 @ X0 ) ) ),
inference(split,[status(esa)],[zip_derived_cl32]) ).
thf(zip_derived_cl75,plain,
( ! [X1: $i] : ( empty @ X1 )
<= ! [X1: $i] : ( empty @ X1 ) ),
inference(split,[status(esa)],[zip_derived_cl32]) ).
thf(rc2_relat_1,axiom,
? [A: $i] :
( ( relation @ A )
& ~ ( empty @ A ) ) ).
thf(zip_derived_cl43,plain,
~ ( empty @ sk__9 ),
inference(cnf,[status(esa)],[rc2_relat_1]) ).
thf('6',plain,
~ ! [X1: $i] : ( empty @ X1 ),
inference('s_sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl43]) ).
thf('7',plain,
( ! [X0: $i] :
( ( empty @ X0 )
| ~ ( disjoint_nonempty @ X0 @ X0 ) )
| ! [X1: $i] : ( empty @ X1 ) ),
inference(split,[status(esa)],[zip_derived_cl32]) ).
thf('8',plain,
! [X0: $i] :
( ( empty @ X0 )
| ~ ( disjoint_nonempty @ X0 @ X0 ) ),
inference('sat_resolution*',[status(thm)],['6','7']) ).
thf(zip_derived_cl79,plain,
! [X0: $i] :
( ( empty @ X0 )
| ~ ( disjoint_nonempty @ X0 @ X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl76,'8']) ).
thf(redefinition_r1_subset_1,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ( ( disjoint_nonempty @ A @ B )
<=> ( disjoint @ A @ B ) ) ) ).
thf(zip_derived_cl54,plain,
! [X0: $i,X1: $i] :
( ( empty @ X0 )
| ( empty @ X1 )
| ( disjoint_nonempty @ X0 @ X1 )
| ~ ( disjoint @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[redefinition_r1_subset_1]) ).
thf(zip_derived_cl320,plain,
! [X0: $i] :
( ( empty @ X0 )
| ( empty @ X0 )
| ( empty @ X0 )
| ~ ( disjoint @ X0 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl79,zip_derived_cl54]) ).
thf(zip_derived_cl321,plain,
! [X0: $i] :
( ~ ( disjoint @ X0 @ X0 )
| ( empty @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl320]) ).
thf(zip_derived_cl327,plain,
! [X0: $i] :
( ( ( set_intersection2 @ X0 @ X0 )
!= empty_set )
| ( empty @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl321]) ).
thf(zip_derived_cl31_025,plain,
! [X0: $i] :
( ( set_intersection2 @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[idempotence_k3_xboole_0]) ).
thf(zip_derived_cl330,plain,
! [X0: $i] :
( ( X0 != empty_set )
| ( empty @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl327,zip_derived_cl31]) ).
thf(fc2_subset_1,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ) ).
thf(zip_derived_cl25,plain,
! [X0: $i] :
~ ( empty @ ( singleton @ X0 ) ),
inference(cnf,[status(esa)],[fc2_subset_1]) ).
thf(zip_derived_cl337,plain,
! [X0: $i] :
( ( singleton @ X0 )
!= empty_set ),
inference('s_sup-',[status(thm)],[zip_derived_cl330,zip_derived_cl25]) ).
thf(zip_derived_cl8356,plain,
( ~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) )
<= ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl8355,zip_derived_cl337]) ).
thf(zip_derived_cl8322,plain,
( ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) )
<= ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl8250]) ).
thf(zip_derived_cl13,plain,
! [X0: $i] :
( ( ( sk__1 @ X0 )
!= ( sk__2 @ X0 ) )
| ( one_to_one @ X0 )
| ~ ( function @ X0 )
| ~ ( relation @ X0 ) ),
inference(cnf,[status(esa)],[d8_funct_1]) ).
thf(zip_derived_cl8399,plain,
( ( ( ( sk__1 @ sk__14 )
!= ( sk__1 @ sk__14 ) )
| ( one_to_one @ sk__14 )
| ~ ( function @ sk__14 )
| ~ ( relation @ sk__14 ) )
<= ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl8322,zip_derived_cl13]) ).
thf(zip_derived_cl61_026,plain,
~ ( one_to_one @ sk__14 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_027,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl59_028,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8406,plain,
( ( ( sk__1 @ sk__14 )
!= ( sk__1 @ sk__14 ) )
<= ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8399,zip_derived_cl61,zip_derived_cl60,zip_derived_cl59]) ).
thf('9',plain,
( ( sk__1 @ sk__14 )
!= ( sk__2 @ sk__14 ) ),
inference(simplify,[status(thm)],[zip_derived_cl8406]) ).
thf('10',plain,
( ( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set )
| ( ( sk__1 @ sk__14 )
= ( sk__2 @ sk__14 ) ) ),
inference(split,[status(esa)],[zip_derived_cl8250]) ).
thf('11',plain,
( ( relation_image @ sk__14 @ ( singleton @ ( sk__2 @ sk__14 ) ) )
= empty_set ),
inference('sat_resolution*',[status(thm)],['9','10']) ).
thf(zip_derived_cl8529,plain,
~ ( in @ ( sk__2 @ sk__14 ) @ ( relation_dom @ sk__14 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl8356,'11']) ).
thf(zip_derived_cl8532,plain,
( ~ ( relation @ sk__14 )
| ~ ( function @ sk__14 )
| ( one_to_one @ sk__14 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl8529]) ).
thf(zip_derived_cl59_029,plain,
relation @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60_030,plain,
function @ sk__14,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8534,plain,
one_to_one @ sk__14,
inference(demod,[status(thm)],[zip_derived_cl8532,zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl8538,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl61,zip_derived_cl8534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.V2H0Afbpa0 true
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 13:38:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.89/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.89/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.89/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.89/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.89/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.89/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 8.41/1.80 % Solved by fo/fo1_av.sh.
% 8.41/1.80 % done 1078 iterations in 1.022s
% 8.41/1.80 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.41/1.80 % SZS output start Refutation
% See solution above
% 8.41/1.80
% 8.41/1.80
% 8.41/1.81 % Terminating...
% 8.75/1.86 % Runner terminated.
% 8.75/1.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------