%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET004^4 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n029.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 : Wed Feb 25 09:30:54 AM UTC 2026
% Result : Theorem 1.97s 1.52s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 125 ( 58 unt; 0 typ; 6 def)
% Number of atoms : 831 ( 136 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1203 ( 74 ~; 64 |; 31 &; 962 @)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 14 con; 0-3 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 224 ( 198 ^; 26 !; 0 ?; 224 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_16,type,
equal_set: $i > $i > mworld > $o ).
thf(func_def_17,type,
member: $i > $i > mworld > $o ).
thf(func_def_18,type,
subset: $i > $i > mworld > $o ).
thf(func_def_19,type,
singleton: $i > $i ).
thf(func_def_20,type,
product: $i > $i ).
thf(func_def_21,type,
unordered_pair: $i > $i > $i ).
thf(func_def_22,type,
intersection: $i > $i > $i ).
thf(func_def_23,type,
difference: $i > $i > $i ).
thf(func_def_24,type,
sum: $i > $i ).
thf(func_def_25,type,
union: $i > $i > $i ).
thf(func_def_26,type,
power_set: $i > $i ).
thf(func_def_45,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f639,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f463,f522,f545,f556,f592,f615,f638]) ).
thf(f638,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f637]) ).
thf(f637,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f636]) ).
thf(f636,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f609,f587]) ).
thf(f587,plain,
( ( $false
= ( member @ sK5 @ sK2 @ mactual ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f585]) ).
thf(f585,definition,
( spl0_5
<=> ( $false
= ( member @ sK5 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f609,plain,
( ( $true
= ( member @ sK5 @ sK2 @ mactual ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f608]) ).
thf(f608,plain,
( ( ( ( member @ sK5 @ sK1 @ mactual )
& ( member @ sK5 @ sK2 @ mactual ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f605]) ).
thf(f605,plain,
( ( ( $true
= ( ( member @ sK5 @ sK1 @ mactual )
& ( member @ sK5 @ sK2 @ mactual ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f420,f571]) ).
thf(f571,plain,
( ( $true
= ( member @ sK5 @ ( intersection @ sK2 @ sK1 ) @ mactual ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f569,plain,
( ( $false
= ( ( member @ sK5 @ ( intersection @ sK2 @ sK1 ) @ mactual )
=> ( member @ sK5 @ ( intersection @ sK1 @ sK2 ) @ mactual ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f568]) ).
thf(f568,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual ) )
@ sK5 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f567]) ).
thf(f567,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f566]) ).
thf(f566,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f557]) ).
thf(f557,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual ) ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f296,f458]) ).
thf(f458,plain,
( ( $false
= ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f456]) ).
thf(f456,definition,
( spl0_1
<=> ( $false
= ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f295]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f294]) ).
thf(f294,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f293]) ).
thf(f293,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f292]) ).
thf(f292,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f202]) ).
thf(f202,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f164,f150,f159,f159,f179,f159,f160]) ).
thf(f160,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
thf(f87,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mimplies_def) ).
thf(f179,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
thf(f69,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mequiv_def) ).
thf(f159,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
thf(f134,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f133]) ).
thf(f133,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mforall_di_def) ).
thf(f150,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
thf(f110,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mlocal_def) ).
thf(f164,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f76]) ).
thf(f76,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] :
( mequiv @ ( subset @ X1 @ X3 )
@ ( mforall_di
@ ^ [X6: $i] : ( mimplies @ ( member @ X6 @ X1 ) @ ( member @ X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',subset_0) ).
thf(f420,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( member @ X1 @ ( intersection @ X2 @ X3 ) @ mactual )
= ( ( member @ X1 @ X3 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f419]) ).
thf(f419,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( member @ X1 @ ( intersection @ X2 @ Y0 ) @ mactual )
= ( ( member @ X1 @ Y0 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f418]) ).
thf(f418,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ X1 @ ( intersection @ X2 @ Y0 ) @ mactual )
= ( ( member @ X1 @ Y0 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f417]) ).
thf(f417,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( member @ X1 @ ( intersection @ Y0 @ Y1 ) @ mactual )
= ( ( member @ X1 @ Y1 @ mactual )
& ( member @ X1 @ Y0 @ mactual ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f416]) ).
thf(f416,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( member @ X1 @ ( intersection @ Y0 @ Y1 ) @ mactual )
= ( ( member @ X1 @ Y1 @ mactual )
& ( member @ X1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f415]) ).
thf(f415,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) @ mactual )
= ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f414]) ).
thf(f414,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) @ mactual )
= ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f203]) ).
thf(f203,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f165,f150,f159,f159,f159,f179,f157]) ).
thf(f157,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
thf(f83,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f82]) ).
thf(f82,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mand_def) ).
thf(f165,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) ) @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f109]) ).
thf(f109,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) ) @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f108]) ).
thf(f108,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( member @ X0 @ ( intersection @ X1 @ X2 ) ) @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
( mlocal
@ ( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( member @ X6 @ ( intersection @ X1 @ X3 ) ) @ ( mand @ ( member @ X6 @ X1 ) @ ( member @ X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',intersection_0) ).
thf(f615,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f614]) ).
thf(f614,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f613]) ).
thf(f613,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f610,f591]) ).
thf(f591,plain,
( ( ( member @ sK5 @ sK1 @ mactual )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f589]) ).
thf(f589,definition,
( spl0_6
<=> ( ( member @ sK5 @ sK1 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f610,plain,
( ( ( member @ sK5 @ sK1 @ mactual )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f608]) ).
thf(f592,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f580,f456,f589,f585]) ).
thf(f580,plain,
( ( ( member @ sK5 @ sK1 @ mactual )
= $false )
| ( $false
= ( member @ sK5 @ sK2 @ mactual ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f579]) ).
thf(f579,plain,
( ( $false
= ( ( member @ sK5 @ sK2 @ mactual )
& ( member @ sK5 @ sK1 @ mactual ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f578]) ).
thf(f578,plain,
( ( ( ~ ( ( member @ sK5 @ sK2 @ mactual )
& ( member @ sK5 @ sK1 @ mactual ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f572]) ).
thf(f572,plain,
( ( ( $false
= ( ( member @ sK5 @ sK2 @ mactual )
& ( member @ sK5 @ sK1 @ mactual ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f420,f570]) ).
thf(f570,plain,
( ( $false
= ( member @ sK5 @ ( intersection @ sK1 @ sK2 ) @ mactual ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f556,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f555]) ).
thf(f555,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f554]) ).
thf(f554,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f540,f521]) ).
thf(f521,plain,
( ( $false
= ( member @ sK4 @ sK1 @ mactual ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f519]) ).
thf(f519,definition,
( spl0_4
<=> ( $false
= ( member @ sK4 @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f540,plain,
( ( ( member @ sK4 @ sK1 @ mactual )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f539]) ).
thf(f539,plain,
( ( ( ( member @ sK4 @ sK2 @ mactual )
& ( member @ sK4 @ sK1 @ mactual ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f535]) ).
thf(f535,plain,
( ( ( $true
= ( ( member @ sK4 @ sK2 @ mactual )
& ( member @ sK4 @ sK1 @ mactual ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f420,f501]) ).
thf(f501,plain,
( ( ( member @ sK4 @ ( intersection @ sK1 @ sK2 ) @ mactual )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
( ( $false
= ( ( member @ sK4 @ ( intersection @ sK1 @ sK2 ) @ mactual )
=> ( member @ sK4 @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f498]) ).
thf(f498,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual ) )
@ sK4 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f495]) ).
thf(f495,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ sK2 ) @ mactual )
=> ( member @ Y0 @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f296,f462]) ).
thf(f462,plain,
( ( ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f460]) ).
thf(f460,definition,
( spl0_2
<=> ( ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f545,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f544]) ).
thf(f544,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f543]) ).
thf(f543,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f541,f517]) ).
thf(f517,plain,
( ( $false
= ( member @ sK4 @ sK2 @ mactual ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f515]) ).
thf(f515,definition,
( spl0_3
<=> ( $false
= ( member @ sK4 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f541,plain,
( ( ( member @ sK4 @ sK2 @ mactual )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f539]) ).
thf(f522,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f510,f460,f519,f515]) ).
thf(f510,plain,
( ( $false
= ( member @ sK4 @ sK2 @ mactual ) )
| ( $false
= ( member @ sK4 @ sK1 @ mactual ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f509]) ).
thf(f509,plain,
( ( $false
= ( ( member @ sK4 @ sK1 @ mactual )
& ( member @ sK4 @ sK2 @ mactual ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f508]) ).
thf(f508,plain,
( ( ( ~ ( ( member @ sK4 @ sK1 @ mactual )
& ( member @ sK4 @ sK2 @ mactual ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f502]) ).
thf(f502,plain,
( ( ( $false
= ( ( member @ sK4 @ sK1 @ mactual )
& ( member @ sK4 @ sK2 @ mactual ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f420,f500]) ).
thf(f500,plain,
( ( $false
= ( member @ sK4 @ ( intersection @ sK2 @ sK1 ) @ mactual ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f499]) ).
thf(f463,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f454,f460,f456]) ).
thf(f454,plain,
( ( $false
= ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual ) )
| ( ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual )
& ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( ~ ( ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual )
& ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f451]) ).
thf(f451,plain,
( ( $false
= ( ( subset @ ( intersection @ sK2 @ sK1 ) @ ( intersection @ sK1 @ sK2 ) @ mactual )
& ( subset @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual ) ) )
= $true ),
inference(superposition,[status(thm)],[f323,f235]) ).
thf(f235,plain,
( $false
= ( equal_set @ ( intersection @ sK1 @ sK2 ) @ ( intersection @ sK2 @ sK1 ) @ mactual ) ),
inference(beta_eta_normalization,[status(thm)],[f234]) ).
thf(f234,plain,
( $false
= ( ^ [Y0: $i] : ( equal_set @ ( intersection @ sK1 @ Y0 ) @ ( intersection @ Y0 @ sK1 ) @ mactual )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ sK1 @ Y0 ) @ ( intersection @ Y0 @ sK1 ) @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f232]) ).
thf(f232,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) @ mactual ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) @ mactual ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f183,f150,f159,f159]) ).
thf(f183,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f137]) ).
thf(f137,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f81]) ).
thf(f81,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( equal_set @ ( intersection @ Y0 @ Y1 ) @ ( intersection @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f80]) ).
thf(f80,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( equal_set @ ( intersection @ X0 @ X1 ) @ ( intersection @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( equal_set @ ( intersection @ X1 @ X3 ) @ ( intersection @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
thf(f45,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( equal_set @ ( intersection @ X1 @ X3 ) @ ( intersection @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',thI06) ).
thf(f323,plain,
! [X2: $i,X1: $i] :
( ( ( equal_set @ X1 @ X2 @ mactual )
= ( ( subset @ X2 @ X1 @ mactual )
& ( subset @ X1 @ X2 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f322]) ).
thf(f322,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f321]) ).
thf(f321,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f320]) ).
thf(f320,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f319]) ).
thf(f319,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f195]) ).
thf(f195,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( equal_set @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f153,f150,f159,f159,f179,f157]) ).
thf(f153,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f89]) ).
thf(f89,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f88]) ).
thf(f88,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( equal_set @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( equal_set @ X1 @ X3 ) @ ( mand @ ( subset @ X1 @ X3 ) @ ( subset @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',equal_set_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET004^4 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:48:29 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET004^4 : TPTP v9.2.1. Released v8.1.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPTP problem SET013+4.p with axiomatized equality
% 0.31/0.46 % Version : [BP13] axioms.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.31/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.31/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.31/0.46 % Source : [TPTP]
% 0.31/0.46 % Names : SET013+1 [QMLTP]
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0
% 0.31/0.46 % Syntax : Number of formulae : 71 ( 11 unt; 26 typ; 10 def)
% 0.31/0.46 % Number of atoms : 270 ( 10 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 10 ( 6 avg)
% 0.31/0.46 % Number of connectives : 460 ( 1 ~; 1 |; 3 &; 451 @)
% 0.31/0.46 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 14 ( 9 avg)
% 0.31/0.46 % Number of types : 3 ( 1 usr)
% 0.31/0.46 % Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 26 ( 25 usr; 2 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 117 ( 109 ^; 6 !; 2 ?; 117 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.31/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.31/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.31/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.31/0.46 % $modalities == $modal_system_S4].
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(mworld,type,
% 0.31/0.46 mworld: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_type,type,
% 0.31/0.46 mrel: mworld > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mactual_type,type,
% 0.31/0.46 mactual: mworld ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_type,type,
% 0.31/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_def,definition,
% 0.31/0.46 ( mlocal
% 0.31/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_type,type,
% 0.31/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mand_type,type,
% 0.31/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mor_type,type,
% 0.31/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_type,type,
% 0.31/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_type,type,
% 0.31/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_def,definition,
% 0.31/0.46 ( mnot
% 0.31/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/0.46 ~ ( A @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mand_def,definition,
% 0.31/0.46 ( mand
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 & ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mor_def,definition,
% 0.31/0.46 ( mor
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 | ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_def,definition,
% 0.31/0.46 ( mimplies
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 => ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_def,definition,
% 0.31/0.46 ( mequiv
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 <=> ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_type,type,
% 0.31/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_def,definition,
% 0.31/0.46 ( mbox
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ! [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 => ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_type,type,
% 0.31/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_def,definition,
% 0.31/0.46 ( mdia
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ? [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 & ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_reflexive,axiom,
% 0.31/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_transitive,axiom,
% 0.31/0.46 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/0.46 ( ( ( mrel @ W @ V )
% 0.31/0.46 & ( mrel @ V @ U ) )
% 0.31/0.46 => ( mrel @ W @ U ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mforall_di_type,type,
% 0.31/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mforall_di_def,definition,
% 0.31/0.46 ( mforall_di
% 0.31/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mexists_di_type,type,
% 0.31/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mexists_di_def,definition,
% 0.31/0.46 ( mexists_di
% 0.31/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(empty_set_decl,type,
% 0.31/0.46 empty_set: $i ).
% 0.31/0.46
% 0.31/0.46 thf(qmltpeq_decl,type,
% 0.31/0.46 qmltpeq: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(equal_set_decl,type,
% 0.31/0.46 equal_set: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(member_decl,type,
% 0.31/0.46 member: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(subset_decl,type,
% 0.31/0.46 subset: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_decl,type,
% 0.31/0.46 singleton: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(product_decl,type,
% 0.31/0.46 product: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(unordered_pair_decl,type,
% 0.31/0.46 unordered_pair: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(intersection_decl,type,
% 0.31/0.46 intersection: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(difference_decl,type,
% 0.31/0.46 difference: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(sum_decl,type,
% 0.31/0.46 sum: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(union_decl,type,
% 0.31/0.46 union: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(power_set_decl,type,
% 0.31/0.46 power_set: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(reflexivity,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(symmetry,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(transitivity,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Y: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(difference_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(difference_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(intersection_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(intersection_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(power_set_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(product_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sum_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(union_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(union_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(unordered_pair_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(unordered_pair_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(equal_set_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(equal_set_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(member_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(member_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(subset_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(subset_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(subset_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mequiv @ ( subset @ A @ B )
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(equal_set_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(power_set_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(intersection_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(union_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(empty_set_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(difference_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(unordered_pair_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sum_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.31/0.46 @ ( mexists_di
% 0.31/0.46 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(product_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(thI06,conjecture,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( equal_set @ ( intersection @ A @ B ) @ ( intersection @ B @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.88/1.33 ---- Embedded in THF ---
% 1.88/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.88/1.33 %%% Generated on Tue Feb 24 11:48:30 EST 2026
% 1.88/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.88/1.33 %%% Logic specification used:
% 1.88/1.33 %%% thf(spec, logic, $$dhol).
% 1.88/1.33
% 1.88/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2DTF29004.p
% See solution above
% 1.88/1.33 ------------------------
% 1.88/1.35 ---- Cleaned THF ---
% 1.88/1.35 thf(mworld,type,
% 1.88/1.35 mworld: $tType ).
% 1.88/1.35
% 1.88/1.35 thf(mrel_type,type,
% 1.88/1.35 mrel: mworld > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mactual_type,type,
% 1.88/1.35 mactual: mworld ).
% 1.88/1.35
% 1.88/1.35 thf(mlocal_type,type,
% 1.88/1.35 mlocal: ( mworld > $o ) > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mlocal_def,definition,
% 1.88/1.35 ( mlocal
% 1.88/1.35 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mnot_type,type,
% 1.88/1.35 mnot: ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mand_type,type,
% 1.88/1.35 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mor_type,type,
% 1.88/1.35 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mimplies_type,type,
% 1.88/1.35 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mequiv_type,type,
% 1.88/1.35 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mnot_def,definition,
% 1.88/1.35 ( mnot
% 1.88/1.35 = ( ^ [A: mworld > $o,W: mworld] :
% 1.88/1.35 ~ ( A @ W ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mand_def,definition,
% 1.88/1.35 ( mand
% 1.88/1.35 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.88/1.35 ( ( A @ W )
% 1.88/1.35 & ( B @ W ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mor_def,definition,
% 1.88/1.35 ( mor
% 1.88/1.35 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.88/1.35 ( ( A @ W )
% 1.88/1.35 | ( B @ W ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mimplies_def,definition,
% 1.88/1.35 ( mimplies
% 1.88/1.35 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.88/1.35 ( ( A @ W )
% 1.88/1.35 => ( B @ W ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mequiv_def,definition,
% 1.88/1.35 ( mequiv
% 1.88/1.35 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.88/1.35 ( ( A @ W )
% 1.88/1.35 <=> ( B @ W ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mbox_type,type,
% 1.88/1.35 mbox: ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mbox_def,definition,
% 1.88/1.35 ( mbox
% 1.88/1.35 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.88/1.35 ! [V: mworld] :
% 1.88/1.35 ( ( mrel @ W @ V )
% 1.88/1.35 => ( Phi @ V ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mdia_type,type,
% 1.88/1.35 mdia: ( mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mdia_def,definition,
% 1.88/1.35 ( mdia
% 1.88/1.35 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.88/1.35 ? [V: mworld] :
% 1.88/1.35 ( ( mrel @ W @ V )
% 1.88/1.35 & ( Phi @ V ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mrel_reflexive,axiom,
% 1.88/1.35 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.88/1.35
% 1.88/1.35 thf(mrel_transitive,axiom,
% 1.88/1.35 ! [W: mworld,V: mworld,U: mworld] :
% 1.88/1.35 ( ( ( mrel @ W @ V )
% 1.88/1.35 & ( mrel @ V @ U ) )
% 1.88/1.35 => ( mrel @ W @ U ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mforall_di_type,type,
% 1.88/1.35 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mforall_di_def,definition,
% 1.88/1.35 ( mforall_di
% 1.88/1.35 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.88/1.35 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(mexists_di_type,type,
% 1.88/1.35 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(mexists_di_def,definition,
% 1.88/1.35 ( mexists_di
% 1.88/1.35 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.88/1.35 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(empty_set_decl,type,
% 1.88/1.35 empty_set: $i ).
% 1.88/1.35
% 1.88/1.35 thf(qmltpeq_decl,type,
% 1.88/1.35 qmltpeq: $i > $i > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(equal_set_decl,type,
% 1.88/1.35 equal_set: $i > $i > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(member_decl,type,
% 1.88/1.35 member: $i > $i > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(subset_decl,type,
% 1.88/1.35 subset: $i > $i > mworld > $o ).
% 1.88/1.35
% 1.88/1.35 thf(singleton_decl,type,
% 1.88/1.35 singleton: $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(product_decl,type,
% 1.88/1.35 product: $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(unordered_pair_decl,type,
% 1.88/1.35 unordered_pair: $i > $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(intersection_decl,type,
% 1.88/1.35 intersection: $i > $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(difference_decl,type,
% 1.88/1.35 difference: $i > $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(sum_decl,type,
% 1.88/1.35 sum: $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(union_decl,type,
% 1.88/1.35 union: $i > $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(power_set_decl,type,
% 1.88/1.35 power_set: $i > $i ).
% 1.88/1.35
% 1.88/1.35 thf(reflexivity,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(symmetry,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(transitivity,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [Y: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(difference_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(difference_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(intersection_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(intersection_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(power_set_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(product_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(singleton_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(sum_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(union_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(union_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(unordered_pair_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(unordered_pair_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(equal_set_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(equal_set_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(member_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(member_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(subset_substitution_1,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(subset_substitution_2,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(subset_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mequiv @ ( subset @ A @ B )
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(equal_set_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(power_set_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(intersection_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(union_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(empty_set_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(difference_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [B: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(singleton_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(unordered_pair_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(sum_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 1.88/1.35 @ ( mexists_di
% 1.88/1.35 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(product_0,axiom,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [X: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mequiv @ ( member @ X @ ( product @ A ) )
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 1.88/1.35
% 1.88/1.35 thf(thI06,conjecture,
% 1.88/1.35 ( mlocal
% 1.88/1.35 @ ( mforall_di
% 1.88/1.35 @ ^ [A: $i] :
% 1.88/1.35 ( mforall_di
% 1.88/1.35 @ ^ [B: $i] : ( equal_set @ ( intersection @ A @ B ) @ ( intersection @ B @ A ) ) ) ) ) ).
% 1.88/1.35 ------------------------
% 1.88/1.36 % (29306)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/18Mi)
% 1.88/1.37 % (29306)Instruction limit reached!
% 1.88/1.37 % (29306)------------------------------
% 1.88/1.37 % (29306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.37 % (29306)Termination reason: Unknown
% 1.88/1.37 % (29306)Termination phase: Property scanning
% 1.88/1.37
% 1.88/1.37 % (29306)Memory used [KB]: 1151
% 1.88/1.37 % (29306)Time elapsed: 0.006 s
% 1.88/1.37 % (29306)Instructions burned: 18 (million)
% 1.88/1.37 % (29306)------------------------------
% 1.88/1.37 % (29306)------------------------------
% 1.88/1.37 % (29300)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/183Mi)
% 1.88/1.37 % (29301)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/4Mi)
% 1.88/1.37 % (29303)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/2Mi)
% 1.88/1.37 % (29302)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/27Mi)
% 1.88/1.37 % (29304)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/2Mi)
% 1.88/1.37 % (29305)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/275Mi)
% 1.88/1.37 % (29303)Instruction limit reached!
% 1.88/1.37 % (29303)------------------------------
% 1.88/1.37 % (29303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.37 % (29303)Termination reason: Unknown
% 1.88/1.37 % (29303)Termination phase: shuffling
% 1.88/1.37
% 1.88/1.37 % (29303)Memory used [KB]: 1023
% 1.88/1.37 % (29303)Time elapsed: 0.003 s
% 1.88/1.37 % (29303)Instructions burned: 2 (million)
% 1.88/1.37 % (29303)------------------------------
% 1.88/1.37 % (29303)------------------------------
% 1.88/1.37 % (29304)Instruction limit reached!
% 1.88/1.37 % (29304)------------------------------
% 1.88/1.37 % (29304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.37 % (29304)Termination reason: Unknown
% 1.88/1.37 % (29304)Termination phase: shuffling
% 1.88/1.37
% 1.88/1.37 % (29304)Memory used [KB]: 1023
% 1.88/1.37 % (29304)Time elapsed: 0.003 s
% 1.88/1.37 % (29304)Instructions burned: 2 (million)
% 1.88/1.37 % (29304)------------------------------
% 1.88/1.37 % (29304)------------------------------
% 1.88/1.37 % (29301)Instruction limit reached!
% 1.88/1.37 % (29301)------------------------------
% 1.88/1.37 % (29301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.37 % (29301)Termination reason: Unknown
% 1.88/1.37 % (29301)Termination phase: shuffling
% 1.88/1.37
% 1.88/1.37 % (29301)Memory used [KB]: 1023
% 1.88/1.37 % (29301)Time elapsed: 0.004 s
% 1.88/1.37 % (29301)Instructions burned: 4 (million)
% 1.88/1.37 % (29301)------------------------------
% 1.88/1.37 % (29301)------------------------------
% 1.88/1.38 % (29305)Refutation not found, incomplete strategy
% 1.88/1.38 % (29305)------------------------------
% 1.88/1.38 % (29305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.38 % (29305)Termination reason: Refutation not found, incomplete strategy
% 1.88/1.38
% 1.88/1.38
% 1.88/1.38 % (29305)Memory used [KB]: 5628
% 1.88/1.38 % (29305)Time elapsed: 0.010 s
% 1.88/1.38 % (29305)Instructions burned: 14 (million)
% 1.88/1.38 % (29305)------------------------------
% 1.88/1.38 % (29305)------------------------------
% 1.88/1.38 % (29307)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/3Mi)
% 1.88/1.38 % (29307)Instruction limit reached!
% 1.88/1.38 % (29307)------------------------------
% 1.88/1.38 % (29307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.38 % (29307)Termination reason: Unknown
% 1.88/1.38 % (29307)Termination phase: shuffling
% 1.88/1.38
% 1.88/1.38 % (29307)Memory used [KB]: 1023
% 1.88/1.38 % (29307)Time elapsed: 0.003 s
% 1.88/1.38 % (29307)Instructions burned: 5 (million)
% 1.88/1.38 % (29307)------------------------------
% 1.88/1.38 % (29307)------------------------------
% 1.88/1.38 % (29302)Instruction limit reached!
% 1.88/1.38 % (29302)------------------------------
% 1.88/1.38 % (29302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.38 % (29302)Termination reason: Unknown
% 1.88/1.38 % (29302)Termination phase: Saturation
% 1.88/1.38
% 1.88/1.38 % (29302)Memory used [KB]: 5756
% 1.88/1.38 % (29302)Time elapsed: 0.015 s
% 1.88/1.38 % (29302)Instructions burned: 27 (million)
% 1.88/1.38 % (29302)------------------------------
% 1.88/1.38 % (29302)------------------------------
% 1.88/1.39 % (29308)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/37Mi)
% 1.88/1.39 % (29309)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/15Mi)
% 1.88/1.39 % (29310)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/3Mi)
% 1.88/1.39 % (29312)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/7Mi)
% 1.88/1.39 % (29310)Instruction limit reached!
% 1.88/1.39 % (29310)------------------------------
% 1.88/1.39 % (29310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.39 % (29310)Termination reason: Unknown
% 1.88/1.39 % (29310)Termination phase: shuffling
% 1.88/1.39
% 1.88/1.39 % (29310)Memory used [KB]: 1023
% 1.88/1.39 % (29310)Time elapsed: 0.004 s
% 1.88/1.39 % (29310)Instructions burned: 5 (million)
% 1.88/1.39 % (29310)------------------------------
% 1.88/1.39 % (29310)------------------------------
% 1.88/1.39 % (29312)Instruction limit reached!
% 1.88/1.39 % (29312)------------------------------
% 1.88/1.39 % (29312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.39 % (29312)Termination reason: Unknown
% 1.88/1.39 % (29312)Termination phase: Property scanning
% 1.88/1.39
% 1.88/1.39 % (29312)Memory used [KB]: 1151
% 1.88/1.39 % (29312)Time elapsed: 0.004 s
% 1.88/1.39 % (29312)Instructions burned: 8 (million)
% 1.88/1.39 % (29312)------------------------------
% 1.88/1.39 % (29312)------------------------------
% 1.88/1.39 % (29309)Instruction limit reached!
% 1.88/1.39 % (29309)------------------------------
% 1.88/1.39 % (29309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.39 % (29309)Termination reason: Unknown
% 1.88/1.39 % (29309)Termination phase: Function definition elimination
% 1.88/1.39
% 1.88/1.39 % (29309)Memory used [KB]: 1151
% 1.88/1.39 % (29309)Time elapsed: 0.009 s
% 1.88/1.39 % (29309)Instructions burned: 15 (million)
% 1.88/1.39 % (29309)------------------------------
% 1.88/1.39 % (29309)------------------------------
% 1.88/1.39 % (29311)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/1041Mi)
% 1.97/1.40 % (29313)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/16Mi)
% 1.97/1.40 % (29315)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/3Mi)
% 1.97/1.40 % (29315)Instruction limit reached!
% 1.97/1.40 % (29315)------------------------------
% 1.97/1.40 % (29315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.40 % (29315)Termination reason: Unknown
% 1.97/1.40 % (29315)Termination phase: shuffling
% 1.97/1.40
% 1.97/1.40 % (29315)Memory used [KB]: 1023
% 1.97/1.40 % (29315)Time elapsed: 0.003 s
% 1.97/1.40 % (29315)Instructions burned: 5 (million)
% 1.97/1.40 % (29315)------------------------------
% 1.97/1.40 % (29315)------------------------------
% 1.97/1.40 % (29308)Instruction limit reached!
% 1.97/1.40 % (29308)------------------------------
% 1.97/1.40 % (29308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.40 % (29308)Termination reason: Unknown
% 1.97/1.40 % (29308)Termination phase: Saturation
% 1.97/1.40
% 1.97/1.40 % (29308)Memory used [KB]: 5884
% 1.97/1.40 % (29308)Time elapsed: 0.020 s
% 1.97/1.40 % (29308)Instructions burned: 38 (million)
% 1.97/1.40 % (29308)------------------------------
% 1.97/1.40 % (29308)------------------------------
% 1.97/1.41 % (29313)Instruction limit reached!
% 1.97/1.41 % (29313)------------------------------
% 1.97/1.41 % (29313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.41 % (29313)Termination reason: Unknown
% 1.97/1.41 % (29313)Termination phase: Function definition elimination
% 1.97/1.41
% 1.97/1.41 % (29313)Memory used [KB]: 1151
% 1.97/1.41 % (29313)Time elapsed: 0.010 s
% 1.97/1.41 % (29313)Instructions burned: 16 (million)
% 1.97/1.41 % (29313)------------------------------
% 1.97/1.41 % (29313)------------------------------
% 1.97/1.41 % (29314)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/3Mi)
% 1.97/1.41 % (29314)Instruction limit reached!
% 1.97/1.41 % (29314)------------------------------
% 1.97/1.41 % (29314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.41 % (29314)Termination reason: Unknown
% 1.97/1.41 % (29314)Termination phase: shuffling
% 1.97/1.41
% 1.97/1.41 % (29314)Memory used [KB]: 1023
% 1.97/1.41 % (29314)Time elapsed: 0.004 s
% 1.97/1.41 % (29314)Instructions burned: 4 (million)
% 1.97/1.41 % (29314)------------------------------
% 1.97/1.41 % (29314)------------------------------
% 1.97/1.41 % (29316)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/7Mi)
% 1.97/1.41 % (29317)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/3Mi)
% 1.97/1.41 % (29317)Instruction limit reached!
% 1.97/1.41 % (29317)------------------------------
% 1.97/1.41 % (29317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.41 % (29317)Termination reason: Unknown
% 1.97/1.41 % (29317)Termination phase: shuffling
% 1.97/1.41
% 1.97/1.41 % (29317)Memory used [KB]: 1151
% 1.97/1.41 % (29317)Time elapsed: 0.003 s
% 1.97/1.41 % (29317)Instructions burned: 5 (million)
% 1.97/1.41 % (29317)------------------------------
% 1.97/1.41 % (29317)------------------------------
% 1.97/1.41 % (29316)Instruction limit reached!
% 1.97/1.41 % (29316)------------------------------
% 1.97/1.41 % (29316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.41 % (29316)Termination reason: Unknown
% 1.97/1.41 % (29316)Termination phase: shuffling
% 1.97/1.41
% 1.97/1.41 % (29316)Memory used [KB]: 1151
% 1.97/1.41 % (29316)Time elapsed: 0.005 s
% 1.97/1.41 % (29316)Instructions burned: 7 (million)
% 1.97/1.41 % (29316)------------------------------
% 1.97/1.41 % (29316)------------------------------
% 1.97/1.42 % (29318)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/4Mi)
% 1.97/1.42 % (29321)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/6Mi)
% 1.97/1.42 % (29319)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/18Mi)
% 1.97/1.42 % (29318)Instruction limit reached!
% 1.97/1.42 % (29318)------------------------------
% 1.97/1.42 % (29318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.42 % (29318)Termination reason: Unknown
% 1.97/1.42 % (29318)Termination phase: shuffling
% 1.97/1.42
% 1.97/1.42 % (29318)Memory used [KB]: 1023
% 1.97/1.42 % (29318)Time elapsed: 0.004 s
% 1.97/1.42 % (29318)Instructions burned: 5 (million)
% 1.97/1.42 % (29318)------------------------------
% 1.97/1.42 % (29318)------------------------------
% 1.97/1.43 % (29321)Instruction limit reached!
% 1.97/1.43 % (29321)------------------------------
% 1.97/1.43 % (29321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.43 % (29321)Termination reason: Unknown
% 1.97/1.43 % (29321)Termination phase: Property scanning
% 1.97/1.43
% 1.97/1.43 % (29321)Memory used [KB]: 1151
% 1.97/1.43 % (29321)Time elapsed: 0.004 s
% 1.97/1.43 % (29321)Instructions burned: 8 (million)
% 1.97/1.43 % (29321)------------------------------
% 1.97/1.43 % (29321)------------------------------
% 1.97/1.43 % (29320)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/710Mi)
% 1.97/1.43 % (29322)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/902Mi)
% 1.97/1.43 % (29319)Instruction limit reached!
% 1.97/1.43 % (29319)------------------------------
% 1.97/1.43 % (29319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.43 % (29319)Termination reason: Unknown
% 1.97/1.43 % (29319)Termination phase: Saturation
% 1.97/1.43
% 1.97/1.43 % (29319)Memory used [KB]: 5628
% 1.97/1.43 % (29319)Time elapsed: 0.011 s
% 1.97/1.43 % (29319)Instructions burned: 19 (million)
% 1.97/1.43 % (29319)------------------------------
% 1.97/1.43 % (29319)------------------------------
% 1.97/1.44 % (29324)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/5Mi)
% 1.97/1.44 % (29324)Instruction limit reached!
% 1.97/1.44 % (29324)------------------------------
% 1.97/1.44 % (29324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.44 % (29324)Termination reason: Unknown
% 1.97/1.44 % (29324)Termination phase: shuffling
% 1.97/1.44
% 1.97/1.44 % (29324)Memory used [KB]: 1151
% 1.97/1.44 % (29324)Time elapsed: 0.003 s
% 1.97/1.44 % (29324)Instructions burned: 5 (million)
% 1.97/1.44 % (29324)------------------------------
% 1.97/1.44 % (29324)------------------------------
% 1.97/1.44 % (29322)Refutation not found, incomplete strategy
% 1.97/1.44 % (29322)------------------------------
% 1.97/1.44 % (29322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.44 % (29322)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.44
% 1.97/1.44
% 1.97/1.44 % (29322)Memory used [KB]: 5628
% 1.97/1.44 % (29322)Time elapsed: 0.011 s
% 1.97/1.44 % (29322)Instructions burned: 16 (million)
% 1.97/1.44 % (29322)------------------------------
% 1.97/1.44 % (29322)------------------------------
% 1.97/1.44 % (29323)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/21Mi)
% 1.97/1.45 % (29326)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/377Mi)
% 1.97/1.45 % (29325)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/6Mi)
% 1.97/1.45 % (29323)Instruction limit reached!
% 1.97/1.45 % (29323)------------------------------
% 1.97/1.45 % (29323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.45 % (29323)Termination reason: Unknown
% 1.97/1.45 % (29323)Termination phase: Property scanning
% 1.97/1.45
% 1.97/1.45 % (29323)Memory used [KB]: 1151
% 1.97/1.45 % (29323)Time elapsed: 0.012 s
% 1.97/1.45 % (29323)Instructions burned: 21 (million)
% 1.97/1.45 % (29323)------------------------------
% 1.97/1.45 % (29323)------------------------------
% 1.97/1.45 % (29325)Instruction limit reached!
% 1.97/1.45 % (29325)------------------------------
% 1.97/1.45 % (29325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.45 % (29325)Termination reason: Unknown
% 1.97/1.45 % (29325)Termination phase: shuffling
% 1.97/1.45
% 1.97/1.45 % (29325)Memory used [KB]: 1151
% 1.97/1.45 % (29325)Time elapsed: 0.005 s
% 1.97/1.45 % (29325)Instructions burned: 6 (million)
% 1.97/1.45 % (29325)------------------------------
% 1.97/1.45 % (29325)------------------------------
% 1.97/1.45 % (29300)Instruction limit reached!
% 1.97/1.45 % (29300)------------------------------
% 1.97/1.45 % (29300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.45 % (29300)Termination reason: Unknown
% 1.97/1.45 % (29300)Termination phase: Saturation
% 1.97/1.45
% 1.97/1.45 % (29300)Memory used [KB]: 6908
% 1.97/1.45 % (29300)Time elapsed: 0.088 s
% 1.97/1.45 % (29300)Instructions burned: 185 (million)
% 1.97/1.45 % (29300)------------------------------
% 1.97/1.45 % (29300)------------------------------
% 1.97/1.46 % (29327)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/779Mi)
% 1.97/1.46 % (29330)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/17Mi)
% 1.97/1.47 % (29320)Refutation not found, incomplete strategy
% 1.97/1.47 % (29320)------------------------------
% 1.97/1.47 % (29320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.47 % (29320)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.47
% 1.97/1.47
% 1.97/1.47 % (29320)Memory used [KB]: 6140
% 1.97/1.47 % (29320)Time elapsed: 0.042 s
% 1.97/1.47 % (29320)Instructions burned: 77 (million)
% 1.97/1.47 % (29320)------------------------------
% 1.97/1.47 % (29320)------------------------------
% 1.97/1.47 % (29328)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/19Mi)
% 1.97/1.47 % (29329)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29004 for (2999ds/879Mi)
% 1.97/1.47 % (29330)Instruction limit reached!
% 1.97/1.47 % (29330)------------------------------
% 1.97/1.47 % (29330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.47 % (29330)Termination reason: Unknown
% 1.97/1.47 % (29330)Termination phase: Property scanning
% 1.97/1.47
% 1.97/1.47 % (29330)Memory used [KB]: 1151
% 1.97/1.47 % (29330)Time elapsed: 0.007 s
% 1.97/1.47 % (29330)Instructions burned: 20 (million)
% 1.97/1.47 % (29330)------------------------------
% 1.97/1.47 % (29330)------------------------------
% 1.97/1.48 % (29328)Refutation not found, incomplete strategy
% 1.97/1.48 % (29328)------------------------------
% 1.97/1.48 % (29328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.48 % (29328)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.48
% 1.97/1.48
% 1.97/1.48 % (29328)Memory used [KB]: 5628
% 1.97/1.48 % (29328)Time elapsed: 0.008 s
% 1.97/1.48 % (29328)Instructions burned: 16 (million)
% 1.97/1.48 % (29328)------------------------------
% 1.97/1.48 % (29328)------------------------------
% 1.97/1.48 % (29331)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/3Mi)
% 1.97/1.48 % (29327)Refutation not found, incomplete strategy
% 1.97/1.48 % (29327)------------------------------
% 1.97/1.48 % (29327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.48 % (29327)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.48
% 1.97/1.48
% 1.97/1.48 % (29327)Memory used [KB]: 5756
% 1.97/1.48 % (29327)Time elapsed: 0.021 s
% 1.97/1.48 % (29327)Instructions burned: 52 (million)
% 1.97/1.48 % (29327)------------------------------
% 1.97/1.48 % (29327)------------------------------
% 1.97/1.48 % (29331)Instruction limit reached!
% 1.97/1.48 % (29331)------------------------------
% 1.97/1.48 % (29331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.48 % (29331)Termination reason: Unknown
% 1.97/1.48 % (29331)Termination phase: shuffling
% 1.97/1.48
% 1.97/1.48 % (29331)Memory used [KB]: 1023
% 1.97/1.48 % (29331)Time elapsed: 0.003 s
% 1.97/1.48 % (29331)Instructions burned: 5 (million)
% 1.97/1.48 % (29331)------------------------------
% 1.97/1.48 % (29331)------------------------------
% 1.97/1.48 % (29332)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/30Mi)
% 1.97/1.49 % (29332)Instruction limit reached!
% 1.97/1.49 % (29332)------------------------------
% 1.97/1.49 % (29332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.49 % (29332)Termination reason: Unknown
% 1.97/1.49 % (29332)Termination phase: Saturation
% 1.97/1.49
% 1.97/1.49 % (29332)Memory used [KB]: 5756
% 1.97/1.49 % (29332)Time elapsed: 0.010 s
% 1.97/1.49 % (29332)Instructions burned: 31 (million)
% 1.97/1.49 % (29332)------------------------------
% 1.97/1.49 % (29332)------------------------------
% 1.97/1.49 % (29334)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/100Mi)
% 1.97/1.49 % (29333)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/127Mi)
% 1.97/1.49 % (29335)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/3Mi)
% 1.97/1.49 % (29335)Instruction limit reached!
% 1.97/1.49 % (29335)------------------------------
% 1.97/1.49 % (29335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.49 % (29335)Termination reason: Unknown
% 1.97/1.49 % (29335)Termination phase: shuffling
% 1.97/1.49
% 1.97/1.49 % (29335)Memory used [KB]: 1151
% 1.97/1.49 % (29335)Time elapsed: 0.003 s
% 1.97/1.49 % (29335)Instructions burned: 5 (million)
% 1.97/1.49 % (29335)------------------------------
% 1.97/1.49 % (29335)------------------------------
% 1.97/1.50 % (29336)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/20Mi)
% 1.97/1.50 % (29337)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/86Mi)
% 1.97/1.50 % (29336)Instruction limit reached!
% 1.97/1.50 % (29336)------------------------------
% 1.97/1.50 % (29336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.50 % (29336)Termination reason: Unknown
% 1.97/1.50 % (29336)Termination phase: Saturation
% 1.97/1.50
% 1.97/1.50 % (29336)Memory used [KB]: 5628
% 1.97/1.50 % (29336)Time elapsed: 0.033 s
% 1.97/1.50 % (29336)Instructions burned: 21 (million)
% 1.97/1.50 % (29336)------------------------------
% 1.97/1.50 % (29336)------------------------------
% 1.97/1.51 % (29333)First to succeed.
% 1.97/1.51 % (29338)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29004 for (2998ds/107Mi)
% 1.97/1.52 % (29333)Refutation found. Thanks to Tanya!
% 1.97/1.52 % SZS status Theorem for DTF2THF_29004
% 1.97/1.52 % SZS output start Proof for DTF2THF_29004
% 1.97/1.52 thf(type_def_5, type, mworld: $tType).
% 1.97/1.52 thf(func_def_0, type, mworld: $tType).
% 1.97/1.52 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.97/1.52 thf(func_def_2, type, mactual: mworld).
% 1.97/1.52 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.97/1.52 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.97/1.52 thf(func_def_15, type, qmltpeq: $i > $i > mworld > $o).
% 1.97/1.52 thf(func_def_16, type, equal_set: $i > $i > mworld > $o).
% 1.97/1.52 thf(func_def_17, type, member: $i > $i > mworld > $o).
% 1.97/1.52 thf(func_def_18, type, subset: $i > $i > mworld > $o).
% 1.97/1.52 thf(func_def_19, type, singleton: $i > $i).
% 1.97/1.52 thf(func_def_20, type, product: $i > $i).
% 1.97/1.52 thf(func_def_21, type, unordered_pair: $i > $i > $i).
% 1.97/1.52 thf(func_def_22, type, intersection: $i > $i > $i).
% 1.97/1.52 thf(func_def_23, type, difference: $i > $i > $i).
% 1.97/1.52 thf(func_def_24, type, sum: $i > $i).
% 1.97/1.52 thf(func_def_25, type, union: $i > $i > $i).
% 1.97/1.52 thf(func_def_26, type, power_set: $i > $i).
% 1.97/1.52 thf(func_def_45, type, ph3: !>[X0: $tType]:(X0)).
% 1.97/1.52 thf(f639,plain,(
% 1.97/1.52 $false),
% 1.97/1.52 inference(avatar_sat_refutation,[status(thm)],[f463,f522,f545,f556,f592,f615,f638])).
% 1.97/1.52 thf(f638,plain,(
% 1.97/1.52 ~spl0_1 | ~spl0_5),
% 1.97/1.52 inference(avatar_contradiction_clause,[status(thm)],[f637])).
% 1.97/1.52 thf(f637,plain,(
% 1.97/1.52 $false | (~spl0_1 | ~spl0_5)),
% 1.97/1.52 inference(trivial_inequality_removal,[status(thm)],[f636])).
% 1.97/1.52 thf(f636,plain,(
% 1.97/1.52 ($false = $true) | (~spl0_1 | ~spl0_5)),
% 1.97/1.52 inference(forward_demodulation,[status(thm)],[f609,f587])).
% 1.97/1.52 thf(f587,plain,(
% 1.97/1.52 ($false = (member @ sK5 @ sK2 @ mactual)) | ~spl0_5),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f585])).
% 1.97/1.52 thf(f585,definition,(
% 1.97/1.52 spl0_5 <=> ($false = (member @ sK5 @ sK2 @ mactual))),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.97/1.52 thf(f609,plain,(
% 1.97/1.52 ($true = (member @ sK5 @ sK2 @ mactual)) | ~spl0_1),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f608])).
% 1.97/1.52 thf(f608,plain,(
% 1.97/1.52 (((member @ sK5 @ sK1 @ mactual) & (member @ sK5 @ sK2 @ mactual)) = $true) | ~spl0_1),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f605])).
% 1.97/1.52 thf(f605,plain,(
% 1.97/1.52 (($true = ((member @ sK5 @ sK1 @ mactual) & (member @ sK5 @ sK2 @ mactual))) = $true) | ~spl0_1),
% 1.97/1.52 inference(superposition,[status(thm)],[f420,f571])).
% 1.97/1.52 thf(f571,plain,(
% 1.97/1.52 ($true = (member @ sK5 @ (intersection @ sK2 @ sK1) @ mactual)) | ~spl0_1),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 1.97/1.52 thf(f569,plain,(
% 1.97/1.52 ($false = ((member @ sK5 @ (intersection @ sK2 @ sK1) @ mactual) => (member @ sK5 @ (intersection @ sK1 @ sK2) @ mactual))) | ~spl0_1),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f568])).
% 1.97/1.52 thf(f568,plain,(
% 1.97/1.52 ($false = ((^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual) => (member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual))) @ sK5)) | ~spl0_1),
% 1.97/1.52 inference(sigma_clausification,[status(thm)],[f567])).
% 1.97/1.52 thf(f567,plain,(
% 1.97/1.52 ($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual) => (member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual))))) | ~spl0_1),
% 1.97/1.52 inference(not_proxy_clausification,[status(thm)],[f566])).
% 1.97/1.52 thf(f566,plain,(
% 1.97/1.52 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual) => (member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual)))))) | ~spl0_1),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f557])).
% 1.97/1.52 thf(f557,plain,(
% 1.97/1.52 (($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual) => (member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual))))) = $true) | ~spl0_1),
% 1.97/1.52 inference(superposition,[status(thm)],[f296,f458])).
% 1.97/1.52 thf(f458,plain,(
% 1.97/1.52 ($false = (subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual)) | ~spl0_1),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f456])).
% 1.97/1.52 thf(f456,definition,(
% 1.97/1.52 spl0_1 <=> ($false = (subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual))),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.97/1.52 thf(f296,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2 @ mactual) = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))))) = $true)) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f295])).
% 1.97/1.52 thf(f295,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))))) @ X2) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f294])).
% 1.97/1.52 thf(f294,plain,(
% 1.97/1.52 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual))))))))) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f293])).
% 1.97/1.52 thf(f293,plain,(
% 1.97/1.52 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))))))) @ X1) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f292])).
% 1.97/1.52 thf(f292,plain,(
% 1.97/1.52 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual))))))))) = $true)),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f202])).
% 1.97/1.52 thf(f202,plain,(
% 1.97/1.52 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 1.97/1.52 inference(definition_unfolding,[status(thm)],[f164,f150,f159,f159,f179,f159,f160])).
% 1.97/1.52 thf(f160,plain,(
% 1.97/1.52 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f87])).
% 1.97/1.52 thf(f87,plain,(
% 1.97/1.52 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f86])).
% 1.97/1.52 thf(f86,plain,(
% 1.97/1.52 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.97/1.52 inference(rectify,[status(thm)],[f5])).
% 1.97/1.52 thf(f5,axiom,(
% 1.97/1.52 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mimplies_def)).
% 1.97/1.52 thf(f179,plain,(
% 1.97/1.52 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f69])).
% 1.97/1.52 thf(f69,plain,(
% 1.97/1.52 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f68])).
% 1.97/1.52 thf(f68,plain,(
% 1.97/1.52 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 1.97/1.52 inference(rectify,[status(thm)],[f6])).
% 1.97/1.52 thf(f6,axiom,(
% 1.97/1.52 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))) = mequiv)),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mequiv_def)).
% 1.97/1.52 thf(f159,plain,(
% 1.97/1.52 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f134])).
% 1.97/1.52 thf(f134,plain,(
% 1.97/1.52 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f133])).
% 1.97/1.52 thf(f133,plain,(
% 1.97/1.52 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f11])).
% 1.97/1.52 thf(f11,axiom,(
% 1.97/1.52 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : (X1 @ X6 @ X2))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mforall_di_def)).
% 1.97/1.52 thf(f150,plain,(
% 1.97/1.52 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f110])).
% 1.97/1.52 thf(f110,plain,(
% 1.97/1.52 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f1])).
% 1.97/1.52 thf(f1,axiom,(
% 1.97/1.52 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mlocal_def)).
% 1.97/1.52 thf(f164,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f77])).
% 1.97/1.52 thf(f77,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f76])).
% 1.97/1.52 thf(f76,plain,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (subset @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f34])).
% 1.97/1.52 thf(f34,axiom,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (subset @ X1 @ X3) @ (mforall_di @ (^[X6 : $i] : (mimplies @ (member @ X6 @ X1) @ (member @ X6 @ X3))))))))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',subset_0)).
% 1.97/1.52 thf(f420,plain,(
% 1.97/1.52 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((member @ X1 @ (intersection @ X2 @ X3) @ mactual) = ((member @ X1 @ X3 @ mactual) & (member @ X1 @ X2 @ mactual))) = $true)) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f419])).
% 1.97/1.52 thf(f419,plain,(
% 1.97/1.52 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((member @ X1 @ (intersection @ X2 @ Y0) @ mactual) = ((member @ X1 @ Y0 @ mactual) & (member @ X1 @ X2 @ mactual)))) @ X3) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f418])).
% 1.97/1.52 thf(f418,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((member @ X1 @ (intersection @ X2 @ Y0) @ mactual) = ((member @ X1 @ Y0 @ mactual) & (member @ X1 @ X2 @ mactual))))))) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f417])).
% 1.97/1.52 thf(f417,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((member @ X1 @ (intersection @ Y0 @ Y1) @ mactual) = ((member @ X1 @ Y1 @ mactual) & (member @ X1 @ Y0 @ mactual)))))) @ X2) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f416])).
% 1.97/1.52 thf(f416,plain,(
% 1.97/1.52 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((member @ X1 @ (intersection @ Y0 @ Y1) @ mactual) = ((member @ X1 @ Y1 @ mactual) & (member @ X1 @ Y0 @ mactual))))))))) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f415])).
% 1.97/1.52 thf(f415,plain,(
% 1.97/1.52 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((member @ Y0 @ (intersection @ Y1 @ Y2) @ mactual) = ((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual)))))))) @ X1) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f414])).
% 1.97/1.52 thf(f414,plain,(
% 1.97/1.52 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((member @ Y0 @ (intersection @ Y1 @ Y2) @ mactual) = ((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual))))))))) = $true)),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f203])).
% 1.97/1.52 thf(f203,plain,(
% 1.97/1.52 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) = (Y4 @ Y5))))))) @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))))),
% 1.97/1.52 inference(definition_unfolding,[status(thm)],[f165,f150,f159,f159,f159,f179,f157])).
% 1.97/1.52 thf(f157,plain,(
% 1.97/1.52 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f83])).
% 1.97/1.52 thf(f83,plain,(
% 1.97/1.52 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f82])).
% 1.97/1.52 thf(f82,plain,(
% 1.97/1.52 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f3])).
% 1.97/1.52 thf(f3,axiom,(
% 1.97/1.52 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',mand_def)).
% 1.97/1.52 thf(f165,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f109])).
% 1.97/1.52 thf(f109,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f108])).
% 1.97/1.52 thf(f108,plain,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mequiv @ (member @ X0 @ (intersection @ X1 @ X2)) @ (mand @ (member @ X0 @ X1) @ (member @ X0 @ X2))))))))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f37])).
% 1.97/1.52 thf(f37,axiom,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (member @ X6 @ (intersection @ X1 @ X3)) @ (mand @ (member @ X6 @ X1) @ (member @ X6 @ X3))))))))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',intersection_0)).
% 1.97/1.52 thf(f615,plain,(
% 1.97/1.52 ~spl0_1 | ~spl0_6),
% 1.97/1.52 inference(avatar_contradiction_clause,[status(thm)],[f614])).
% 1.97/1.52 thf(f614,plain,(
% 1.97/1.52 $false | (~spl0_1 | ~spl0_6)),
% 1.97/1.52 inference(trivial_inequality_removal,[status(thm)],[f613])).
% 1.97/1.52 thf(f613,plain,(
% 1.97/1.52 ($false = $true) | (~spl0_1 | ~spl0_6)),
% 1.97/1.52 inference(forward_demodulation,[status(thm)],[f610,f591])).
% 1.97/1.52 thf(f591,plain,(
% 1.97/1.52 ((member @ sK5 @ sK1 @ mactual) = $false) | ~spl0_6),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f589])).
% 1.97/1.52 thf(f589,definition,(
% 1.97/1.52 spl0_6 <=> ((member @ sK5 @ sK1 @ mactual) = $false)),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.97/1.52 thf(f610,plain,(
% 1.97/1.52 ((member @ sK5 @ sK1 @ mactual) = $true) | ~spl0_1),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f608])).
% 1.97/1.52 thf(f592,plain,(
% 1.97/1.52 spl0_5 | spl0_6 | ~spl0_1),
% 1.97/1.52 inference(avatar_split_clause,[status(thm)],[f580,f456,f589,f585])).
% 1.97/1.52 thf(f580,plain,(
% 1.97/1.52 ((member @ sK5 @ sK1 @ mactual) = $false) | ($false = (member @ sK5 @ sK2 @ mactual)) | ~spl0_1),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f579])).
% 1.97/1.52 thf(f579,plain,(
% 1.97/1.52 ($false = ((member @ sK5 @ sK2 @ mactual) & (member @ sK5 @ sK1 @ mactual))) | ~spl0_1),
% 1.97/1.52 inference(not_proxy_clausification,[status(thm)],[f578])).
% 1.97/1.52 thf(f578,plain,(
% 1.97/1.52 ((~ ((member @ sK5 @ sK2 @ mactual) & (member @ sK5 @ sK1 @ mactual))) = $true) | ~spl0_1),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f572])).
% 1.97/1.52 thf(f572,plain,(
% 1.97/1.52 (($false = ((member @ sK5 @ sK2 @ mactual) & (member @ sK5 @ sK1 @ mactual))) = $true) | ~spl0_1),
% 1.97/1.52 inference(superposition,[status(thm)],[f420,f570])).
% 1.97/1.52 thf(f570,plain,(
% 1.97/1.52 ($false = (member @ sK5 @ (intersection @ sK1 @ sK2) @ mactual)) | ~spl0_1),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 1.97/1.52 thf(f556,plain,(
% 1.97/1.52 ~spl0_2 | ~spl0_4),
% 1.97/1.52 inference(avatar_contradiction_clause,[status(thm)],[f555])).
% 1.97/1.52 thf(f555,plain,(
% 1.97/1.52 $false | (~spl0_2 | ~spl0_4)),
% 1.97/1.52 inference(trivial_inequality_removal,[status(thm)],[f554])).
% 1.97/1.52 thf(f554,plain,(
% 1.97/1.52 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.97/1.52 inference(forward_demodulation,[status(thm)],[f540,f521])).
% 1.97/1.52 thf(f521,plain,(
% 1.97/1.52 ($false = (member @ sK4 @ sK1 @ mactual)) | ~spl0_4),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f519])).
% 1.97/1.52 thf(f519,definition,(
% 1.97/1.52 spl0_4 <=> ($false = (member @ sK4 @ sK1 @ mactual))),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.97/1.52 thf(f540,plain,(
% 1.97/1.52 ((member @ sK4 @ sK1 @ mactual) = $true) | ~spl0_2),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f539])).
% 1.97/1.52 thf(f539,plain,(
% 1.97/1.52 (((member @ sK4 @ sK2 @ mactual) & (member @ sK4 @ sK1 @ mactual)) = $true) | ~spl0_2),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f535])).
% 1.97/1.52 thf(f535,plain,(
% 1.97/1.52 (($true = ((member @ sK4 @ sK2 @ mactual) & (member @ sK4 @ sK1 @ mactual))) = $true) | ~spl0_2),
% 1.97/1.52 inference(superposition,[status(thm)],[f420,f501])).
% 1.97/1.52 thf(f501,plain,(
% 1.97/1.52 ((member @ sK4 @ (intersection @ sK1 @ sK2) @ mactual) = $true) | ~spl0_2),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f499])).
% 1.97/1.52 thf(f499,plain,(
% 1.97/1.52 ($false = ((member @ sK4 @ (intersection @ sK1 @ sK2) @ mactual) => (member @ sK4 @ (intersection @ sK2 @ sK1) @ mactual))) | ~spl0_2),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f498])).
% 1.97/1.52 thf(f498,plain,(
% 1.97/1.52 ($false = ((^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual) => (member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual))) @ sK4)) | ~spl0_2),
% 1.97/1.52 inference(sigma_clausification,[status(thm)],[f497])).
% 1.97/1.52 thf(f497,plain,(
% 1.97/1.52 ($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual) => (member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual))))) | ~spl0_2),
% 1.97/1.52 inference(not_proxy_clausification,[status(thm)],[f496])).
% 1.97/1.52 thf(f496,plain,(
% 1.97/1.52 ((~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual) => (member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual))))) = $true) | ~spl0_2),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f495])).
% 1.97/1.52 thf(f495,plain,(
% 1.97/1.52 (($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ sK2) @ mactual) => (member @ Y0 @ (intersection @ sK2 @ sK1) @ mactual))))) = $true) | ~spl0_2),
% 1.97/1.52 inference(superposition,[status(thm)],[f296,f462])).
% 1.97/1.52 thf(f462,plain,(
% 1.97/1.52 ((subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual) = $false) | ~spl0_2),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f460])).
% 1.97/1.52 thf(f460,definition,(
% 1.97/1.52 spl0_2 <=> ((subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual) = $false)),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.97/1.52 thf(f545,plain,(
% 1.97/1.52 ~spl0_2 | ~spl0_3),
% 1.97/1.52 inference(avatar_contradiction_clause,[status(thm)],[f544])).
% 1.97/1.52 thf(f544,plain,(
% 1.97/1.52 $false | (~spl0_2 | ~spl0_3)),
% 1.97/1.52 inference(trivial_inequality_removal,[status(thm)],[f543])).
% 1.97/1.52 thf(f543,plain,(
% 1.97/1.52 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.97/1.52 inference(forward_demodulation,[status(thm)],[f541,f517])).
% 1.97/1.52 thf(f517,plain,(
% 1.97/1.52 ($false = (member @ sK4 @ sK2 @ mactual)) | ~spl0_3),
% 1.97/1.52 inference(avatar_component_clause,[status(thm)],[f515])).
% 1.97/1.52 thf(f515,definition,(
% 1.97/1.52 spl0_3 <=> ($false = (member @ sK4 @ sK2 @ mactual))),
% 1.97/1.52 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.97/1.52 thf(f541,plain,(
% 1.97/1.52 ((member @ sK4 @ sK2 @ mactual) = $true) | ~spl0_2),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f539])).
% 1.97/1.52 thf(f522,plain,(
% 1.97/1.52 spl0_3 | spl0_4 | ~spl0_2),
% 1.97/1.52 inference(avatar_split_clause,[status(thm)],[f510,f460,f519,f515])).
% 1.97/1.52 thf(f510,plain,(
% 1.97/1.52 ($false = (member @ sK4 @ sK2 @ mactual)) | ($false = (member @ sK4 @ sK1 @ mactual)) | ~spl0_2),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f509])).
% 1.97/1.52 thf(f509,plain,(
% 1.97/1.52 ($false = ((member @ sK4 @ sK1 @ mactual) & (member @ sK4 @ sK2 @ mactual))) | ~spl0_2),
% 1.97/1.52 inference(not_proxy_clausification,[status(thm)],[f508])).
% 1.97/1.52 thf(f508,plain,(
% 1.97/1.52 ((~ ((member @ sK4 @ sK1 @ mactual) & (member @ sK4 @ sK2 @ mactual))) = $true) | ~spl0_2),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f502])).
% 1.97/1.52 thf(f502,plain,(
% 1.97/1.52 (($false = ((member @ sK4 @ sK1 @ mactual) & (member @ sK4 @ sK2 @ mactual))) = $true) | ~spl0_2),
% 1.97/1.52 inference(superposition,[status(thm)],[f420,f500])).
% 1.97/1.52 thf(f500,plain,(
% 1.97/1.52 ($false = (member @ sK4 @ (intersection @ sK2 @ sK1) @ mactual)) | ~spl0_2),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f499])).
% 1.97/1.52 thf(f463,plain,(
% 1.97/1.52 spl0_1 | spl0_2),
% 1.97/1.52 inference(avatar_split_clause,[status(thm)],[f454,f460,f456])).
% 1.97/1.52 thf(f454,plain,(
% 1.97/1.52 ($false = (subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual)) | ((subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual) = $false)),
% 1.97/1.52 inference(binary_proxy_clausification,[status(thm)],[f453])).
% 1.97/1.52 thf(f453,plain,(
% 1.97/1.52 (((subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual) & (subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual)) = $false)),
% 1.97/1.52 inference(not_proxy_clausification,[status(thm)],[f452])).
% 1.97/1.52 thf(f452,plain,(
% 1.97/1.52 ((~ ((subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual) & (subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual))) = $true)),
% 1.97/1.52 inference(boolean_simplification,[status(thm)],[f451])).
% 1.97/1.52 thf(f451,plain,(
% 1.97/1.52 (($false = ((subset @ (intersection @ sK2 @ sK1) @ (intersection @ sK1 @ sK2) @ mactual) & (subset @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual))) = $true)),
% 1.97/1.52 inference(superposition,[status(thm)],[f323,f235])).
% 1.97/1.52 thf(f235,plain,(
% 1.97/1.52 ($false = (equal_set @ (intersection @ sK1 @ sK2) @ (intersection @ sK2 @ sK1) @ mactual))),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f234])).
% 1.97/1.52 thf(f234,plain,(
% 1.97/1.52 ($false = ((^[Y0 : $i]: (equal_set @ (intersection @ sK1 @ Y0) @ (intersection @ Y0 @ sK1) @ mactual)) @ sK2))),
% 1.97/1.52 inference(sigma_clausification,[status(thm)],[f233])).
% 1.97/1.52 thf(f233,plain,(
% 1.97/1.52 ($false = (!! @ $i @ (^[Y0 : $i]: (equal_set @ (intersection @ sK1 @ Y0) @ (intersection @ Y0 @ sK1) @ mactual))))),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f232])).
% 1.97/1.52 thf(f232,plain,(
% 1.97/1.52 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0) @ mactual)))) @ sK1))),
% 1.97/1.52 inference(sigma_clausification,[status(thm)],[f231])).
% 1.97/1.52 thf(f231,plain,(
% 1.97/1.52 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0) @ mactual))))) != $true)),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.97/1.52 thf(f216,plain,(
% 1.97/1.52 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0))))))) != $true)),
% 1.97/1.52 inference(definition_unfolding,[status(thm)],[f183,f150,f159,f159])).
% 1.97/1.52 thf(f183,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0))))))) != $true)),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f137])).
% 1.97/1.52 thf(f137,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0))))))) != $true)),
% 1.97/1.52 inference(flattening,[status(thm)],[f81])).
% 1.97/1.52 thf(f81,plain,(
% 1.97/1.52 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (equal_set @ (intersection @ Y0 @ Y1) @ (intersection @ Y1 @ Y0))))))) = $true)),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f80])).
% 1.97/1.52 thf(f80,plain,(
% 1.97/1.52 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (equal_set @ (intersection @ X0 @ X1) @ (intersection @ X1 @ X0)))))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f46])).
% 1.97/1.52 thf(f46,negated_conjecture,(
% 1.97/1.52 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (equal_set @ (intersection @ X1 @ X3) @ (intersection @ X3 @ X1)))))))),
% 1.97/1.52 inference(negated_conjecture,[status(cth)],[f45])).
% 1.97/1.52 thf(f45,conjecture,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (equal_set @ (intersection @ X1 @ X3) @ (intersection @ X3 @ X1)))))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',thI06)).
% 1.97/1.52 thf(f323,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : ((((equal_set @ X1 @ X2 @ mactual) = ((subset @ X2 @ X1 @ mactual) & (subset @ X1 @ X2 @ mactual))) = $true)) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f322])).
% 1.97/1.52 thf(f322,plain,(
% 1.97/1.52 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual)))) @ X2))) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f321])).
% 1.97/1.52 thf(f321,plain,(
% 1.97/1.52 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual))))) = $true)) )),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f320])).
% 1.97/1.52 thf(f320,plain,(
% 1.97/1.52 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)))))) @ X1) = $true)) )),
% 1.97/1.52 inference(pi_clausification,[status(thm)],[f319])).
% 1.97/1.52 thf(f319,plain,(
% 1.97/1.52 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual))))))) = $true)),
% 1.97/1.52 inference(beta_eta_normalization,[status(thm)],[f195])).
% 1.97/1.52 thf(f195,plain,(
% 1.97/1.52 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (equal_set @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 1.97/1.52 inference(definition_unfolding,[status(thm)],[f153,f150,f159,f159,f179,f157])).
% 1.97/1.52 thf(f153,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 1.97/1.52 inference(cnf_transformation,[status(thm)],[f89])).
% 1.97/1.52 thf(f89,plain,(
% 1.97/1.52 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 1.97/1.52 inference(fool_elimination,[status(thm)],[f88])).
% 1.97/1.52 thf(f88,plain,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (equal_set @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 1.97/1.52 inference(rectify,[status(thm)],[f35])).
% 1.97/1.52 thf(f35,axiom,(
% 1.97/1.52 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (equal_set @ X1 @ X3) @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1))))))))),
% 1.97/1.52 file('/export/starexec/sandbox/tmp/tmp.zy7AuFsBi7/DTF2THF_29004.p',equal_set_0)).
% 1.97/1.52 % SZS output end Proof for DTF2THF_29004
% 1.97/1.52 % (29333)------------------------------
% 1.97/1.52 % (29333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.52 % (29333)Termination reason: Refutation
% 1.97/1.52
% 1.97/1.52 % (29333)Memory used [KB]: 6396
% 1.97/1.52 % (29333)Time elapsed: 0.050 s
% 1.97/1.52 % (29333)Instructions burned: 82 (million)
% 1.97/1.52 % (29333)------------------------------
% 1.97/1.52 % (29333)------------------------------
% 1.97/1.52 % (29299)Success in time 0.172 s
%------------------------------------------------------------------------------