TSTP Solution File: NUM609+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Zsn2C3QXZJ true
% Computer : n011.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 12:42:43 EDT 2023
% Result : Theorem 21.71s 3.78s
% Output : Refutation 22.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 129 ( 36 unt; 15 typ; 0 def)
% Number of atoms : 460 ( 96 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1066 ( 123 ~; 99 |; 85 &; 629 @)
% ( 31 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-2 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 160 ( 54 ^; 106 !; 0 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(xQ_type,type,
xQ: $i ).
thf(xP_type,type,
xP: $i ).
thf(isCountable0_type,type,
isCountable0: $i > $o ).
thf(aElement0_type,type,
aElement0: $i > $o ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(slcrc0_type,type,
slcrc0: $i ).
thf(xO_type,type,
xO: $i ).
thf(xp_type,type,
xp: $i ).
thf(szNzAzT0_type,type,
szNzAzT0: $i ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i > $i > $i ).
thf(m__5106,axiom,
aSubsetOf0 @ xQ @ szNzAzT0 ).
thf(zip_derived_cl100,plain,
aSubsetOf0 @ xQ @ szNzAzT0,
inference(cnf,[status(esa)],[m__5106]) ).
thf(mDefSub,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
<=> ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) )
& ( aSet0 @ W1 ) ) ) ) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( ( aSet0 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( aSubsetOf0 @ Y1 @ Y0 )
<=> ( ( !!
@ ^ [Y2: $i] :
( ( aElementOf0 @ Y2 @ Y1 )
=> ( aElementOf0 @ Y2 @ Y0 ) ) )
& ( aSet0 @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[mDefSub]) ).
thf(zip_derived_cl217,plain,
! [X2: $i] :
( ( aSet0 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( aSubsetOf0 @ Y0 @ X2 )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
=> ( aElementOf0 @ Y1 @ X2 ) ) )
& ( aSet0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl218,plain,
! [X2: $i] :
( ~ ( aSet0 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( aSubsetOf0 @ Y0 @ X2 )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
=> ( aElementOf0 @ Y1 @ X2 ) ) )
& ( aSet0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl217]) ).
thf(zip_derived_cl219,plain,
! [X2: $i,X4: $i] :
( ( ( aSubsetOf0 @ X4 @ X2 )
<=> ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) ) )
| ~ ( aSet0 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl218]) ).
thf(zip_derived_cl220,plain,
! [X2: $i,X4: $i] :
( ( ( aSubsetOf0 @ X4 @ X2 )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) ) )
| ~ ( aSet0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl227,plain,
! [X2: $i,X4: $i] :
( ~ ( aSubsetOf0 @ X4 @ X2 )
| ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) )
| ~ ( aSet0 @ X2 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl476,plain,
! [X2: $i,X4: $i] :
( ( aSet0 @ X4 )
| ~ ( aSet0 @ X2 )
| ~ ( aSubsetOf0 @ X4 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl489,plain,
( ( aSet0 @ xQ )
| ~ ( aSet0 @ szNzAzT0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl100,zip_derived_cl476]) ).
thf(mNATSet,axiom,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ) ).
thf(zip_derived_cl22,plain,
( ( aSet0 @ szNzAzT0 )
& ( isCountable0 @ szNzAzT0 ) ),
inference(cnf,[status(esa)],[mNATSet]) ).
thf(zip_derived_cl128,plain,
aSet0 @ szNzAzT0,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl494,plain,
aSet0 @ xQ,
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl128]) ).
thf(m__5164,axiom,
( ( aSet0 @ xP )
& ( xP
= ( sdtmndt0 @ xQ @ ( szmzizndt0 @ xQ ) ) ) ) ).
thf(zip_derived_cl103,plain,
( ( aSet0 @ xP )
& ( xP
= ( sdtmndt0 @ xQ @ ( szmzizndt0 @ xQ ) ) ) ),
inference(cnf,[status(esa)],[m__5164]) ).
thf(m__5147,axiom,
( xp
= ( szmzizndt0 @ xQ ) ) ).
thf(zip_derived_cl102,plain,
( xp
= ( szmzizndt0 @ xQ ) ),
inference(cnf,[status(esa)],[m__5147]) ).
thf(zip_derived_cl255,plain,
( ( aSet0 @ xP )
& ( xP
= ( sdtmndt0 @ xQ @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl103,zip_derived_cl102]) ).
thf(zip_derived_cl256,plain,
aSet0 @ xP,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl220_001,plain,
! [X2: $i,X4: $i] :
( ( ( aSubsetOf0 @ X4 @ X2 )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) ) )
| ~ ( aSet0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl226,plain,
! [X2: $i,X4: $i] :
( ( aSubsetOf0 @ X4 @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) )
| ~ ( aSet0 @ X2 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl235,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
| ~ ( aSet0 @ X4 )
| ~ ( aSet0 @ X2 )
| ( aSubsetOf0 @ X4 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl226]) ).
thf(zip_derived_cl236,plain,
! [X2: $i,X4: $i] :
( ~ ( ( aElementOf0 @ ( '#sk2' @ X2 @ X4 ) @ X4 )
=> ( aElementOf0 @ ( '#sk2' @ X2 @ X4 ) @ X2 ) )
| ( aSubsetOf0 @ X4 @ X2 )
| ~ ( aSet0 @ X2 )
| ~ ( aSet0 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl235]) ).
thf(zip_derived_cl237,plain,
! [X2: $i,X4: $i] :
( ( aElementOf0 @ ( '#sk2' @ X2 @ X4 ) @ X4 )
| ~ ( aSet0 @ X4 )
| ~ ( aSet0 @ X2 )
| ( aSubsetOf0 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl236]) ).
thf(zip_derived_cl262,plain,
! [X0: $i] :
( ( aElementOf0 @ ( '#sk2' @ X0 @ xP ) @ xP )
| ~ ( aSet0 @ X0 )
| ( aSubsetOf0 @ xP @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl256,zip_derived_cl237]) ).
thf(zip_derived_cl4238,plain,
( ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xP )
| ( aSubsetOf0 @ xP @ xQ ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl494,zip_derived_cl262]) ).
thf(m__,conjecture,
aSubsetOf0 @ xP @ xQ ).
thf(zf_stmt_0,negated_conjecture,
~ ( aSubsetOf0 @ xP @ xQ ),
inference('cnf.neg',[status(esa)],[m__]) ).
thf(zip_derived_cl106,plain,
~ ( aSubsetOf0 @ xP @ xQ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4240,plain,
aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xP,
inference(demod,[status(thm)],[zip_derived_cl4238,zip_derived_cl106]) ).
thf(zip_derived_cl4240_002,plain,
aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xP,
inference(demod,[status(thm)],[zip_derived_cl4238,zip_derived_cl106]) ).
thf(mEOfElem,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( ( aSet0 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
=> ( aElement0 @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[mEOfElem]) ).
thf(zip_derived_cl112,plain,
! [X2: $i] :
( ( aSet0 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( aElement0 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl113,plain,
! [X2: $i] :
( ~ ( aSet0 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( aElement0 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl114,plain,
! [X2: $i,X4: $i] :
( ( ( aElementOf0 @ X4 @ X2 )
=> ( aElement0 @ X4 ) )
| ~ ( aSet0 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl115,plain,
! [X2: $i,X4: $i] :
( ~ ( aElementOf0 @ X4 @ X2 )
| ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl4241,plain,
( ( aElement0 @ ( '#sk2' @ xQ @ xP ) )
| ~ ( aSet0 @ xP ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4240,zip_derived_cl115]) ).
thf(zip_derived_cl256_003,plain,
aSet0 @ xP,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl4250,plain,
aElement0 @ ( '#sk2' @ xQ @ xP ),
inference(demod,[status(thm)],[zip_derived_cl4241,zip_derived_cl256]) ).
thf(zip_derived_cl257,plain,
( xP
= ( sdtmndt0 @ xQ @ xp ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl258,plain,
( xP
= ( sdtmndt0 @ xQ @ xp ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl257]) ).
thf(mDefDiff,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W1 )
& ( aSet0 @ W0 ) )
=> ! [W2: $i] :
( ( W2
= ( sdtmndt0 @ W0 @ W1 ) )
<=> ( ! [W3: $i] :
( ( aElementOf0 @ W3 @ W2 )
<=> ( ( W3 != W1 )
& ( aElementOf0 @ W3 @ W0 )
& ( aElement0 @ W3 ) ) )
& ( aSet0 @ W2 ) ) ) ) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( aElement0 @ Y1 )
& ( aSet0 @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( Y2
= ( sdtmndt0 @ Y0 @ Y1 ) )
<=> ( ( !!
@ ^ [Y3: $i] :
( ( aElementOf0 @ Y3 @ Y2 )
<=> ( ( Y3 != Y1 )
& ( aElementOf0 @ Y3 @ Y0 )
& ( aElement0 @ Y3 ) ) ) )
& ( aSet0 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[mDefDiff]) ).
thf(zip_derived_cl578,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( aElement0 @ Y0 )
& ( aSet0 @ X2 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y1
= ( sdtmndt0 @ X2 @ Y0 ) )
<=> ( ( !!
@ ^ [Y2: $i] :
( ( aElementOf0 @ Y2 @ Y1 )
<=> ( ( Y2 != Y0 )
& ( aElementOf0 @ Y2 @ X2 )
& ( aElement0 @ Y2 ) ) ) )
& ( aSet0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl579,plain,
! [X2: $i,X4: $i] :
( ( ( aElement0 @ X4 )
& ( aSet0 @ X2 ) )
=> ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( sdtmndt0 @ X2 @ X4 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
<=> ( ( Y1 != X4 )
& ( aElementOf0 @ Y1 @ X2 )
& ( aElement0 @ Y1 ) ) ) )
& ( aSet0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl578]) ).
thf(zip_derived_cl580,plain,
! [X2: $i,X4: $i] :
( ~ ( ( aElement0 @ X4 )
& ( aSet0 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( sdtmndt0 @ X2 @ X4 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
<=> ( ( Y1 != X4 )
& ( aElementOf0 @ Y1 @ X2 )
& ( aElement0 @ Y1 ) ) ) )
& ( aSet0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl579]) ).
thf(zip_derived_cl581,plain,
! [X2: $i,X4: $i] :
( ~ ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( sdtmndt0 @ X2 @ X4 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ Y0 )
<=> ( ( Y1 != X4 )
& ( aElementOf0 @ Y1 @ X2 )
& ( aElement0 @ Y1 ) ) ) )
& ( aSet0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl580]) ).
thf(zip_derived_cl582,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( X6
= ( sdtmndt0 @ X2 @ X4 ) )
<=> ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X6 )
<=> ( ( Y0 != X4 )
& ( aElementOf0 @ Y0 @ X2 )
& ( aElement0 @ Y0 ) ) ) )
& ( aSet0 @ X6 ) ) )
| ~ ( aSet0 @ X2 )
| ~ ( aElement0 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl581]) ).
thf(zip_derived_cl583,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( X6
= ( sdtmndt0 @ X2 @ X4 ) )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X6 )
<=> ( ( Y0 != X4 )
& ( aElementOf0 @ Y0 @ X2 )
& ( aElement0 @ Y0 ) ) ) )
& ( aSet0 @ X6 ) ) )
| ~ ( aSet0 @ X2 )
| ~ ( aElement0 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl582]) ).
thf(zip_derived_cl592,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
!= ( sdtmndt0 @ X2 @ X4 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X6 )
<=> ( ( Y0 != X4 )
& ( aElementOf0 @ Y0 @ X2 )
& ( aElement0 @ Y0 ) ) ) )
& ( aSet0 @ X6 ) )
| ~ ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl583]) ).
thf(zip_derived_cl597,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
!= ( sdtmndt0 @ X2 @ X4 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X6 )
<=> ( ( Y0 != X4 )
& ( aElementOf0 @ Y0 @ X2 )
& ( aElement0 @ Y0 ) ) ) )
& ( aSet0 @ X6 ) )
| ~ ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl592]) ).
thf(zip_derived_cl1026,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X6 )
<=> ( ( Y0 != X4 )
& ( aElementOf0 @ Y0 @ X2 )
& ( aElement0 @ Y0 ) ) ) )
| ~ ( aSet0 @ X2 )
| ~ ( aElement0 @ X4 )
| ( X6
!= ( sdtmndt0 @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl597]) ).
thf(zip_derived_cl1028,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( aElementOf0 @ X8 @ X6 )
<=> ( ( X8 != X4 )
& ( aElementOf0 @ X8 @ X2 )
& ( aElement0 @ X8 ) ) )
| ( X6
!= ( sdtmndt0 @ X2 @ X4 ) )
| ~ ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1026]) ).
thf(zip_derived_cl1029,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( aElementOf0 @ X8 @ X6 )
= ( ( X8 != X4 )
& ( aElementOf0 @ X8 @ X2 )
& ( aElement0 @ X8 ) ) )
| ( X6
!= ( sdtmndt0 @ X2 @ X4 ) )
| ~ ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1028]) ).
thf(zip_derived_cl1040,plain,
! [X0: $i,X1: $i] :
( ( ( aElementOf0 @ X1 @ X0 )
= ( ( X1 != xp )
& ( aElementOf0 @ X1 @ xQ )
& ( aElement0 @ X1 ) ) )
| ( X0 != xP )
| ~ ( aElement0 @ xp )
| ~ ( aSet0 @ xQ ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl258,zip_derived_cl1029]) ).
thf(m__5182,axiom,
aElementOf0 @ xp @ xO ).
thf(zip_derived_cl105,plain,
aElementOf0 @ xp @ xO,
inference(cnf,[status(esa)],[m__5182]) ).
thf(zip_derived_cl115_004,plain,
! [X2: $i,X4: $i] :
( ~ ( aElementOf0 @ X4 @ X2 )
| ( aElement0 @ X4 )
| ~ ( aSet0 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl122,plain,
( ( aElement0 @ xp )
| ~ ( aSet0 @ xO ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl115]) ).
thf(m__4908,axiom,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ) ).
thf(zip_derived_cl95,plain,
( ( aSet0 @ xO )
& ( isCountable0 @ xO ) ),
inference(cnf,[status(esa)],[m__4908]) ).
thf(zip_derived_cl158,plain,
aSet0 @ xO,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl166,plain,
aElement0 @ xp,
inference(demod,[status(thm)],[zip_derived_cl122,zip_derived_cl158]) ).
thf(zip_derived_cl494_005,plain,
aSet0 @ xQ,
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl128]) ).
thf(zip_derived_cl1053,plain,
! [X0: $i,X1: $i] :
( ( ( aElementOf0 @ X1 @ X0 )
= ( ( X1 != xp )
& ( aElementOf0 @ X1 @ xQ )
& ( aElement0 @ X1 ) ) )
| ( X0 != xP ) ),
inference(demod,[status(thm)],[zip_derived_cl1040,zip_derived_cl166,zip_derived_cl494]) ).
thf(zip_derived_cl17189,plain,
! [X0: $i] :
( ( ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ X0 )
= ( ( ( '#sk2' @ xQ @ xP )
!= xp )
& ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xQ )
& $true ) )
| ( X0 != xP ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4250,zip_derived_cl1053]) ).
thf(zip_derived_cl4240_006,plain,
aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xP,
inference(demod,[status(thm)],[zip_derived_cl4238,zip_derived_cl106]) ).
thf(zip_derived_cl256_007,plain,
aSet0 @ xP,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl220_008,plain,
! [X2: $i,X4: $i] :
( ( ( aSubsetOf0 @ X4 @ X2 )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X4 )
=> ( aElementOf0 @ Y0 @ X2 ) ) )
& ( aSet0 @ X4 ) ) )
| ~ ( aSet0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl261,plain,
! [X0: $i] :
( ( ( aSubsetOf0 @ xP @ X0 )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ xP )
=> ( aElementOf0 @ Y0 @ X0 ) ) )
& $true ) )
| ~ ( aSet0 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl256,zip_derived_cl220]) ).
thf(zip_derived_cl265,plain,
! [X0: $i] :
( ( ( aSubsetOf0 @ xP @ X0 )
= ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ xP )
=> ( aElementOf0 @ Y0 @ X0 ) ) ) )
| ~ ( aSet0 @ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl261]) ).
thf(zip_derived_cl4305,plain,
! [X0: $i] :
( ( ( aSubsetOf0 @ xP @ X0 )
= ( ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ xP )
=> ( aElementOf0 @ Y0 @ X0 ) )
@ ( '#sk2' @ X0 @ xP ) ) )
| ~ ( aSet0 @ X0 ) ),
inference(quantifier_rw,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl4306,plain,
! [X0: $i] :
( ( ( aSubsetOf0 @ xP @ X0 )
= ( ( aElementOf0 @ ( '#sk2' @ X0 @ xP ) @ xP )
=> ( aElementOf0 @ ( '#sk2' @ X0 @ xP ) @ X0 ) ) )
| ~ ( aSet0 @ X0 ) ),
inference(rw,[status(thm)],[zip_derived_cl4305]) ).
thf(zip_derived_cl4310,plain,
( ( ( aSubsetOf0 @ xP @ xQ )
= ( $true
=> ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xQ ) ) )
| ~ ( aSet0 @ xQ ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4240,zip_derived_cl4306]) ).
thf(zip_derived_cl106_009,plain,
~ ( aSubsetOf0 @ xP @ xQ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl494_010,plain,
aSet0 @ xQ,
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl128]) ).
thf(zip_derived_cl4315,plain,
~ ( $true
=> ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xQ ) ),
inference(demod,[status(thm)],[zip_derived_cl4310,zip_derived_cl106,zip_derived_cl494]) ).
thf(zip_derived_cl4316,plain,
~ ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ xQ ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl4315]) ).
thf(zip_derived_cl17242,plain,
! [X0: $i] :
( ( ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ X0 )
= ( ( ( '#sk2' @ xQ @ xP )
!= xp )
& $false
& $true ) )
| ( X0 != xP ) ),
inference(demod,[status(thm)],[zip_derived_cl17189,zip_derived_cl4316]) ).
thf(zip_derived_cl100_011,plain,
aSubsetOf0 @ xQ @ szNzAzT0,
inference(cnf,[status(esa)],[m__5106]) ).
thf(mDefMin,axiom,
! [W0: $i] :
( ( ( W0 != slcrc0 )
& ( aSubsetOf0 @ W0 @ szNzAzT0 ) )
=> ! [W1: $i] :
( ( W1
= ( szmzizndt0 @ W0 ) )
<=> ( ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( sdtlseqdt0 @ W1 @ W2 ) )
& ( aElementOf0 @ W1 @ W0 ) ) ) ) ).
thf(zip_derived_cl46,plain,
( !!
@ ^ [Y0: $i] :
( ( ( Y0 != slcrc0 )
& ( aSubsetOf0 @ Y0 @ szNzAzT0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y1
= ( szmzizndt0 @ Y0 ) )
<=> ( ( !!
@ ^ [Y2: $i] :
( ( aElementOf0 @ Y2 @ Y0 )
=> ( sdtlseqdt0 @ Y1 @ Y2 ) ) )
& ( aElementOf0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[mDefMin]) ).
thf(zip_derived_cl1244,plain,
! [X2: $i] :
( ( ( X2 != slcrc0 )
& ( aSubsetOf0 @ X2 @ szNzAzT0 ) )
=> ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( szmzizndt0 @ X2 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ X2 )
=> ( sdtlseqdt0 @ Y0 @ Y1 ) ) )
& ( aElementOf0 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl1245,plain,
! [X2: $i] :
( ~ ( ( X2 != slcrc0 )
& ( aSubsetOf0 @ X2 @ szNzAzT0 ) )
| ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( szmzizndt0 @ X2 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ X2 )
=> ( sdtlseqdt0 @ Y0 @ Y1 ) ) )
& ( aElementOf0 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1244]) ).
thf(zip_derived_cl1246,plain,
! [X2: $i] :
( ( X2 != slcrc0 )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 )
| ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( szmzizndt0 @ X2 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ X2 )
=> ( sdtlseqdt0 @ Y0 @ Y1 ) ) )
& ( aElementOf0 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1245]) ).
thf(zip_derived_cl1247,plain,
! [X2: $i] :
( ( X2 = slcrc0 )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 )
| ( !!
@ ^ [Y0: $i] :
( ( Y0
= ( szmzizndt0 @ X2 ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( ( aElementOf0 @ Y1 @ X2 )
=> ( sdtlseqdt0 @ Y0 @ Y1 ) ) )
& ( aElementOf0 @ Y0 @ X2 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1246]) ).
thf(zip_derived_cl1248,plain,
! [X2: $i,X4: $i] :
( ( ( X4
= ( szmzizndt0 @ X2 ) )
<=> ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( sdtlseqdt0 @ X4 @ Y0 ) ) )
& ( aElementOf0 @ X4 @ X2 ) ) )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 )
| ( X2 = slcrc0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1247]) ).
thf(zip_derived_cl1249,plain,
! [X2: $i,X4: $i] :
( ( ( X4
= ( szmzizndt0 @ X2 ) )
= ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( sdtlseqdt0 @ X4 @ Y0 ) ) )
& ( aElementOf0 @ X4 @ X2 ) ) )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 )
| ( X2 = slcrc0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1248]) ).
thf(zip_derived_cl1271,plain,
! [X2: $i,X4: $i] :
( ( X4
!= ( szmzizndt0 @ X2 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( sdtlseqdt0 @ X4 @ Y0 ) ) )
& ( aElementOf0 @ X4 @ X2 ) )
| ( X2 = slcrc0 )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl1249]) ).
thf(zip_derived_cl1276,plain,
! [X2: $i,X4: $i] :
( ( X4
!= ( szmzizndt0 @ X2 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( aElementOf0 @ Y0 @ X2 )
=> ( sdtlseqdt0 @ X4 @ Y0 ) ) )
& ( aElementOf0 @ X4 @ X2 ) )
| ( X2 = slcrc0 )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1271]) ).
thf(zip_derived_cl1469,plain,
! [X2: $i,X4: $i] :
( ( aElementOf0 @ X4 @ X2 )
| ~ ( aSubsetOf0 @ X2 @ szNzAzT0 )
| ( X2 = slcrc0 )
| ( X4
!= ( szmzizndt0 @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1276]) ).
thf(zip_derived_cl1476,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ xQ )
| ( xQ = slcrc0 )
| ( X0
!= ( szmzizndt0 @ xQ ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl100,zip_derived_cl1469]) ).
thf(zip_derived_cl102_012,plain,
( xp
= ( szmzizndt0 @ xQ ) ),
inference(cnf,[status(esa)],[m__5147]) ).
thf(zip_derived_cl1481,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ xQ )
| ( xQ = slcrc0 )
| ( X0 != xp ) ),
inference(demod,[status(thm)],[zip_derived_cl1476,zip_derived_cl102]) ).
thf(m__5093,axiom,
( ( aSubsetOf0 @ xQ @ xO )
& ( xQ != slcrc0 ) ) ).
thf(zip_derived_cl99,plain,
( ( aSubsetOf0 @ xQ @ xO )
& ( xQ != slcrc0 ) ),
inference(cnf,[status(esa)],[m__5093]) ).
thf(zip_derived_cl206,plain,
xQ != slcrc0,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl207,plain,
xQ != slcrc0,
inference('simplify nested equalities',[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl1482,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ xQ )
| ( X0 != xp ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1481,zip_derived_cl207]) ).
thf(zip_derived_cl238,plain,
! [X2: $i,X4: $i] :
( ~ ( aElementOf0 @ ( '#sk2' @ X2 @ X4 ) @ X2 )
| ~ ( aSet0 @ X4 )
| ~ ( aSet0 @ X2 )
| ( aSubsetOf0 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl236]) ).
thf(zip_derived_cl1514,plain,
! [X0: $i] :
( ( ( '#sk2' @ xQ @ X0 )
!= xp )
| ~ ( aSet0 @ X0 )
| ~ ( aSet0 @ xQ )
| ( aSubsetOf0 @ X0 @ xQ ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1482,zip_derived_cl238]) ).
thf(zip_derived_cl494_013,plain,
aSet0 @ xQ,
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl128]) ).
thf(zip_derived_cl1525,plain,
! [X0: $i] :
( ( ( '#sk2' @ xQ @ X0 )
!= xp )
| ~ ( aSet0 @ X0 )
| ( aSubsetOf0 @ X0 @ xQ ) ),
inference(demod,[status(thm)],[zip_derived_cl1514,zip_derived_cl494]) ).
thf(zip_derived_cl106_014,plain,
~ ( aSubsetOf0 @ xP @ xQ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2848,plain,
( ~ ( aSet0 @ xP )
| ( ( '#sk2' @ xQ @ xP )
!= xp ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1525,zip_derived_cl106]) ).
thf(zip_derived_cl256_015,plain,
aSet0 @ xP,
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl2862,plain,
( ( '#sk2' @ xQ @ xP )
!= xp ),
inference(demod,[status(thm)],[zip_derived_cl2848,zip_derived_cl256]) ).
thf(zip_derived_cl17243,plain,
! [X0: $i] :
( ( ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ X0 )
= ( $true
& $false
& $true ) )
| ( X0 != xP ) ),
inference(inner_simplify_reflect,[status(thm)],[zip_derived_cl17242,zip_derived_cl2862]) ).
thf(zip_derived_cl17244,plain,
! [X0: $i] :
( ~ ( aElementOf0 @ ( '#sk2' @ xQ @ xP ) @ X0 )
| ( X0 != xP ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl17243]) ).
thf(zip_derived_cl17267,plain,
xP != xP,
inference('s_sup-',[status(thm)],[zip_derived_cl4240,zip_derived_cl17244]) ).
thf(zip_derived_cl17269,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl17267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Zsn2C3QXZJ true
% 0.13/0.34 % Computer : n011.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 : Fri Aug 25 17:54:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.21/0.62 % Total configuration time : 435
% 0.21/0.62 % Estimated wc time : 1092
% 0.21/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.48/0.81 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 21.71/3.78 % Solved by fo/fo1_lcnf.sh.
% 21.71/3.78 % done 2922 iterations in 2.926s
% 21.71/3.78 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 21.71/3.78 % SZS output start Refutation
% See solution above
% 22.22/3.78
% 22.22/3.78
% 22.22/3.78 % Terminating...
% 22.22/3.85 % Runner terminated.
% 22.22/3.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------