%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET019^4 : 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 : n018.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 09:30:58 AM UTC 2026
% Result : Theorem 1.95s 1.42s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 47 unt; 0 typ; 4 def)
% Number of atoms : 485 ( 94 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 673 ( 23 ~; 36 |; 23 &; 531 @)
% ( 6 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 10 con; 0-3 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 130 ( 113 ^; 17 !; 0 ?; 130 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_13,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_17,type,
equal_set: $i > $i > mworld > $o ).
thf(func_def_18,type,
member: $i > $i > mworld > $o ).
thf(func_def_19,type,
subset: $i > $i > mworld > $o ).
thf(func_def_20,type,
singleton: $i > $i ).
thf(func_def_21,type,
product: $i > $i ).
thf(func_def_22,type,
unordered_pair: $i > $i > $i ).
thf(func_def_23,type,
intersection: $i > $i > $i ).
thf(func_def_24,type,
difference: $i > $i > $i ).
thf(func_def_25,type,
sum: $i > $i ).
thf(func_def_26,type,
union: $i > $i > $i ).
thf(func_def_27,type,
power_set: $i > $i ).
thf(func_def_41,type,
sK0: mworld > $i ).
thf(func_def_45,type,
sK2: $i > $i > $i ).
thf(func_def_46,type,
sK3: $i > $i > $i ).
thf(func_def_49,type,
sK6: $i > $i > $i ).
thf(f824,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f779,f788,f797,f810,f822]) ).
thf(f822,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[status(thm)],[f821]) ).
thf(f821,plain,
( $false
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f815]) ).
thf(f815,plain,
( ( $false = $true )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f777,f568]) ).
thf(f568,plain,
( ( subset @ sK4 @ sK5 @ mactual )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f566]) ).
thf(f566,plain,
( ( ( subset @ sK4 @ sK5 @ mactual )
& ( subset @ sK5 @ sK4 @ mactual ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f563]) ).
thf(f563,plain,
( $false
= ( ( ( subset @ sK4 @ sK5 @ mactual )
& ( subset @ sK5 @ sK4 @ mactual ) )
=> ( equal_set @ sK4 @ sK5 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f562]) ).
thf(f562,plain,
( $false
= ( ( eiw_di @ sK5 @ mactual )
=> ( ( ( subset @ sK4 @ sK5 @ mactual )
& ( subset @ sK5 @ sK4 @ mactual ) )
=> ( equal_set @ sK4 @ sK5 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f561]) ).
thf(f561,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK4 @ Y0 @ mactual )
& ( subset @ Y0 @ sK4 @ mactual ) )
=> ( equal_set @ sK4 @ Y0 @ mactual ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f559]) ).
thf(f559,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK4 @ Y0 @ mactual )
& ( subset @ Y0 @ sK4 @ mactual ) )
=> ( equal_set @ sK4 @ Y0 @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f558]) ).
thf(f558,plain,
( $false
= ( ( eiw_di @ sK4 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK4 @ Y0 @ mactual )
& ( subset @ Y0 @ sK4 @ mactual ) )
=> ( equal_set @ sK4 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f557]) ).
thf(f557,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
=> ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f556]) ).
thf(f556,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
=> ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f207]) ).
thf(f207,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( equal_set @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f168,f173,f176,f176,f154,f160]) ).
thf(f160,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
thf(f124,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mand_def) ).
thf(f154,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
thf(f106,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f105]) ).
thf(f105,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.1DI5ytlWYR/DTF2THF_6821.p',mimplies_def) ).
thf(f176,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
thf(f114,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] :
( ( eiw_di @ X5 @ X2 )
=> ( X1 @ X5 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mforall_di_def) ).
thf(f173,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
thf(f135,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mlocal_def) ).
thf(f168,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f140]) ).
thf(f140,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f68]) ).
thf(f68,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f67]) ).
thf(f67,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( equal_set @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mimplies @ ( mand @ ( subset @ X1 @ X3 ) @ ( subset @ X3 @ X1 ) ) @ ( equal_set @ X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
thf(f46,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mimplies @ ( mand @ ( subset @ X1 @ X3 ) @ ( subset @ X3 @ X1 ) ) @ ( equal_set @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',thI02) ).
thf(f777,plain,
( ( $false
= ( subset @ sK4 @ sK5 @ mactual ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f775]) ).
thf(f775,definition,
( spl1_7
<=> ( $false
= ( subset @ sK4 @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f810,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[status(thm)],[f809]) ).
thf(f809,plain,
( $false
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f803]) ).
thf(f803,plain,
( ( $false = $true )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f560,f773]) ).
thf(f773,plain,
( ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f771]) ).
thf(f771,definition,
( spl1_6
<=> ( $false
= ( eiw_di @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f560,plain,
( ( eiw_di @ sK4 @ mactual )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f558]) ).
thf(f797,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[status(thm)],[f796]) ).
thf(f796,plain,
( $false
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f791]) ).
thf(f791,plain,
( ( $false = $true )
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f564,f769]) ).
thf(f769,plain,
( ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f767]) ).
thf(f767,definition,
( spl1_5
<=> ( $false
= ( eiw_di @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f564,plain,
( $true
= ( eiw_di @ sK5 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f562]) ).
thf(f788,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[status(thm)],[f787]) ).
thf(f787,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f782]) ).
thf(f782,plain,
( ( $false = $true )
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f567,f765]) ).
thf(f765,plain,
( ( $false
= ( subset @ sK5 @ sK4 @ mactual ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f763]) ).
thf(f763,definition,
( spl1_4
<=> ( $false
= ( subset @ sK5 @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f567,plain,
( $true
= ( subset @ sK5 @ sK4 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f566]) ).
thf(f779,plain,
( spl1_6
| spl1_5
| spl1_7
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f754,f763,f775,f767,f771]) ).
thf(f754,plain,
( ( $false
= ( subset @ sK4 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( subset @ sK5 @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f751]) ).
thf(f751,plain,
( ( $false
= ( subset @ sK4 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false = $true )
| ( $false
= ( subset @ sK5 @ sK4 @ mactual ) ) ),
inference(superposition,[status(thm)],[f565,f507]) ).
thf(f507,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( equal_set @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f506]) ).
thf(f506,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( equal_set @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f504]) ).
thf(f504,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) )
= ( equal_set @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f503]) ).
thf(f503,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) )
= ( equal_set @ X1 @ X2 @ mactual ) )
= $true )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f502]) ).
thf(f502,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) )
= ( equal_set @ X1 @ X2 @ mactual ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f501]) ).
thf(f501,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) )
= ( equal_set @ X1 @ Y0 @ mactual ) ) )
@ X2 )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) )
= ( equal_set @ X1 @ Y0 @ mactual ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) )
= ( equal_set @ X1 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f498]) ).
thf(f498,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
= ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
= ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( equal_set @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f146,f173,f176,f176,f161,f160]) ).
thf(f161,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
thf(f108,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mequiv_def) ).
thf(f146,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
thf(f122,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f121]) ).
thf(f121,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)],[f36]) ).
thf(f36,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.1DI5ytlWYR/DTF2THF_6821.p',equal_set_0) ).
thf(f565,plain,
( $false
= ( equal_set @ sK4 @ sK5 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET019^4 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 11:48:46 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SET019^4 : TPTP v9.2.1. Released v8.1.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : TPTP problem SET019+4.p with axiomatized equality
% 0.18/0.44 % Version : [BP13] axioms.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.18/0.44 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.18/0.44 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.18/0.44 % Source : [TPTP]
% 0.18/0.44 % Names : SET019+1 [QMLTP]
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.18/0.44 % Syntax : Number of formulae : 73 ( 12 unt; 27 typ; 10 def)
% 0.18/0.44 % Number of atoms : 277 ( 10 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 10 ( 6 avg)
% 0.18/0.44 % Number of connectives : 472 ( 1 ~; 1 |; 4 &; 461 @)
% 0.18/0.44 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 14 ( 9 avg)
% 0.18/0.44 % Number of types : 3 ( 1 usr)
% 0.18/0.44 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 27 ( 26 usr; 2 con; 0-3 aty)
% 0.18/0.44 % Number of variables : 119 ( 109 ^; 7 !; 3 ?; 119 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.18/0.44 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.18/0.44 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.18/0.44 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.18/0.44 % $modalities == $modal_system_T].
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(mworld,type,
% 0.18/0.44 mworld: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(mrel_type,type,
% 0.18/0.44 mrel: mworld > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mactual_type,type,
% 0.18/0.44 mactual: mworld ).
% 0.18/0.44
% 0.18/0.44 thf(mlocal_type,type,
% 0.18/0.44 mlocal: ( mworld > $o ) > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mlocal_def,definition,
% 0.18/0.44 ( mlocal
% 0.18/0.44 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mnot_type,type,
% 0.18/0.44 mnot: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mand_type,type,
% 0.18/0.44 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mor_type,type,
% 0.18/0.44 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mimplies_type,type,
% 0.18/0.44 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mequiv_type,type,
% 0.18/0.44 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mnot_def,definition,
% 0.18/0.44 ( mnot
% 0.18/0.44 = ( ^ [A: mworld > $o,W: mworld] :
% 0.18/0.44 ~ ( A @ W ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mand_def,definition,
% 0.18/0.44 ( mand
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 & ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mor_def,definition,
% 0.18/0.44 ( mor
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 | ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mimplies_def,definition,
% 0.18/0.44 ( mimplies
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 => ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mequiv_def,definition,
% 0.18/0.44 ( mequiv
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 <=> ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mbox_type,type,
% 0.18/0.44 mbox: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mbox_def,definition,
% 0.18/0.44 ( mbox
% 0.18/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.44 ! [V: mworld] :
% 0.18/0.44 ( ( mrel @ W @ V )
% 0.18/0.44 => ( Phi @ V ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mdia_type,type,
% 0.18/0.44 mdia: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mdia_def,definition,
% 0.18/0.44 ( mdia
% 0.18/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.44 ? [V: mworld] :
% 0.18/0.44 ( ( mrel @ W @ V )
% 0.18/0.44 & ( Phi @ V ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mrel_reflexive,axiom,
% 0.18/0.44 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_type,type,
% 0.18/0.44 eiw_di: $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_nonempty,axiom,
% 0.18/0.44 ! [W: mworld] :
% 0.18/0.44 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_decr,axiom,
% 0.18/0.44 ! [W: mworld,V: mworld,X: $i] :
% 0.18/0.44 ( ( ( eiw_di @ X @ W )
% 0.18/0.44 & ( mrel @ V @ W ) )
% 0.18/0.44 => ( eiw_di @ X @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mforall_di_type,type,
% 0.18/0.44 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mforall_di_def,definition,
% 0.18/0.44 ( mforall_di
% 0.18/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.18/0.44 ! [X: $i] :
% 0.18/0.44 ( ( eiw_di @ X @ W )
% 0.18/0.44 => ( A @ X @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mexists_di_type,type,
% 0.18/0.44 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mexists_di_def,definition,
% 0.18/0.44 ( mexists_di
% 0.18/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.18/0.44 ? [X: $i] :
% 0.18/0.44 ( ( eiw_di @ X @ W )
% 0.18/0.44 & ( A @ X @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(empty_set_decl,type,
% 0.18/0.44 empty_set: $i ).
% 0.18/0.44
% 0.18/0.44 thf(qmltpeq_decl,type,
% 0.18/0.44 qmltpeq: $i > $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(equal_set_decl,type,
% 0.18/0.44 equal_set: $i > $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(member_decl,type,
% 0.18/0.44 member: $i > $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(subset_decl,type,
% 0.18/0.44 subset: $i > $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(singleton_decl,type,
% 0.18/0.44 singleton: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(product_decl,type,
% 0.18/0.44 product: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(unordered_pair_decl,type,
% 0.18/0.44 unordered_pair: $i > $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(intersection_decl,type,
% 0.18/0.44 intersection: $i > $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(difference_decl,type,
% 0.18/0.44 difference: $i > $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(sum_decl,type,
% 0.18/0.45 sum: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(union_decl,type,
% 0.18/0.45 union: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(power_set_decl,type,
% 0.18/0.45 power_set: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(reflexivity,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(symmetry,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(transitivity,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [Y: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(difference_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(difference_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(intersection_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(intersection_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(power_set_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(product_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(singleton_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sum_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(union_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(union_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(unordered_pair_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(unordered_pair_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(equal_set_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(equal_set_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(member_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(member_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subset_substitution_1,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subset_substitution_2,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subset_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mequiv @ ( subset @ A @ B )
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(equal_set_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(power_set_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(intersection_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(union_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(empty_set_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(difference_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [B: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(singleton_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(unordered_pair_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(sum_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.18/0.45 @ ( mexists_di
% 0.18/0.45 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(product_0,axiom,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(thI02,conjecture,
% 0.18/0.45 ( mlocal
% 0.18/0.45 @ ( mforall_di
% 0.18/0.45 @ ^ [A: $i] :
% 0.18/0.45 ( mforall_di
% 0.18/0.45 @ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 0.29/1.30 ---- Embedded in THF ---
% 0.29/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.29/1.30 %%% Generated on Tue Feb 24 11:48:47 EST 2026
% 0.29/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.29/1.30 %%% Logic specification used:
% 0.29/1.30 %%% thf(spec, logic, $$dhol).
% 0.29/1.30
% 0.29/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2DTF6821.p
% See solution above
% 0.29/1.30 ------------------------
% 0.29/1.32 ---- Cleaned THF ---
% 0.29/1.32 thf(mworld,type,
% 0.29/1.32 mworld: $tType ).
% 0.29/1.32
% 0.29/1.32 thf(mrel_type,type,
% 0.29/1.32 mrel: mworld > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mactual_type,type,
% 0.29/1.32 mactual: mworld ).
% 0.29/1.32
% 0.29/1.32 thf(mlocal_type,type,
% 0.29/1.32 mlocal: ( mworld > $o ) > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mlocal_def,definition,
% 0.29/1.32 ( mlocal
% 0.29/1.32 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mnot_type,type,
% 0.29/1.32 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mand_type,type,
% 0.29/1.32 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mor_type,type,
% 0.29/1.32 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mimplies_type,type,
% 0.29/1.32 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mequiv_type,type,
% 0.29/1.32 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mnot_def,definition,
% 0.29/1.32 ( mnot
% 0.29/1.32 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/1.32 ~ ( A @ W ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mand_def,definition,
% 0.29/1.32 ( mand
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 & ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mor_def,definition,
% 0.29/1.32 ( mor
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 | ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mimplies_def,definition,
% 0.29/1.32 ( mimplies
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 => ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mequiv_def,definition,
% 0.29/1.32 ( mequiv
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 <=> ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mbox_type,type,
% 0.29/1.32 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mbox_def,definition,
% 0.29/1.32 ( mbox
% 0.29/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/1.32 ! [V: mworld] :
% 0.29/1.32 ( ( mrel @ W @ V )
% 0.29/1.32 => ( Phi @ V ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mdia_type,type,
% 0.29/1.32 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mdia_def,definition,
% 0.29/1.32 ( mdia
% 0.29/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/1.32 ? [V: mworld] :
% 0.29/1.32 ( ( mrel @ W @ V )
% 0.29/1.32 & ( Phi @ V ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mrel_reflexive,axiom,
% 0.29/1.32 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.29/1.32
% 0.29/1.32 thf(eiw_di_type,type,
% 0.29/1.32 eiw_di: $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(eiw_di_nonempty,axiom,
% 0.29/1.32 ! [W: mworld] :
% 0.29/1.32 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.29/1.32
% 0.29/1.32 thf(eiw_di_decr,axiom,
% 0.29/1.32 ! [W: mworld,V: mworld,X: $i] :
% 0.29/1.32 ( ( ( eiw_di @ X @ W )
% 0.29/1.32 & ( mrel @ V @ W ) )
% 0.29/1.32 => ( eiw_di @ X @ V ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mforall_di_type,type,
% 0.29/1.32 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mforall_di_def,definition,
% 0.29/1.32 ( mforall_di
% 0.29/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/1.32 ! [X: $i] :
% 0.29/1.32 ( ( eiw_di @ X @ W )
% 0.29/1.32 => ( A @ X @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mexists_di_type,type,
% 0.29/1.32 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mexists_di_def,definition,
% 0.29/1.32 ( mexists_di
% 0.29/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/1.32 ? [X: $i] :
% 0.29/1.32 ( ( eiw_di @ X @ W )
% 0.29/1.32 & ( A @ X @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(empty_set_decl,type,
% 0.29/1.32 empty_set: $i ).
% 0.29/1.32
% 0.29/1.32 thf(qmltpeq_decl,type,
% 0.29/1.32 qmltpeq: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(equal_set_decl,type,
% 0.29/1.32 equal_set: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(member_decl,type,
% 0.29/1.32 member: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(subset_decl,type,
% 0.29/1.32 subset: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(singleton_decl,type,
% 0.29/1.32 singleton: $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(product_decl,type,
% 0.29/1.32 product: $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(unordered_pair_decl,type,
% 0.29/1.32 unordered_pair: $i > $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(intersection_decl,type,
% 0.29/1.32 intersection: $i > $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(difference_decl,type,
% 0.29/1.32 difference: $i > $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(sum_decl,type,
% 0.29/1.32 sum: $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(union_decl,type,
% 0.29/1.32 union: $i > $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(power_set_decl,type,
% 0.29/1.32 power_set: $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(reflexivity,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(symmetry,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(transitivity,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Y: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(difference_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(difference_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(intersection_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(intersection_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(power_set_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(product_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(singleton_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(sum_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(union_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(union_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(unordered_pair_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(unordered_pair_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(equal_set_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(equal_set_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(member_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(member_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(subset_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(subset_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(subset_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mequiv @ ( subset @ A @ B )
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(equal_set_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(power_set_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(intersection_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(union_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(empty_set_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(difference_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(singleton_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(unordered_pair_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(sum_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.29/1.32 @ ( mexists_di
% 0.29/1.32 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(product_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(thI02,conjecture,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ) ).
% 0.29/1.32 ------------------------
% 0.29/1.33 % (7141)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/18Mi)
% 0.29/1.33 % (7137)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_6821 for (2999ds/27Mi)
% 0.29/1.34 % (7141)Instruction limit reached!
% 0.29/1.34 % (7141)------------------------------
% 0.29/1.34 % (7141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (7141)Termination reason: Unknown
% 0.29/1.34 % (7141)Termination phase: Property scanning
% 0.29/1.34
% 0.29/1.34 % (7141)Memory used [KB]: 1151
% 0.29/1.34 % (7141)Time elapsed: 0.007 s
% 0.29/1.34 % (7141)Instructions burned: 21 (million)
% 0.29/1.34 % (7141)------------------------------
% 0.29/1.34 % (7141)------------------------------
% 0.29/1.34 % (7135)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/183Mi)
% 0.29/1.34 % (7136)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_6821 for (2999ds/4Mi)
% 0.29/1.34 % (7138)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/2Mi)
% 0.29/1.34 % (7139)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_6821 for (2999ds/2Mi)
% 0.29/1.34 % (7140)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_6821 for (2999ds/275Mi)
% 0.29/1.34 % (7137)Instruction limit reached!
% 0.29/1.34 % (7137)------------------------------
% 0.29/1.34 % (7137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (7137)Termination reason: Unknown
% 0.29/1.34 % (7137)Termination phase: Saturation
% 0.29/1.34
% 0.29/1.34 % (7137)Memory used [KB]: 5756
% 0.29/1.34 % (7137)Time elapsed: 0.009 s
% 0.29/1.34 % (7137)Instructions burned: 29 (million)
% 0.29/1.34 % (7137)------------------------------
% 0.29/1.34 % (7137)------------------------------
% 0.29/1.34 % (7138)Instruction limit reached!
% 0.29/1.34 % (7138)------------------------------
% 0.29/1.34 % (7138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (7138)Termination reason: Unknown
% 0.29/1.34 % (7138)Termination phase: shuffling
% 0.29/1.34
% 0.29/1.34 % (7138)Memory used [KB]: 1023
% 0.29/1.34 % (7138)Time elapsed: 0.003 s
% 0.29/1.34 % (7138)Instructions burned: 2 (million)
% 0.29/1.34 % (7138)------------------------------
% 0.29/1.34 % (7138)------------------------------
% 0.29/1.34 % (7139)Instruction limit reached!
% 0.29/1.34 % (7139)------------------------------
% 0.29/1.34 % (7139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (7139)Termination reason: Unknown
% 0.29/1.34 % (7139)Termination phase: shuffling
% 0.29/1.34
% 0.29/1.34 % (7139)Memory used [KB]: 1023
% 0.29/1.34 % (7139)Time elapsed: 0.003 s
% 0.29/1.34 % (7139)Instructions burned: 2 (million)
% 0.29/1.34 % (7139)------------------------------
% 0.29/1.34 % (7139)------------------------------
% 0.29/1.34 % (7136)Instruction limit reached!
% 0.29/1.34 % (7136)------------------------------
% 0.29/1.34 % (7136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (7136)Termination reason: Unknown
% 0.29/1.34 % (7136)Termination phase: shuffling
% 0.29/1.34
% 0.29/1.34 % (7136)Memory used [KB]: 1023
% 0.29/1.34 % (7136)Time elapsed: 0.004 s
% 0.29/1.34 % (7136)Instructions burned: 4 (million)
% 0.29/1.34 % (7136)------------------------------
% 0.29/1.34 % (7136)------------------------------
% 0.29/1.35 % (7142)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/3Mi)
% 0.29/1.35 % (7140)Refutation not found, incomplete strategy
% 0.29/1.35 % (7140)------------------------------
% 0.29/1.35 % (7140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.35 % (7140)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.35
% 0.29/1.35
% 0.29/1.35 % (7140)Memory used [KB]: 5628
% 0.29/1.35 % (7140)Time elapsed: 0.010 s
% 0.29/1.35 % (7140)Instructions burned: 13 (million)
% 0.29/1.35 % (7140)------------------------------
% 0.29/1.35 % (7140)------------------------------
% 0.29/1.35 % (7142)Instruction limit reached!
% 0.29/1.35 % (7142)------------------------------
% 0.29/1.35 % (7142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.35 % (7142)Termination reason: Unknown
% 0.29/1.35 % (7142)Termination phase: shuffling
% 0.29/1.35
% 0.29/1.35 % (7142)Memory used [KB]: 1023
% 0.29/1.35 % (7142)Time elapsed: 0.002 s
% 0.29/1.35 % (7142)Instructions burned: 4 (million)
% 0.29/1.35 % (7142)------------------------------
% 0.29/1.35 % (7142)------------------------------
% 0.29/1.35 % (7143)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_6821 for (2999ds/37Mi)
% 0.29/1.36 % (7147)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/7Mi)
% 0.29/1.36 % (7144)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_6821 for (2999ds/15Mi)
% 0.29/1.36 % (7145)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_6821 for (2999ds/3Mi)
% 0.29/1.36 % (7146)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_6821 for (2999ds/1041Mi)
% 0.29/1.36 % (7147)Instruction limit reached!
% 0.29/1.36 % (7147)------------------------------
% 0.29/1.36 % (7147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.36 % (7147)Termination reason: Unknown
% 0.29/1.36 % (7147)Termination phase: shuffling
% 0.29/1.36
% 0.29/1.36 % (7147)Memory used [KB]: 1151
% 0.29/1.36 % (7147)Time elapsed: 0.003 s
% 0.29/1.36 % (7147)Instructions burned: 7 (million)
% 0.29/1.36 % (7147)------------------------------
% 0.29/1.36 % (7147)------------------------------
% 0.29/1.36 % (7145)Instruction limit reached!
% 0.29/1.36 % (7145)------------------------------
% 0.29/1.36 % (7145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.36 % (7145)Termination reason: Unknown
% 0.29/1.36 % (7145)Termination phase: shuffling
% 0.29/1.36
% 0.29/1.36 % (7145)Memory used [KB]: 1023
% 0.29/1.36 % (7145)Time elapsed: 0.004 s
% 0.29/1.36 % (7145)Instructions burned: 4 (million)
% 0.29/1.36 % (7145)------------------------------
% 0.29/1.36 % (7145)------------------------------
% 0.29/1.36 % (7143)Instruction limit reached!
% 0.29/1.36 % (7143)------------------------------
% 0.29/1.36 % (7143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.36 % (7143)Termination reason: Unknown
% 0.29/1.36 % (7143)Termination phase: Saturation
% 0.29/1.36
% 0.29/1.36 % (7143)Memory used [KB]: 5884
% 0.29/1.36 % (7143)Time elapsed: 0.012 s
% 0.29/1.36 % (7143)Instructions burned: 38 (million)
% 0.29/1.36 % (7143)------------------------------
% 0.29/1.36 % (7143)------------------------------
% 0.29/1.37 % (7148)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/16Mi)
% 0.29/1.37 % (7144)Instruction limit reached!
% 0.29/1.37 % (7144)------------------------------
% 0.29/1.37 % (7144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (7144)Termination reason: Unknown
% 0.29/1.37 % (7144)Termination phase: Function definition elimination
% 0.29/1.37
% 0.29/1.37 % (7144)Memory used [KB]: 1151
% 0.29/1.37 % (7144)Time elapsed: 0.010 s
% 0.29/1.37 % (7144)Instructions burned: 17 (million)
% 0.29/1.37 % (7144)------------------------------
% 0.29/1.37 % (7144)------------------------------
% 0.29/1.37 % (7149)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_6821 for (2999ds/3Mi)
% 0.29/1.37 % (7149)Instruction limit reached!
% 0.29/1.37 % (7149)------------------------------
% 0.29/1.37 % (7149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (7149)Termination reason: Unknown
% 0.29/1.37 % (7149)Termination phase: shuffling
% 0.29/1.37
% 0.29/1.37 % (7149)Memory used [KB]: 1023
% 0.29/1.37 % (7149)Time elapsed: 0.002 s
% 0.29/1.37 % (7149)Instructions burned: 4 (million)
% 0.29/1.37 % (7149)------------------------------
% 0.29/1.37 % (7149)------------------------------
% 0.29/1.37 % (7151)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/7Mi)
% 0.29/1.37 % (7151)Instruction limit reached!
% 0.29/1.37 % (7151)------------------------------
% 0.29/1.37 % (7151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (7151)Termination reason: Unknown
% 0.29/1.37 % (7151)Termination phase: Property scanning
% 0.29/1.37
% 0.29/1.37 % (7151)Memory used [KB]: 1151
% 0.29/1.37 % (7151)Time elapsed: 0.004 s
% 0.29/1.37 % (7151)Instructions burned: 8 (million)
% 0.29/1.37 % (7151)------------------------------
% 0.29/1.37 % (7151)------------------------------
% 0.29/1.37 % (7148)Instruction limit reached!
% 0.29/1.37 % (7148)------------------------------
% 0.29/1.37 % (7148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (7148)Termination reason: Unknown
% 0.29/1.37 % (7148)Termination phase: Twee Goal Transformation
% 0.29/1.37
% 0.29/1.37 % (7148)Memory used [KB]: 1151
% 0.29/1.37 % (7148)Time elapsed: 0.010 s
% 0.29/1.37 % (7148)Instructions burned: 17 (million)
% 0.29/1.37 % (7148)------------------------------
% 0.29/1.37 % (7148)------------------------------
% 0.29/1.38 % (7150)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_6821 for (2999ds/3Mi)
% 0.29/1.38 % (7153)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/4Mi)
% 0.29/1.38 % (7150)Instruction limit reached!
% 0.29/1.38 % (7150)------------------------------
% 0.29/1.38 % (7150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.38 % (7150)Termination reason: Unknown
% 0.29/1.38 % (7150)Termination phase: shuffling
% 0.29/1.38
% 0.29/1.38 % (7150)Memory used [KB]: 1023
% 0.29/1.38 % (7150)Time elapsed: 0.004 s
% 0.29/1.38 % (7150)Instructions burned: 5 (million)
% 0.29/1.38 % (7150)------------------------------
% 0.29/1.38 % (7150)------------------------------
% 0.29/1.38 % (7153)Instruction limit reached!
% 0.29/1.38 % (7153)------------------------------
% 0.29/1.38 % (7153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.38 % (7153)Termination reason: Unknown
% 0.29/1.38 % (7153)Termination phase: shuffling
% 0.29/1.38
% 0.29/1.38 % (7153)Memory used [KB]: 1023
% 0.29/1.38 % (7153)Time elapsed: 0.002 s
% 0.29/1.38 % (7153)Instructions burned: 4 (million)
% 0.29/1.38 % (7153)------------------------------
% 0.29/1.38 % (7153)------------------------------
% 0.29/1.38 % (7154)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/18Mi)
% 0.29/1.38 % (7152)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/3Mi)
% 0.29/1.39 % (7152)Instruction limit reached!
% 0.29/1.39 % (7152)------------------------------
% 0.29/1.39 % (7152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.39 % (7152)Termination reason: Unknown
% 0.29/1.39 % (7152)Termination phase: shuffling
% 0.29/1.39
% 0.29/1.39 % (7152)Memory used [KB]: 1023
% 0.29/1.39 % (7152)Time elapsed: 0.003 s
% 0.29/1.39 % (7152)Instructions burned: 3 (million)
% 0.29/1.39 % (7152)------------------------------
% 0.29/1.39 % (7152)------------------------------
% 0.29/1.39 % (7154)Instruction limit reached!
% 0.29/1.39 % (7154)------------------------------
% 0.29/1.39 % (7154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.39 % (7154)Termination reason: Unknown
% 0.29/1.39 % (7154)Termination phase: Saturation
% 0.29/1.39
% 0.29/1.39 % (7154)Memory used [KB]: 5628
% 0.29/1.39 % (7154)Time elapsed: 0.007 s
% 0.29/1.39 % (7154)Instructions burned: 19 (million)
% 0.29/1.39 % (7154)------------------------------
% 0.29/1.39 % (7154)------------------------------
% 0.29/1.39 % (7157)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_6821 for (2999ds/902Mi)
% 0.29/1.39 % (7155)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/710Mi)
% 0.29/1.40 % (7157)Refutation not found, incomplete strategy
% 0.29/1.40 % (7157)------------------------------
% 0.29/1.40 % (7157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.40 % (7157)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.40
% 0.29/1.40
% 0.29/1.40 % (7157)Memory used [KB]: 5628
% 0.29/1.40 % (7157)Time elapsed: 0.006 s
% 0.29/1.40 % (7157)Instructions burned: 18 (million)
% 0.29/1.40 % (7157)------------------------------
% 0.29/1.40 % (7157)------------------------------
% 1.95/1.40 % (7156)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/6Mi)
% 1.95/1.40 % (7159)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/5Mi)
% 1.95/1.40 % (7156)Instruction limit reached!
% 1.95/1.40 % (7156)------------------------------
% 1.95/1.40 % (7156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.40 % (7156)Termination reason: Unknown
% 1.95/1.40 % (7156)Termination phase: shuffling
% 1.95/1.40
% 1.95/1.40 % (7156)Memory used [KB]: 1151
% 1.95/1.40 % (7156)Time elapsed: 0.004 s
% 1.95/1.40 % (7156)Instructions burned: 6 (million)
% 1.95/1.40 % (7156)------------------------------
% 1.95/1.40 % (7156)------------------------------
% 1.95/1.40 % (7159)Instruction limit reached!
% 1.95/1.40 % (7159)------------------------------
% 1.95/1.40 % (7159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.40 % (7159)Termination reason: Unknown
% 1.95/1.40 % (7159)Termination phase: shuffling
% 1.95/1.40
% 1.95/1.40 % (7159)Memory used [KB]: 1151
% 1.95/1.40 % (7159)Time elapsed: 0.003 s
% 1.95/1.40 % (7159)Instructions burned: 5 (million)
% 1.95/1.40 % (7159)------------------------------
% 1.95/1.40 % (7159)------------------------------
% 1.95/1.40 % (7158)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_6821 for (2999ds/21Mi)
% 1.95/1.41 % (7160)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_6821 for (2999ds/6Mi)
% 1.95/1.41 % (7160)Instruction limit reached!
% 1.95/1.41 % (7160)------------------------------
% 1.95/1.41 % (7160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.41 % (7160)Termination reason: Unknown
% 1.95/1.41 % (7160)Termination phase: Property scanning
% 1.95/1.41
% 1.95/1.41 % (7160)Memory used [KB]: 1151
% 1.95/1.41 % (7160)Time elapsed: 0.003 s
% 1.95/1.41 % (7160)Instructions burned: 8 (million)
% 1.95/1.41 % (7160)------------------------------
% 1.95/1.41 % (7160)------------------------------
% 1.95/1.41 % (7162)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_6821 for (2999ds/779Mi)
% 1.95/1.41 % (7158)Instruction limit reached!
% 1.95/1.41 % (7158)------------------------------
% 1.95/1.41 % (7158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.41 % (7158)Termination reason: Unknown
% 1.95/1.41 % (7158)Termination phase: Property scanning
% 1.95/1.41
% 1.95/1.41 % (7158)Memory used [KB]: 1151
% 1.95/1.41 % (7158)Time elapsed: 0.012 s
% 1.95/1.41 % (7158)Instructions burned: 21 (million)
% 1.95/1.41 % (7158)------------------------------
% 1.95/1.41 % (7158)------------------------------
% 1.95/1.41 % (7161)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6821 for (2999ds/377Mi)
% 1.95/1.42 % (7163)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_6821 for (2999ds/19Mi)
% 1.95/1.42 % (7135)First to succeed.
% 1.95/1.42 % (7163)Refutation not found, incomplete strategy
% 1.95/1.42 % (7163)------------------------------
% 1.95/1.42 % (7163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.42 % (7163)Termination reason: Refutation not found, incomplete strategy
% 1.95/1.42
% 1.95/1.42
% 1.95/1.42 % (7163)Memory used [KB]: 5628
% 1.95/1.42 % (7163)Time elapsed: 0.005 s
% 1.95/1.42 % (7163)Instructions burned: 15 (million)
% 1.95/1.42 % (7163)------------------------------
% 1.95/1.42 % (7163)------------------------------
% 1.95/1.42 % (7162)Refutation not found, incomplete strategy
% 1.95/1.42 % (7162)------------------------------
% 1.95/1.42 % (7162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.42 % (7162)Termination reason: Refutation not found, incomplete strategy
% 1.95/1.42
% 1.95/1.42
% 1.95/1.42 % (7162)Memory used [KB]: 5756
% 1.95/1.42 % (7162)Time elapsed: 0.013 s
% 1.95/1.42 % (7162)Instructions burned: 38 (million)
% 1.95/1.42 % (7162)------------------------------
% 1.95/1.42 % (7162)------------------------------
% 1.95/1.42 % (7135)Refutation found. Thanks to Tanya!
% 1.95/1.42 % SZS status Theorem for DTF2THF_6821
% 1.95/1.42 % SZS output start Proof for DTF2THF_6821
% 1.95/1.42 thf(type_def_5, type, mworld: $tType).
% 1.95/1.42 thf(func_def_0, type, mworld: $tType).
% 1.95/1.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.95/1.42 thf(func_def_2, type, mactual: mworld).
% 1.95/1.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.95/1.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.95/1.42 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.95/1.42 thf(func_def_16, type, qmltpeq: $i > $i > mworld > $o).
% 1.95/1.42 thf(func_def_17, type, equal_set: $i > $i > mworld > $o).
% 1.95/1.42 thf(func_def_18, type, member: $i > $i > mworld > $o).
% 1.95/1.42 thf(func_def_19, type, subset: $i > $i > mworld > $o).
% 1.95/1.42 thf(func_def_20, type, singleton: $i > $i).
% 1.95/1.42 thf(func_def_21, type, product: $i > $i).
% 1.95/1.42 thf(func_def_22, type, unordered_pair: $i > $i > $i).
% 1.95/1.42 thf(func_def_23, type, intersection: $i > $i > $i).
% 1.95/1.42 thf(func_def_24, type, difference: $i > $i > $i).
% 1.95/1.42 thf(func_def_25, type, sum: $i > $i).
% 1.95/1.42 thf(func_def_26, type, union: $i > $i > $i).
% 1.95/1.42 thf(func_def_27, type, power_set: $i > $i).
% 1.95/1.42 thf(func_def_41, type, sK0: mworld > $i).
% 1.95/1.42 thf(func_def_45, type, sK2: $i > $i > $i).
% 1.95/1.42 thf(func_def_46, type, sK3: $i > $i > $i).
% 1.95/1.42 thf(func_def_49, type, sK6: $i > $i > $i).
% 1.95/1.42 thf(f824,plain,(
% 1.95/1.42 $false),
% 1.95/1.42 inference(avatar_sat_refutation,[status(thm)],[f779,f788,f797,f810,f822])).
% 1.95/1.42 thf(f822,plain,(
% 1.95/1.42 ~spl1_7),
% 1.95/1.42 inference(avatar_contradiction_clause,[status(thm)],[f821])).
% 1.95/1.42 thf(f821,plain,(
% 1.95/1.42 $false | ~spl1_7),
% 1.95/1.42 inference(trivial_inequality_removal,[status(thm)],[f815])).
% 1.95/1.42 thf(f815,plain,(
% 1.95/1.42 ($false = $true) | ~spl1_7),
% 1.95/1.42 inference(superposition,[status(thm)],[f777,f568])).
% 1.95/1.42 thf(f568,plain,(
% 1.95/1.42 ((subset @ sK4 @ sK5 @ mactual) = $true)),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f566])).
% 1.95/1.42 thf(f566,plain,(
% 1.95/1.42 (((subset @ sK4 @ sK5 @ mactual) & (subset @ sK5 @ sK4 @ mactual)) = $true)),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f563])).
% 1.95/1.42 thf(f563,plain,(
% 1.95/1.42 ($false = (((subset @ sK4 @ sK5 @ mactual) & (subset @ sK5 @ sK4 @ mactual)) => (equal_set @ sK4 @ sK5 @ mactual)))),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f562])).
% 1.95/1.42 thf(f562,plain,(
% 1.95/1.42 ($false = ((eiw_di @ sK5 @ mactual) => (((subset @ sK4 @ sK5 @ mactual) & (subset @ sK5 @ sK4 @ mactual)) => (equal_set @ sK4 @ sK5 @ mactual))))),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f561])).
% 1.95/1.42 thf(f561,plain,(
% 1.95/1.42 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK4 @ Y0 @ mactual) & (subset @ Y0 @ sK4 @ mactual)) => (equal_set @ sK4 @ Y0 @ mactual)))) @ sK5))),
% 1.95/1.42 inference(sigma_clausification,[status(thm)],[f559])).
% 1.95/1.42 thf(f559,plain,(
% 1.95/1.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK4 @ Y0 @ mactual) & (subset @ Y0 @ sK4 @ mactual)) => (equal_set @ sK4 @ Y0 @ mactual))))))),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f558])).
% 1.95/1.42 thf(f558,plain,(
% 1.95/1.42 ($false = ((eiw_di @ sK4 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK4 @ Y0 @ mactual) & (subset @ Y0 @ sK4 @ mactual)) => (equal_set @ sK4 @ Y0 @ mactual)))))))),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f557])).
% 1.95/1.42 thf(f557,plain,(
% 1.95/1.42 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) => (equal_set @ Y0 @ Y1 @ mactual))))))) @ sK4))),
% 1.95/1.42 inference(sigma_clausification,[status(thm)],[f556])).
% 1.95/1.42 thf(f556,plain,(
% 1.95/1.42 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) => (equal_set @ Y0 @ Y1 @ mactual)))))))) != $true)),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f207])).
% 1.95/1.42 thf(f207,plain,(
% 1.95/1.42 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))))),
% 1.95/1.42 inference(definition_unfolding,[status(thm)],[f168,f173,f176,f176,f154,f160])).
% 1.95/1.42 thf(f160,plain,(
% 1.95/1.42 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f124])).
% 1.95/1.42 thf(f124,plain,(
% 1.95/1.42 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f123])).
% 1.95/1.42 thf(f123,plain,(
% 1.95/1.42 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.95/1.42 inference(rectify,[status(thm)],[f3])).
% 1.95/1.42 thf(f3,axiom,(
% 1.95/1.42 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mand_def)).
% 1.95/1.42 thf(f154,plain,(
% 1.95/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f106])).
% 1.95/1.42 thf(f106,plain,(
% 1.95/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f105])).
% 1.95/1.42 thf(f105,plain,(
% 1.95/1.42 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.95/1.42 inference(rectify,[status(thm)],[f5])).
% 1.95/1.42 thf(f5,axiom,(
% 1.95/1.42 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mimplies_def)).
% 1.95/1.42 thf(f176,plain,(
% 1.95/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f114])).
% 1.95/1.42 thf(f114,plain,(
% 1.95/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f113])).
% 1.95/1.42 thf(f113,plain,(
% 1.95/1.42 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.95/1.42 inference(rectify,[status(thm)],[f12])).
% 1.95/1.42 thf(f12,axiom,(
% 1.95/1.42 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))) = mforall_di)),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mforall_di_def)).
% 1.95/1.42 thf(f173,plain,(
% 1.95/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f135])).
% 1.95/1.42 thf(f135,plain,(
% 1.95/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f1])).
% 1.95/1.42 thf(f1,axiom,(
% 1.95/1.42 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mlocal_def)).
% 1.95/1.42 thf(f168,plain,(
% 1.95/1.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) != $true)),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f140])).
% 1.95/1.42 thf(f140,plain,(
% 1.95/1.42 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) != $true)),
% 1.95/1.42 inference(flattening,[status(thm)],[f68])).
% 1.95/1.42 thf(f68,plain,(
% 1.95/1.42 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) = $true)),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f67])).
% 1.95/1.42 thf(f67,plain,(
% 1.95/1.42 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mimplies @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0)) @ (equal_set @ X0 @ X1)))))))),
% 1.95/1.42 inference(rectify,[status(thm)],[f47])).
% 1.95/1.42 thf(f47,negated_conjecture,(
% 1.95/1.42 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mimplies @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1)) @ (equal_set @ X1 @ X3)))))))),
% 1.95/1.42 inference(negated_conjecture,[status(cth)],[f46])).
% 1.95/1.42 thf(f46,conjecture,(
% 1.95/1.42 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mimplies @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1)) @ (equal_set @ X1 @ X3)))))))),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',thI02)).
% 1.95/1.42 thf(f777,plain,(
% 1.95/1.42 ($false = (subset @ sK4 @ sK5 @ mactual)) | ~spl1_7),
% 1.95/1.42 inference(avatar_component_clause,[status(thm)],[f775])).
% 1.95/1.42 thf(f775,definition,(
% 1.95/1.42 spl1_7 <=> ($false = (subset @ sK4 @ sK5 @ mactual))),
% 1.95/1.42 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.95/1.42 thf(f810,plain,(
% 1.95/1.42 ~spl1_6),
% 1.95/1.42 inference(avatar_contradiction_clause,[status(thm)],[f809])).
% 1.95/1.42 thf(f809,plain,(
% 1.95/1.42 $false | ~spl1_6),
% 1.95/1.42 inference(trivial_inequality_removal,[status(thm)],[f803])).
% 1.95/1.42 thf(f803,plain,(
% 1.95/1.42 ($false = $true) | ~spl1_6),
% 1.95/1.42 inference(superposition,[status(thm)],[f560,f773])).
% 1.95/1.42 thf(f773,plain,(
% 1.95/1.42 ($false = (eiw_di @ sK4 @ mactual)) | ~spl1_6),
% 1.95/1.42 inference(avatar_component_clause,[status(thm)],[f771])).
% 1.95/1.42 thf(f771,definition,(
% 1.95/1.42 spl1_6 <=> ($false = (eiw_di @ sK4 @ mactual))),
% 1.95/1.42 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.95/1.42 thf(f560,plain,(
% 1.95/1.42 ((eiw_di @ sK4 @ mactual) = $true)),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f558])).
% 1.95/1.42 thf(f797,plain,(
% 1.95/1.42 ~spl1_5),
% 1.95/1.42 inference(avatar_contradiction_clause,[status(thm)],[f796])).
% 1.95/1.42 thf(f796,plain,(
% 1.95/1.42 $false | ~spl1_5),
% 1.95/1.42 inference(trivial_inequality_removal,[status(thm)],[f791])).
% 1.95/1.42 thf(f791,plain,(
% 1.95/1.42 ($false = $true) | ~spl1_5),
% 1.95/1.42 inference(superposition,[status(thm)],[f564,f769])).
% 1.95/1.42 thf(f769,plain,(
% 1.95/1.42 ($false = (eiw_di @ sK5 @ mactual)) | ~spl1_5),
% 1.95/1.42 inference(avatar_component_clause,[status(thm)],[f767])).
% 1.95/1.42 thf(f767,definition,(
% 1.95/1.42 spl1_5 <=> ($false = (eiw_di @ sK5 @ mactual))),
% 1.95/1.42 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.95/1.42 thf(f564,plain,(
% 1.95/1.42 ($true = (eiw_di @ sK5 @ mactual))),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f562])).
% 1.95/1.42 thf(f788,plain,(
% 1.95/1.42 ~spl1_4),
% 1.95/1.42 inference(avatar_contradiction_clause,[status(thm)],[f787])).
% 1.95/1.42 thf(f787,plain,(
% 1.95/1.42 $false | ~spl1_4),
% 1.95/1.42 inference(trivial_inequality_removal,[status(thm)],[f782])).
% 1.95/1.42 thf(f782,plain,(
% 1.95/1.42 ($false = $true) | ~spl1_4),
% 1.95/1.42 inference(superposition,[status(thm)],[f567,f765])).
% 1.95/1.42 thf(f765,plain,(
% 1.95/1.42 ($false = (subset @ sK5 @ sK4 @ mactual)) | ~spl1_4),
% 1.95/1.42 inference(avatar_component_clause,[status(thm)],[f763])).
% 1.95/1.42 thf(f763,definition,(
% 1.95/1.42 spl1_4 <=> ($false = (subset @ sK5 @ sK4 @ mactual))),
% 1.95/1.42 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.95/1.42 thf(f567,plain,(
% 1.95/1.42 ($true = (subset @ sK5 @ sK4 @ mactual))),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f566])).
% 1.95/1.42 thf(f779,plain,(
% 1.95/1.42 spl1_6 | spl1_5 | spl1_7 | spl1_4),
% 1.95/1.42 inference(avatar_split_clause,[status(thm)],[f754,f763,f775,f767,f771])).
% 1.95/1.42 thf(f754,plain,(
% 1.95/1.42 ($false = (subset @ sK4 @ sK5 @ mactual)) | ($false = (eiw_di @ sK5 @ mactual)) | ($false = (subset @ sK5 @ sK4 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual))),
% 1.95/1.42 inference(trivial_inequality_removal,[status(thm)],[f751])).
% 1.95/1.42 thf(f751,plain,(
% 1.95/1.42 ($false = (subset @ sK4 @ sK5 @ mactual)) | ($false = (eiw_di @ sK5 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual)) | ($false = $true) | ($false = (subset @ sK5 @ sK4 @ mactual))),
% 1.95/1.42 inference(superposition,[status(thm)],[f565,f507])).
% 1.95/1.42 thf(f507,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (equal_set @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X1 @ mactual)) | ($false = (subset @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ($false = (subset @ X2 @ X1 @ mactual))) )),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f506])).
% 1.95/1.42 thf(f506,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : (($false = ((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual))) | ($false = (eiw_di @ X1 @ mactual)) | ($true = (equal_set @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f504])).
% 1.95/1.42 thf(f504,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | (((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = (equal_set @ X1 @ X2 @ mactual))) )),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f503])).
% 1.95/1.42 thf(f503,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = (equal_set @ X1 @ X2 @ mactual)) = $true) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f502])).
% 1.95/1.42 thf(f502,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => (((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = (equal_set @ X1 @ X2 @ mactual)))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f501])).
% 1.95/1.42 thf(f501,plain,(
% 1.95/1.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual)) = (equal_set @ X1 @ Y0 @ mactual)))) @ X2) = $true) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.95/1.42 inference(pi_clausification,[status(thm)],[f500])).
% 1.95/1.42 thf(f500,plain,(
% 1.95/1.42 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual)) = (equal_set @ X1 @ Y0 @ mactual))))) = $true)) )),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f499])).
% 1.95/1.42 thf(f499,plain,(
% 1.95/1.42 ( ! [X1 : $i] : ((((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual)) = (equal_set @ X1 @ Y0 @ mactual)))))) = $true)) )),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f498])).
% 1.95/1.42 thf(f498,plain,(
% 1.95/1.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) = (equal_set @ Y0 @ Y1 @ mactual))))))) @ X1) = $true)) )),
% 1.95/1.42 inference(pi_clausification,[status(thm)],[f497])).
% 1.95/1.42 thf(f497,plain,(
% 1.95/1.42 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) = (equal_set @ Y0 @ Y1 @ mactual)))))))) = $true)),
% 1.95/1.42 inference(beta_eta_normalization,[status(thm)],[f191])).
% 1.95/1.42 thf(f191,plain,(
% 1.95/1.42 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (equal_set @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 1.95/1.42 inference(definition_unfolding,[status(thm)],[f146,f173,f176,f176,f161,f160])).
% 1.95/1.42 thf(f161,plain,(
% 1.95/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f108])).
% 1.95/1.42 thf(f108,plain,(
% 1.95/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f107])).
% 1.95/1.42 thf(f107,plain,(
% 1.95/1.42 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))) = mequiv)),
% 1.95/1.42 inference(rectify,[status(thm)],[f6])).
% 1.95/1.42 thf(f6,axiom,(
% 1.95/1.42 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))) = mequiv)),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',mequiv_def)).
% 1.95/1.42 thf(f146,plain,(
% 1.95/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 1.95/1.42 inference(cnf_transformation,[status(thm)],[f122])).
% 1.95/1.42 thf(f122,plain,(
% 1.95/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 1.95/1.42 inference(fool_elimination,[status(thm)],[f121])).
% 1.95/1.42 thf(f121,plain,(
% 1.95/1.42 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (equal_set @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 1.95/1.42 inference(rectify,[status(thm)],[f36])).
% 1.95/1.42 thf(f36,axiom,(
% 1.95/1.42 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (equal_set @ X1 @ X3) @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1))))))))),
% 1.95/1.42 file('/export/starexec/sandbox/tmp/tmp.1DI5ytlWYR/DTF2THF_6821.p',equal_set_0)).
% 1.95/1.42 thf(f565,plain,(
% 1.95/1.42 ($false = (equal_set @ sK4 @ sK5 @ mactual))),
% 1.95/1.42 inference(binary_proxy_clausification,[status(thm)],[f563])).
% 1.95/1.42 % SZS output end Proof for DTF2THF_6821
% 1.95/1.42 % (7135)------------------------------
% 1.95/1.42 % (7135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.42 % (7135)Termination reason: Refutation
% 1.95/1.42
% 1.95/1.42 % (7135)Memory used [KB]: 6652
% 1.95/1.42 % (7135)Time elapsed: 0.083 s
% 1.95/1.42 % (7135)Instructions burned: 145 (million)
% 1.95/1.42 % (7135)------------------------------
% 1.95/1.42 % (7135)------------------------------
% 1.95/1.42 % (7134)Success in time 0.088 s
%------------------------------------------------------------------------------