TSTP Solution File: SEU701^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU701^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YpXgKMny0v true
% Computer : n016.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 19:16:21 EDT 2023
% Result : Theorem 123.17s 16.55s
% Output : Refutation 123.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 106 ( 23 unt; 16 typ; 0 def)
% Number of atoms : 753 ( 222 equ; 75 cnn)
% Maximal formula atoms : 48 ( 8 avg)
% Number of connectives : 1819 ( 144 ~; 107 |; 110 &;1027 @)
% ( 10 <=>; 252 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 14 con; 0-4 aty)
% ( 169 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 440 ( 221 ^; 219 !; 0 ?; 440 :)
% Comments :
%------------------------------------------------------------------------------
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setext_type,type,
setext: $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf('#sk5_type',type,
'#sk5': $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf('#sk7_type',type,
'#sk7': $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#l_lift8238_type',type,
'#l_lift8238': $o > $i > $i > $i > $o ).
thf('#sk9_type',type,
'#sk9': $i ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(iffalseProp1_type,type,
iffalseProp1: $o ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(iffalseProp1,axiom,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
thf('0',plain,
( iffalseProp1
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ X6
=> ( in @ X10
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(in__Cong,axiom,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ) ).
thf('1',plain,
( in__Cong
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ! [X8: $i,X10: $i] :
( ( X8 = X10 )
=> ( ( in @ X8 @ X4 )
<=> ( in @ X10 @ X6 ) ) ) ) ) ),
define([status(thm)]) ).
thf(eqinunit,axiom,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
thf('2',plain,
( eqinunit
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(uniqinunit,axiom,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ).
thf('3',plain,
( uniqinunit
= ( ! [X4: $i,X6: $i] :
( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(setext,axiom,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ) ).
thf('4',plain,
( setext
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( in @ X10 @ X4 ) )
=> ( X4 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrER,axiom,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf('5',plain,
( dsetconstrER
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(iffalseProp2,conjecture,
( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ( in__Cong
=> ( iffalseProp1
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ( ! [X10: $i,X12: $i] :
( ! [X14: $i] :
( ( in @ X14 @ X10 )
=> ( in @ X14 @ X12 ) )
=> ( ! [X16: $i] :
( ( in @ X16 @ X12 )
=> ( in @ X16 @ X10 ) )
=> ( X10 = X12 ) ) )
=> ( ! [X18: $i,X20: $i] :
( ( in @ X18 @ ( setadjoin @ X20 @ emptyset ) )
=> ( X18 = X20 ) )
=> ( ! [X22: $i,X24: $i] :
( ( X22 = X24 )
=> ( in @ X22 @ ( setadjoin @ X24 @ emptyset ) ) )
=> ( ! [X26: $i,X28: $i] :
( ( X26 = X28 )
=> ! [X30: $i,X32: $i] :
( ( X30 = X32 )
=> ( ( in @ X30 @ X26 )
<=> ( in @ X32 @ X28 ) ) ) )
=> ( ! [X34: $i,X36: $o,X38: $i] :
( ( in @ X38 @ X34 )
=> ! [X40: $i] :
( ( in @ X40 @ X34 )
=> ( ~ X36
=> ( in @ X40
@ ( dsetconstr @ X34
@ ^ [V_2: $i] :
( ( ( V_2 = X40 )
& ~ X36 )
| ( ( V_2 = X38 )
& X36 ) ) ) ) ) ) )
=> ! [X42: $i,X44: $o,X46: $i] :
( ( in @ X46 @ X42 )
=> ! [X48: $i] :
( ( in @ X48 @ X42 )
=> ( ~ X44
=> ( ( dsetconstr @ X42
@ ^ [V_3: $i] :
( ( ( V_3 = X48 )
& ~ X44 )
| ( ( V_3 = X46 )
& X44 ) ) )
= ( setadjoin @ X48 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ( ! [X10: $i,X12: $i] :
( ! [X14: $i] :
( ( in @ X14 @ X10 )
=> ( in @ X14 @ X12 ) )
=> ( ! [X16: $i] :
( ( in @ X16 @ X12 )
=> ( in @ X16 @ X10 ) )
=> ( X10 = X12 ) ) )
=> ( ! [X18: $i,X20: $i] :
( ( in @ X18 @ ( setadjoin @ X20 @ emptyset ) )
=> ( X18 = X20 ) )
=> ( ! [X22: $i,X24: $i] :
( ( X22 = X24 )
=> ( in @ X22 @ ( setadjoin @ X24 @ emptyset ) ) )
=> ( ! [X26: $i,X28: $i] :
( ( X26 = X28 )
=> ! [X30: $i,X32: $i] :
( ( X30 = X32 )
=> ( ( in @ X30 @ X26 )
<=> ( in @ X32 @ X28 ) ) ) )
=> ( ! [X34: $i,X36: $o,X38: $i] :
( ( in @ X38 @ X34 )
=> ! [X40: $i] :
( ( in @ X40 @ X34 )
=> ( ~ X36
=> ( in @ X40
@ ( dsetconstr @ X34
@ ^ [V_2: $i] :
( ( ( V_2 = X40 )
& ~ X36 )
| ( ( V_2 = X38 )
& X36 ) ) ) ) ) ) )
=> ! [X42: $i,X44: $o,X46: $i] :
( ( in @ X46 @ X42 )
=> ! [X48: $i] :
( ( in @ X48 @ X42 )
=> ( ~ X44
=> ( ( dsetconstr @ X42
@ ^ [V_3: $i] :
( ( ( V_3 = X48 )
& ~ X44 )
| ( ( V_3 = X46 )
& X44 ) ) )
= ( setadjoin @ X48 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( X2 = Y0 )
=> ( in @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ( X2 = X4 )
=> ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl38,plain,
! [X4: $i] : ( in @ X4 @ ( setadjoin @ X4 @ emptyset ) ),
inference(simplify,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( X2 = Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i] :
( ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) )
=> ( X2 = X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) )
| ( X2 = X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) )
| ( X2 = X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y0 = Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) )
=> ( X2 = Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X4 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X4 ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 )
=> ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ~ ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ~ ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ ( '#sk5' @ X4 @ X2 ) @ X4 )
=> ( in @ ( '#sk5' @ X4 @ X2 ) @ X2 ) )
| ~ ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 )
| ( X2 = X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ ( '#sk5' @ X4 @ X2 ) @ X2 )
| ( X2 = X4 )
| ~ ( in @ ( '#sk5' @ X2 @ X4 ) @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl15,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y2 = Y3 )
=> ( ( in @ Y2 @ Y0 )
<=> ( in @ Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl21,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl27,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl34,plain,
~ ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk6' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk6' )
=> ( ( (~) @ Y0 )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y3: $i] :
( ( ( Y3 = Y2 )
& ( (~) @ Y0 ) )
| ( ( Y3 = Y1 )
& Y0 ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl42,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk6' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk6' )
=> ( ( (~) @ '#sk7' )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ '#sk7' ) )
| ( ( Y2 = Y0 )
& '#sk7' ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl51,plain,
~ ( ( in @ '#sk8' @ '#sk6' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk6' )
=> ( ( (~) @ '#sk7' )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ '#sk7' ) )
| ( ( Y1 = '#sk8' )
& '#sk7' ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl59,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk6' )
=> ( ( (~) @ '#sk7' )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ '#sk7' ) )
| ( ( Y1 = '#sk8' )
& '#sk7' ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl62,plain,
~ ( ( in @ '#sk9' @ '#sk6' )
=> ( ( (~) @ '#sk7' )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk9' )
& ( (~) @ '#sk7' ) )
| ( ( Y0 = '#sk8' )
& '#sk7' ) ) )
= ( setadjoin @ '#sk9' @ emptyset ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl66,plain,
in @ '#sk9' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
=> ( X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl73,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X3
@ ^ [Y1: $i] :
( ( ( Y1 = X2 )
& ( (~) @ X0 ) )
| ( ( Y1 = X1 )
& X0 ) ) ) )
=> ( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl85,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) )
=> ( ( ( X5 = X2 )
& ( (~) @ X0 ) )
| ( ( X5 = X1 )
& X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl86,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( ~ ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) )
| ( ( X5 = X2 )
& ( (~) @ X0 ) )
| ( ( X5 = X1 )
& X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl87,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( ( ( X5 = X2 )
& ( (~) @ X0 ) )
| ( ( X5 = X1 )
& X0 )
| ~ ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl88,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( ( X5 = X2 )
| ~ ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) )
| ( ( X5 = X1 )
& X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl90,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( ( X5 = X2 )
| ~ ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) )
| ( ( X5 = X1 )
& X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl92,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( X0
| ~ ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] :
( ( ( Y0 = X2 )
& ( (~) @ X0 ) )
| ( ( Y0 = X1 )
& X0 ) ) ) )
| ( X5 = X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl26,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( (~) @ Y1 )
=> ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( (~) @ Y0 )
=> ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] :
( ( ( Y3 = Y2 )
& ( (~) @ Y0 ) )
| ( ( Y3 = Y1 )
& Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( (~) @ X4 )
=> ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ X4 ) )
| ( ( Y2 = Y0 )
& X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $o,X6: $i] :
( ( in @ X6 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( (~) @ X4 )
=> ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ X4 ) )
| ( ( Y1 = X6 )
& X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $o,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( (~) @ X4 )
=> ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ X4 ) )
| ( ( Y1 = X6 )
& X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $o,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( (~) @ X4 )
=> ( in @ X8
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( Y0 = X8 )
& ( (~) @ X4 ) )
| ( ( Y0 = X6 )
& X4 ) ) ) ) ) )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $o,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( (~) @ X4 )
=> ( in @ X8
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( Y0 = X8 )
& ( (~) @ X4 ) )
| ( ( Y0 = X6 )
& X4 ) ) ) ) )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $o,X6: $i,X8: $i] :
( X4
| ( in @ X8
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( Y0 = X8 )
& ( (~) @ X4 ) )
| ( ( Y0 = X6 )
& X4 ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl7808,plain,
! [X4: $o,X6: $i,X8: $i,X9: $i] :
( ( '#l_lift8238' @ X4 @ X6 @ X8 @ X9 )
= ( ( ( X9 = X8 )
& ( (~) @ X4 ) )
| ( ( X9 = X6 )
& X4 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7813,plain,
! [X0: $o,X1: $i,X2: $i,X3: $i,X5: $i] :
( X0
| ~ ( in @ X5 @ ( dsetconstr @ X3 @ ( '#l_lift8238' @ X0 @ X1 @ X2 ) ) )
| ( X5 = X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl92,zip_derived_cl7808]) ).
thf(zip_derived_cl67,plain,
~ ( ( (~) @ '#sk7' )
=> ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk9' )
& ( (~) @ '#sk7' ) )
| ( ( Y0 = '#sk8' )
& '#sk7' ) ) )
= ( setadjoin @ '#sk9' @ emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl69,plain,
~ '#sk7',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl70,plain,
( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk9' )
& ( (~) @ '#sk7' ) )
| ( ( Y0 = '#sk8' )
& '#sk7' ) ) )
!= ( setadjoin @ '#sk9' @ emptyset ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl71,plain,
( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk9' )
& ( (~) @ '#sk7' ) )
| ( ( Y0 = '#sk8' )
& '#sk7' ) ) )
!= ( setadjoin @ '#sk9' @ emptyset ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl7808_001,plain,
! [X4: $o,X6: $i,X8: $i,X9: $i] :
( ( '#l_lift8238' @ X4 @ X6 @ X8 @ X9 )
= ( ( ( X9 = X8 )
& ( (~) @ X4 ) )
| ( ( X9 = X6 )
& X4 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7810,plain,
( ( dsetconstr @ '#sk6' @ ( '#l_lift8238' @ '#sk7' @ '#sk8' @ '#sk9' ) )
!= ( setadjoin @ '#sk9' @ emptyset ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl71,zip_derived_cl7808]) ).
thf(zip_derived_cl58,plain,
in @ '#sk8' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl68_002,plain,
! [X2: $i,X4: $o,X6: $i,X8: $i] :
( X4
| ( in @ X8
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( Y0 = X8 )
& ( (~) @ X4 ) )
| ( ( Y0 = X6 )
& X4 ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl294,plain,
! [X0: $i,X1: $o] :
( ~ ( in @ X0 @ '#sk6' )
| ( in @ X0
@ ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] :
( ( ( Y0 = X0 )
& ( (~) @ X1 ) )
| ( ( Y0 = '#sk8' )
& X1 ) ) ) )
| X1 ),
inference('sup-',[status(thm)],[zip_derived_cl58,zip_derived_cl68]) ).
thf(zip_derived_cl7808_003,plain,
! [X4: $o,X6: $i,X8: $i,X9: $i] :
( ( '#l_lift8238' @ X4 @ X6 @ X8 @ X9 )
= ( ( ( X9 = X8 )
& ( (~) @ X4 ) )
| ( ( X9 = X6 )
& X4 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7828,plain,
! [X0: $i,X1: $o] :
( ~ ( in @ X0 @ '#sk6' )
| ( in @ X0 @ ( dsetconstr @ '#sk6' @ ( '#l_lift8238' @ X1 @ '#sk8' @ X0 ) ) )
| X1 ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl294,zip_derived_cl7808]) ).
thf(zip_derived_cl30_004,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) )
| ( X2 = X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( in @ Y0 @ X2 ) ) )
| ( X2 = X4 )
| ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ ( '#sk5' @ X4 @ X2 ) @ X4 )
=> ( in @ ( '#sk5' @ X4 @ X2 ) @ X2 ) )
| ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 )
| ( X2 = X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk5' @ X4 @ X2 ) @ X4 )
| ( X2 = X4 )
| ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl139,plain,
! [X0: $i,X1: $i] :
( ( ( '#sk5' @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= X0 )
| ( in @ ( '#sk5' @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ X1 )
| ( X1
= ( setadjoin @ X0 @ emptyset ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl52]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ ( '#sk5' @ X4 @ X2 ) @ X2 )
| ( X2 = X4 )
| ( in @ ( '#sk5' @ X2 @ X4 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl7833,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl38,zip_derived_cl30,zip_derived_cl55,zip_derived_cl66,zip_derived_cl7813,zip_derived_cl69,zip_derived_cl7810,zip_derived_cl7828,zip_derived_cl139,zip_derived_cl53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU701^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YpXgKMny0v true
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 17:59:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.85/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.85/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 123.17/16.55 % Solved by lams/20_acsne_simpl.sh.
% 123.17/16.55 % done 694 iterations in 15.630s
% 123.17/16.55 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 123.17/16.55 % SZS output start Refutation
% See solution above
% 123.17/16.55
% 123.17/16.55
% 123.17/16.55 % Terminating...
% 123.17/16.64 % Runner terminated.
% 123.17/16.65 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------