%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET047^1 : 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 : n015.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 09:31:04 AM UTC 2026
% Result : Theorem 1.70s 1.37s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 86 ( 31 unt; 0 typ; 4 def)
% Number of atoms : 602 ( 155 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 779 ( 34 ~; 82 |; 0 &; 634 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 10 con; 0-3 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 169 ( 102 ^; 67 !; 0 ?; 169 :)
% 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_14,type,
set_equal: $i > $i > mworld > $o ).
thf(func_def_15,type,
element: $i > $i > mworld > $o ).
thf(func_def_34,type,
sK3: $i > $i > $i ).
thf(f477,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f87,f96,f102,f462,f472,f476]) ).
thf(f476,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f475]) ).
thf(f475,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f467,f90]) ).
thf(f90,plain,
( ( $false
!= ( set_equal @ sK1 @ sK2 @ mactual ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl0_3
<=> ( $false
= ( set_equal @ sK1 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f467,plain,
( ( $false
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f466]) ).
thf(f466,plain,
( ( $false = $true )
| ( $false
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f450,f95]) ).
thf(f95,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl0_4
<=> ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f450,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f449]) ).
thf(f449,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f408]) ).
thf(f408,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f245,f216]) ).
thf(f216,plain,
! [X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X1 @ mactual )
= $true )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X1 @ mactual )
= $true ) ),
inference(equality_factoring,[status(thm)],[f115]) ).
thf(f115,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $true )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X1 @ mactual )
= $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X1 @ mactual )
= $true )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $true )
| ( $false = $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) ) ),
inference(superposition,[status(thm)],[f72,f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( element @ X3 @ X2 @ mactual ) )
| ( ( element @ X3 @ X1 @ mactual )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( element @ X3 @ X1 @ mactual )
= ( element @ X3 @ X2 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( element @ X3 @ X2 @ mactual )
= ( element @ X3 @ X1 @ mactual ) )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) )
@ X3 )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) ) )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) ) )
= ( set_equal @ X1 @ X2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) ) )
= ( set_equal @ X1 @ X2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ X1 @ mactual ) ) )
= ( set_equal @ X1 @ Y0 @ mactual ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ X1 @ mactual ) ) )
= ( set_equal @ X1 @ Y0 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( element @ Y2 @ Y1 @ mactual )
= ( element @ Y2 @ Y0 @ mactual ) ) )
= ( set_equal @ Y0 @ Y1 @ mactual ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( element @ Y2 @ Y1 @ mactual )
= ( element @ Y2 @ Y0 @ mactual ) ) )
= ( set_equal @ Y0 @ Y1 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,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] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
= ( Y3 @ Y5 ) )
@ ( element @ Y2 @ Y0 )
@ ( element @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f40,f44,f49,f49,f41,f49,f41]) ).
thf(f41,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',mequiv_def) ).
thf(f49,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',mforall_di_def) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,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.5qRh4fW88Z/DTF2THF_10334.p',mlocal_def) ).
thf(f40,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( set_equal @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y0 ) @ ( element @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( set_equal @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y0 ) @ ( element @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( set_equal @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( element @ X2 @ X0 ) @ ( element @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mlocal
@ ( mforall_di
@ ^ [X5: $i] :
( mforall_di
@ ^ [X6: $i] :
( mequiv @ ( set_equal @ X5 @ X6 )
@ ( mforall_di
@ ^ [X7: $i] : ( mequiv @ ( element @ X7 @ X5 ) @ ( element @ X7 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',pel43_1) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) )
| ( ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $true )
| ( ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual )
!= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $true )
| ( ( ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual )
= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $true )
| ( ( ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) )
@ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X2 @ mactual )
= ( element @ Y0 @ X1 @ mactual ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f245,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f232]) ).
thf(f232,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $false = $true )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) ) ),
inference(superposition,[status(thm)],[f78,f209]) ).
thf(f209,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual ) )
| ( $false = $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f202]) ).
thf(f202,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false = $true )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(superposition,[status(thm)],[f115,f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( element @ X3 @ X2 @ mactual )
= $true )
| ( ( element @ X3 @ X1 @ mactual )
= $false )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f472,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f471]) ).
thf(f471,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f465]) ).
thf(f465,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f82,f95]) ).
thf(f82,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl0_1
<=> ( ( set_equal @ sK2 @ sK1 @ mactual )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f462,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f457,f89,f93]) ).
thf(f457,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f453]) ).
thf(f453,plain,
( ( $false = $true )
| ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f450,f91]) ).
thf(f91,plain,
( ( $false
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f102,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f86,f91]) ).
thf(f86,plain,
( ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl0_2
<=> ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f96,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f60,f93,f89]) ).
thf(f60,plain,
( ( $false
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( set_equal @ sK2 @ sK1 @ mactual )
!= ( set_equal @ sK1 @ sK2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= ( set_equal @ sK1 @ sK2 @ mactual ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ^ [Y0: $i] :
( ( set_equal @ Y0 @ sK1 @ mactual )
= ( set_equal @ sK1 @ Y0 @ mactual ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( set_equal @ Y0 @ sK1 @ mactual )
= ( set_equal @ sK1 @ Y0 @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y1 @ Y0 @ mactual )
= ( set_equal @ Y0 @ Y1 @ mactual ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y1 @ Y0 @ mactual )
= ( set_equal @ Y0 @ Y1 @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,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] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f48,f44,f49,f49,f41]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( set_equal @ X0 @ X1 ) @ ( set_equal @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X5: $i] :
( mforall_di
@ ^ [X6: $i] : ( mequiv @ ( set_equal @ X5 @ X6 ) @ ( set_equal @ X6 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f12,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X5: $i] :
( mforall_di
@ ^ [X6: $i] : ( mequiv @ ( set_equal @ X5 @ X6 ) @ ( set_equal @ X6 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',pel43) ).
thf(f87,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f59,f84,f80]) ).
thf(f59,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $true )
| ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET047^1 : 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
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:50:46 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SET047^1 : TPTP v9.2.1. Released v8.1.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPTP problem SET047+1.p with axiomatized equality
% 0.28/0.46 % Version : [BP13] axioms.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.28/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.28/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.28/0.46 % Source : [TPTP]
% 0.28/0.46 % Names : SET047+1 [QMLTP]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.28/0.46 % Syntax : Number of formulae : 27 ( 10 unt; 15 typ; 10 def)
% 0.28/0.46 % Number of atoms : 37 ( 10 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 9 ( 3 avg)
% 0.28/0.46 % Number of connectives : 50 ( 1 ~; 1 |; 2 &; 43 @)
% 0.28/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 13 ( 3 avg)
% 0.28/0.46 % Number of types : 3 ( 1 usr)
% 0.28/0.46 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 32 ( 28 ^; 2 !; 2 ?; 32 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.28/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.28/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.28/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.28/0.46 % $modalities == $modal_system_K].
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(mworld,type,
% 0.28/0.46 mworld: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(mrel_type,type,
% 0.28/0.46 mrel: mworld > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mactual_type,type,
% 0.28/0.46 mactual: mworld ).
% 0.28/0.46
% 0.28/0.46 thf(mlocal_type,type,
% 0.28/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mlocal_def,definition,
% 0.28/0.46 ( mlocal
% 0.28/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mnot_type,type,
% 0.28/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mand_type,type,
% 0.28/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mor_type,type,
% 0.28/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mimplies_type,type,
% 0.28/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mequiv_type,type,
% 0.28/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mnot_def,definition,
% 0.28/0.46 ( mnot
% 0.28/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.28/0.46 ~ ( A @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mand_def,definition,
% 0.28/0.46 ( mand
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 & ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mor_def,definition,
% 0.28/0.46 ( mor
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 | ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mimplies_def,definition,
% 0.28/0.46 ( mimplies
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 => ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mequiv_def,definition,
% 0.28/0.46 ( mequiv
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 <=> ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mbox_type,type,
% 0.28/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mbox_def,definition,
% 0.28/0.46 ( mbox
% 0.28/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.46 ! [V: mworld] :
% 0.28/0.46 ( ( mrel @ W @ V )
% 0.28/0.46 => ( Phi @ V ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mdia_type,type,
% 0.28/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mdia_def,definition,
% 0.28/0.46 ( mdia
% 0.28/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.46 ? [V: mworld] :
% 0.28/0.46 ( ( mrel @ W @ V )
% 0.28/0.46 & ( Phi @ V ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mforall_di_type,type,
% 0.28/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mforall_di_def,definition,
% 0.28/0.46 ( mforall_di
% 0.28/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mexists_di_type,type,
% 0.28/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mexists_di_def,definition,
% 0.28/0.46 ( mexists_di
% 0.28/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(set_equal_decl,type,
% 0.28/0.46 set_equal: $i > $i > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(element_decl,type,
% 0.28/0.46 element: $i > $i > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(pel43_1,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [X: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [Y: $i] :
% 0.28/0.46 ( mequiv @ ( set_equal @ X @ Y )
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ X ) @ ( element @ Z @ Y ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(pel43,conjecture,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [X: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.53/1.29 ---- Embedded in THF ---
% 1.53/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.29 %%% Generated on Tue Feb 24 11:50:47 EST 2026
% 1.53/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.29 %%% Logic specification used:
% 1.53/1.29 %%% thf(spec, logic, $$dhol).
% 1.53/1.29
% 1.53/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2DTF10334.p
% See solution above
% 1.53/1.29 ------------------------
% 1.70/1.30 ---- Cleaned THF ---
% 1.70/1.30 thf(mworld,type,
% 1.70/1.30 mworld: $tType ).
% 1.70/1.30
% 1.70/1.30 thf(mrel_type,type,
% 1.70/1.30 mrel: mworld > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mactual_type,type,
% 1.70/1.30 mactual: mworld ).
% 1.70/1.30
% 1.70/1.30 thf(mlocal_type,type,
% 1.70/1.30 mlocal: ( mworld > $o ) > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mlocal_def,definition,
% 1.70/1.30 ( mlocal
% 1.70/1.30 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mnot_type,type,
% 1.70/1.30 mnot: ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mand_type,type,
% 1.70/1.30 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mor_type,type,
% 1.70/1.30 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mimplies_type,type,
% 1.70/1.30 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mequiv_type,type,
% 1.70/1.30 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mnot_def,definition,
% 1.70/1.30 ( mnot
% 1.70/1.30 = ( ^ [A: mworld > $o,W: mworld] :
% 1.70/1.30 ~ ( A @ W ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mand_def,definition,
% 1.70/1.30 ( mand
% 1.70/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.70/1.30 ( ( A @ W )
% 1.70/1.30 & ( B @ W ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mor_def,definition,
% 1.70/1.30 ( mor
% 1.70/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.70/1.30 ( ( A @ W )
% 1.70/1.30 | ( B @ W ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mimplies_def,definition,
% 1.70/1.30 ( mimplies
% 1.70/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.70/1.30 ( ( A @ W )
% 1.70/1.30 => ( B @ W ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mequiv_def,definition,
% 1.70/1.30 ( mequiv
% 1.70/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.70/1.30 ( ( A @ W )
% 1.70/1.30 <=> ( B @ W ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mbox_type,type,
% 1.70/1.30 mbox: ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mbox_def,definition,
% 1.70/1.30 ( mbox
% 1.70/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.70/1.30 ! [V: mworld] :
% 1.70/1.30 ( ( mrel @ W @ V )
% 1.70/1.30 => ( Phi @ V ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mdia_type,type,
% 1.70/1.30 mdia: ( mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mdia_def,definition,
% 1.70/1.30 ( mdia
% 1.70/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.70/1.30 ? [V: mworld] :
% 1.70/1.30 ( ( mrel @ W @ V )
% 1.70/1.30 & ( Phi @ V ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mforall_di_type,type,
% 1.70/1.30 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mforall_di_def,definition,
% 1.70/1.30 ( mforall_di
% 1.70/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.70/1.30 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(mexists_di_type,type,
% 1.70/1.30 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(mexists_di_def,definition,
% 1.70/1.30 ( mexists_di
% 1.70/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.70/1.30 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(set_equal_decl,type,
% 1.70/1.30 set_equal: $i > $i > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(element_decl,type,
% 1.70/1.30 element: $i > $i > mworld > $o ).
% 1.70/1.30
% 1.70/1.30 thf(pel43_1,axiom,
% 1.70/1.30 ( mlocal
% 1.70/1.30 @ ( mforall_di
% 1.70/1.30 @ ^ [X: $i] :
% 1.70/1.30 ( mforall_di
% 1.70/1.30 @ ^ [Y: $i] :
% 1.70/1.30 ( mequiv @ ( set_equal @ X @ Y )
% 1.70/1.30 @ ( mforall_di
% 1.70/1.30 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ X ) @ ( element @ Z @ Y ) ) ) ) ) ) ) ).
% 1.70/1.30
% 1.70/1.30 thf(pel43,conjecture,
% 1.70/1.30 ( mlocal
% 1.70/1.30 @ ( mforall_di
% 1.70/1.30 @ ^ [X: $i] :
% 1.70/1.30 ( mforall_di
% 1.70/1.30 @ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ) ).
% 1.70/1.30 ------------------------
% 1.70/1.32 % (10619)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_10334 for (2999ds/275Mi)
% 1.70/1.32 % (10617)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/2Mi)
% 1.70/1.32 % (10619)Refutation not found, incomplete strategy
% 1.70/1.32 % (10619)------------------------------
% 1.70/1.32 % (10619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (10619)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.32
% 1.70/1.32
% 1.70/1.32 % (10619)Memory used [KB]: 5500
% 1.70/1.32 % (10619)Time elapsed: 0.002 s
% 1.70/1.32 % (10619)Instructions burned: 2 (million)
% 1.70/1.32 % (10619)------------------------------
% 1.70/1.32 % (10619)------------------------------
% 1.70/1.32 % (10617)Instruction limit reached!
% 1.70/1.32 % (10617)------------------------------
% 1.70/1.32 % (10617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (10617)Termination reason: Unknown
% 1.70/1.32 % (10617)Termination phase: Function definition elimination
% 1.70/1.32
% 1.70/1.32 % (10617)Memory used [KB]: 1023
% 1.70/1.32 % (10617)Time elapsed: 0.002 s
% 1.70/1.32 % (10617)Instructions burned: 3 (million)
% 1.70/1.32 % (10617)------------------------------
% 1.70/1.32 % (10617)------------------------------
% 1.70/1.32 % (10614)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/183Mi)
% 1.70/1.32 % (10616)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_10334 for (2999ds/27Mi)
% 1.70/1.32 % (10615)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_10334 for (2999ds/4Mi)
% 1.70/1.32 % (10618)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_10334 for (2999ds/2Mi)
% 1.70/1.32 % (10620)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/18Mi)
% 1.70/1.32 % (10618)Instruction limit reached!
% 1.70/1.32 % (10618)------------------------------
% 1.70/1.32 % (10618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.32 % (10618)Termination reason: Unknown
% 1.70/1.32 % (10618)Termination phase: shuffling
% 1.70/1.32
% 1.70/1.32 % (10618)Memory used [KB]: 1023
% 1.70/1.32 % (10618)Time elapsed: 0.003 s
% 1.70/1.32 % (10618)Instructions burned: 2 (million)
% 1.70/1.32 % (10618)------------------------------
% 1.70/1.32 % (10618)------------------------------
% 1.70/1.33 % (10615)Instruction limit reached!
% 1.70/1.33 % (10615)------------------------------
% 1.70/1.33 % (10615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (10615)Termination reason: Unknown
% 1.70/1.33 % (10615)Termination phase: Saturation
% 1.70/1.33
% 1.70/1.33 % (10615)Memory used [KB]: 5500
% 1.70/1.33 % (10615)Time elapsed: 0.005 s
% 1.70/1.33 % (10615)Instructions burned: 5 (million)
% 1.70/1.33 % (10615)------------------------------
% 1.70/1.33 % (10615)------------------------------
% 1.70/1.33 % (10622)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_10334 for (2999ds/37Mi)
% 1.70/1.33 % (10621)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/3Mi)
% 1.70/1.33 % (10621)Instruction limit reached!
% 1.70/1.33 % (10621)------------------------------
% 1.70/1.33 % (10621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (10621)Termination reason: Unknown
% 1.70/1.33 % (10621)Termination phase: Saturation
% 1.70/1.33
% 1.70/1.33 % (10621)Memory used [KB]: 5500
% 1.70/1.33 % (10621)Time elapsed: 0.003 s
% 1.70/1.33 % (10621)Instructions burned: 4 (million)
% 1.70/1.33 % (10621)------------------------------
% 1.70/1.33 % (10621)------------------------------
% 1.70/1.34 % (10620)Instruction limit reached!
% 1.70/1.34 % (10620)------------------------------
% 1.70/1.34 % (10620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (10620)Termination reason: Unknown
% 1.70/1.34 % (10620)Termination phase: Saturation
% 1.70/1.34
% 1.70/1.34 % (10620)Memory used [KB]: 5628
% 1.70/1.34 % (10620)Time elapsed: 0.014 s
% 1.70/1.34 % (10620)Instructions burned: 19 (million)
% 1.70/1.34 % (10620)------------------------------
% 1.70/1.34 % (10620)------------------------------
% 1.70/1.34 % (10616)Instruction limit reached!
% 1.70/1.34 % (10616)------------------------------
% 1.70/1.34 % (10616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (10616)Termination reason: Unknown
% 1.70/1.34 % (10616)Termination phase: Saturation
% 1.70/1.34
% 1.70/1.34 % (10616)Memory used [KB]: 5628
% 1.70/1.34 % (10616)Time elapsed: 0.017 s
% 1.70/1.34 % (10616)Instructions burned: 28 (million)
% 1.70/1.34 % (10616)------------------------------
% 1.70/1.34 % (10616)------------------------------
% 1.70/1.34 % (10622)Instruction limit reached!
% 1.70/1.34 % (10622)------------------------------
% 1.70/1.34 % (10622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (10622)Termination reason: Unknown
% 1.70/1.34 % (10622)Termination phase: Saturation
% 1.70/1.34
% 1.70/1.34 % (10622)Memory used [KB]: 5756
% 1.70/1.34 % (10622)Time elapsed: 0.013 s
% 1.70/1.34 % (10622)Instructions burned: 39 (million)
% 1.70/1.34 % (10622)------------------------------
% 1.70/1.34 % (10622)------------------------------
% 1.70/1.34 % (10625)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_10334 for (2999ds/1041Mi)
% 1.70/1.34 % (10623)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_10334 for (2999ds/15Mi)
% 1.70/1.34 % (10624)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_10334 for (2999ds/3Mi)
% 1.70/1.35 % (10623)Refutation not found, incomplete strategy
% 1.70/1.35 % (10623)------------------------------
% 1.70/1.35 % (10623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (10623)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.35
% 1.70/1.35
% 1.70/1.35 % (10623)Memory used [KB]: 5500
% 1.70/1.35 % (10623)Time elapsed: 0.005 s
% 1.70/1.35 % (10623)Instructions burned: 5 (million)
% 1.70/1.35 % (10623)------------------------------
% 1.70/1.35 % (10623)------------------------------
% 1.70/1.35 % (10624)Instruction limit reached!
% 1.70/1.35 % (10624)------------------------------
% 1.70/1.35 % (10624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (10624)Termination reason: Unknown
% 1.70/1.35 % (10624)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (10624)Memory used [KB]: 5500
% 1.70/1.35 % (10624)Time elapsed: 0.004 s
% 1.70/1.35 % (10624)Instructions burned: 4 (million)
% 1.70/1.35 % (10624)------------------------------
% 1.70/1.35 % (10624)------------------------------
% 1.70/1.35 % (10628)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_10334 for (2999ds/3Mi)
% 1.70/1.35 % (10628)Instruction limit reached!
% 1.70/1.35 % (10628)------------------------------
% 1.70/1.35 % (10628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (10628)Termination reason: Unknown
% 1.70/1.35 % (10628)Termination phase: Property scanning
% 1.70/1.35
% 1.70/1.35 % (10628)Memory used [KB]: 1023
% 1.70/1.35 % (10628)Time elapsed: 0.002 s
% 1.70/1.35 % (10628)Instructions burned: 3 (million)
% 1.70/1.35 % (10628)------------------------------
% 1.70/1.35 % (10628)------------------------------
% 1.70/1.35 % (10627)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/16Mi)
% 1.70/1.35 % (10626)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/7Mi)
% 1.70/1.36 % (10627)Instruction limit reached!
% 1.70/1.36 % (10627)------------------------------
% 1.70/1.36 % (10627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (10627)Termination reason: Unknown
% 1.70/1.36 % (10627)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (10627)Memory used [KB]: 5756
% 1.70/1.36 % (10627)Time elapsed: 0.008 s
% 1.70/1.36 % (10627)Instructions burned: 17 (million)
% 1.70/1.36 % (10627)------------------------------
% 1.70/1.36 % (10627)------------------------------
% 1.70/1.36 % (10626)Instruction limit reached!
% 1.70/1.36 % (10626)------------------------------
% 1.70/1.36 % (10626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (10626)Termination reason: Unknown
% 1.70/1.36 % (10626)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (10626)Memory used [KB]: 1023
% 1.70/1.36 % (10626)Time elapsed: 0.006 s
% 1.70/1.36 % (10626)Instructions burned: 7 (million)
% 1.70/1.36 % (10626)------------------------------
% 1.70/1.36 % (10626)------------------------------
% 1.70/1.36 % (10631)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/3Mi)
% 1.70/1.36 % (10631)Instruction limit reached!
% 1.70/1.36 % (10631)------------------------------
% 1.70/1.36 % (10631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (10631)Termination reason: Unknown
% 1.70/1.36 % (10631)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (10631)Memory used [KB]: 5500
% 1.70/1.36 % (10631)Time elapsed: 0.002 s
% 1.70/1.36 % (10631)Instructions burned: 4 (million)
% 1.70/1.36 % (10631)------------------------------
% 1.70/1.36 % (10631)------------------------------
% 1.70/1.36 % (10614)First to succeed.
% 1.70/1.36 % (10629)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_10334 for (2999ds/3Mi)
% 1.70/1.36 % (10630)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10334 for (2999ds/7Mi)
% 1.70/1.37 % (10614)Refutation found. Thanks to Tanya!
% 1.70/1.37 % SZS status Theorem for DTF2THF_10334
% 1.70/1.37 % SZS output start Proof for DTF2THF_10334
% 1.70/1.37 thf(type_def_5, type, mworld: $tType).
% 1.70/1.37 thf(func_def_0, type, mworld: $tType).
% 1.70/1.37 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.70/1.37 thf(func_def_2, type, mactual: mworld).
% 1.70/1.37 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.70/1.37 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.70/1.37 thf(func_def_14, type, set_equal: $i > $i > mworld > $o).
% 1.70/1.37 thf(func_def_15, type, element: $i > $i > mworld > $o).
% 1.70/1.37 thf(func_def_34, type, sK3: $i > $i > $i).
% 1.70/1.37 thf(f477,plain,(
% 1.70/1.37 $false),
% 1.70/1.37 inference(avatar_sat_refutation,[status(thm)],[f87,f96,f102,f462,f472,f476])).
% 1.70/1.37 thf(f476,plain,(
% 1.70/1.37 spl0_3 | ~spl0_4),
% 1.70/1.37 inference(avatar_contradiction_clause,[status(thm)],[f475])).
% 1.70/1.37 thf(f475,plain,(
% 1.70/1.37 $false | (spl0_3 | ~spl0_4)),
% 1.70/1.37 inference(subsumption_resolution,[status(thm)],[f467,f90])).
% 1.70/1.37 thf(f90,plain,(
% 1.70/1.37 ($false != (set_equal @ sK1 @ sK2 @ mactual)) | spl0_3),
% 1.70/1.37 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.70/1.37 thf(f89,definition,(
% 1.70/1.37 spl0_3 <=> ($false = (set_equal @ sK1 @ sK2 @ mactual))),
% 1.70/1.37 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.70/1.37 thf(f467,plain,(
% 1.70/1.37 ($false = (set_equal @ sK1 @ sK2 @ mactual)) | ~spl0_4),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f466])).
% 1.70/1.37 thf(f466,plain,(
% 1.70/1.37 ($false = $true) | ($false = (set_equal @ sK1 @ sK2 @ mactual)) | ~spl0_4),
% 1.70/1.37 inference(superposition,[status(thm)],[f450,f95])).
% 1.70/1.37 thf(f95,plain,(
% 1.70/1.37 ((set_equal @ sK2 @ sK1 @ mactual) = $false) | ~spl0_4),
% 1.70/1.37 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.70/1.37 thf(f93,definition,(
% 1.70/1.37 spl0_4 <=> ((set_equal @ sK2 @ sK1 @ mactual) = $false)),
% 1.70/1.37 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.70/1.37 thf(f450,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($true = (set_equal @ X0 @ X1 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f449])).
% 1.70/1.37 thf(f449,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 1.70/1.37 inference(duplicate_literal_removal,[status(thm)],[f408])).
% 1.70/1.37 thf(f408,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($true = (set_equal @ X0 @ X1 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($false = $true)) )),
% 1.70/1.37 inference(superposition,[status(thm)],[f245,f216])).
% 1.70/1.37 thf(f216,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.70/1.37 thf(f207,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ((element @ (sK3 @ X0 @ X1) @ X1 @ mactual) = $true)) )),
% 1.70/1.37 inference(equality_factoring,[status(thm)],[f115])).
% 1.70/1.37 thf(f115,plain,(
% 1.70/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $true) | ((element @ (sK3 @ X0 @ X1) @ X1 @ mactual) = $true) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X2 @ X0 @ mactual))) )),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.70/1.37 thf(f110,plain,(
% 1.70/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X1 @ mactual) = $true) | ((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $true) | ($false = $true) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X2 @ X0 @ mactual))) )),
% 1.70/1.37 inference(superposition,[status(thm)],[f72,f77])).
% 1.70/1.37 thf(f77,plain,(
% 1.70/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (element @ X3 @ X2 @ mactual)) | ((element @ X3 @ X1 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.70/1.37 thf(f76,plain,(
% 1.70/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((element @ X3 @ X1 @ mactual) = (element @ X3 @ X2 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.70/1.37 thf(f75,plain,(
% 1.70/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((element @ X3 @ X2 @ mactual) = (element @ X3 @ X1 @ mactual)) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.70/1.37 thf(f74,plain,(
% 1.70/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual))) @ X3) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(pi_clausification,[status(thm)],[f67])).
% 1.70/1.37 thf(f67,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.70/1.37 thf(f66,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = (set_equal @ X1 @ X2 @ mactual))) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.70/1.37 thf(f65,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = (set_equal @ X1 @ X2 @ mactual)) = $true)) )),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.70/1.37 thf(f64,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ X1 @ mactual)))) = (set_equal @ X1 @ Y0 @ mactual))) @ X2))) )),
% 1.70/1.37 inference(pi_clausification,[status(thm)],[f63])).
% 1.70/1.37 thf(f63,plain,(
% 1.70/1.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ X1 @ mactual)))) = (set_equal @ X1 @ Y0 @ mactual)))) = $true)) )),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.70/1.37 thf(f62,plain,(
% 1.70/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y1 @ mactual) = (element @ Y2 @ Y0 @ mactual)))) = (set_equal @ Y0 @ Y1 @ mactual))))) @ X1) = $true)) )),
% 1.70/1.37 inference(pi_clausification,[status(thm)],[f61])).
% 1.70/1.37 thf(f61,plain,(
% 1.70/1.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((element @ Y2 @ Y1 @ mactual) = (element @ Y2 @ Y0 @ mactual)))) = (set_equal @ Y0 @ Y1 @ mactual)))))) = $true)),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.70/1.37 thf(f51,plain,(
% 1.70/1.37 (((^[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]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (set_equal @ Y0 @ Y1) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) = (Y3 @ Y5))))))) @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 1.70/1.37 inference(definition_unfolding,[status(thm)],[f40,f44,f49,f49,f41,f49,f41])).
% 1.70/1.37 thf(f41,plain,(
% 1.70/1.37 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.70/1.37 inference(cnf_transformation,[status(thm)],[f21])).
% 1.70/1.37 thf(f21,plain,(
% 1.70/1.37 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.70/1.37 inference(fool_elimination,[status(thm)],[f20])).
% 1.70/1.37 thf(f20,plain,(
% 1.70/1.37 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))))),
% 1.70/1.37 inference(rectify,[status(thm)],[f6])).
% 1.70/1.37 thf(f6,axiom,(
% 1.70/1.37 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))))),
% 1.70/1.37 file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',mequiv_def)).
% 1.70/1.37 thf(f49,plain,(
% 1.70/1.37 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.70/1.37 inference(cnf_transformation,[status(thm)],[f23])).
% 1.70/1.37 thf(f23,plain,(
% 1.70/1.37 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.70/1.37 inference(fool_elimination,[status(thm)],[f22])).
% 1.70/1.37 thf(f22,plain,(
% 1.70/1.37 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.70/1.37 inference(rectify,[status(thm)],[f9])).
% 1.70/1.37 thf(f9,axiom,(
% 1.70/1.37 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))))),
% 1.70/1.37 file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',mforall_di_def)).
% 1.70/1.37 thf(f44,plain,(
% 1.70/1.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.70/1.37 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.37 thf(f17,plain,(
% 1.70/1.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.70/1.37 inference(fool_elimination,[status(thm)],[f1])).
% 1.70/1.37 thf(f1,axiom,(
% 1.70/1.37 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.70/1.37 file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',mlocal_def)).
% 1.70/1.37 thf(f40,plain,(
% 1.70/1.37 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 1.70/1.37 inference(cnf_transformation,[status(thm)],[f37])).
% 1.70/1.37 thf(f37,plain,(
% 1.70/1.37 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y0) @ (element @ Y2 @ Y1)))))))))) = $true)),
% 1.70/1.37 inference(fool_elimination,[status(thm)],[f36])).
% 1.70/1.37 thf(f36,plain,(
% 1.70/1.37 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (set_equal @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mequiv @ (element @ X2 @ X0) @ (element @ X2 @ X1))))))))))),
% 1.70/1.37 inference(rectify,[status(thm)],[f11])).
% 1.70/1.37 thf(f11,axiom,(
% 1.70/1.37 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (mforall_di @ (^[X7 : $i] : (mequiv @ (element @ X7 @ X5) @ (element @ X7 @ X6))))))))))),
% 1.70/1.37 file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',pel43_1)).
% 1.70/1.37 thf(f72,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (($true = (element @ (sK3 @ X1 @ X2) @ X1 @ mactual)) | ((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) = $true) | ((set_equal @ X1 @ X2 @ mactual) = $true)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.70/1.37 thf(f71,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | ((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) != (element @ (sK3 @ X1 @ X2) @ X1 @ mactual))) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.70/1.37 thf(f70,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | (((element @ (sK3 @ X1 @ X2) @ X2 @ mactual) = (element @ (sK3 @ X1 @ X2) @ X1 @ mactual)) = $false)) )),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.70/1.37 thf(f69,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | (((^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual))) @ (sK3 @ X1 @ X2)) = $false)) )),
% 1.70/1.37 inference(sigma_clausification,[status(thm)],[f68])).
% 1.70/1.37 thf(f68,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (((set_equal @ X1 @ X2 @ mactual) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((element @ Y0 @ X2 @ mactual) = (element @ Y0 @ X1 @ mactual)))) = $false)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.70/1.37 thf(f245,plain,(
% 1.70/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = (set_equal @ X2 @ X0 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f232])).
% 1.70/1.37 thf(f232,plain,(
% 1.70/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (set_equal @ X0 @ X1 @ mactual)) | ((element @ (sK3 @ X0 @ X1) @ X2 @ mactual) = $false) | ($false = $true) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($false = (set_equal @ X2 @ X0 @ mactual))) )),
% 1.70/1.37 inference(superposition,[status(thm)],[f78,f209])).
% 1.70/1.37 thf(f209,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (element @ (sK3 @ X0 @ X1) @ X0 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 1.70/1.37 thf(f208,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($false = (element @ (sK3 @ X0 @ X1) @ X0 @ mactual)) | ($false = $true) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ((set_equal @ X1 @ X0 @ mactual) = $false)) )),
% 1.70/1.37 inference(duplicate_literal_removal,[status(thm)],[f202])).
% 1.70/1.37 thf(f202,plain,(
% 1.70/1.37 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (element @ (sK3 @ X0 @ X1) @ X0 @ mactual)) | ($true = (set_equal @ X0 @ X1 @ mactual)) | ($false = $true) | ((set_equal @ X1 @ X0 @ mactual) = $false) | ($true = (set_equal @ X0 @ X1 @ mactual))) )),
% 1.70/1.37 inference(superposition,[status(thm)],[f115,f73])).
% 1.70/1.37 thf(f73,plain,(
% 1.70/1.37 ( ! [X2 : $i,X1 : $i] : (($false = (element @ (sK3 @ X1 @ X2) @ X2 @ mactual)) | ((set_equal @ X1 @ X2 @ mactual) = $true) | ($false = (element @ (sK3 @ X1 @ X2) @ X1 @ mactual))) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.70/1.37 thf(f78,plain,(
% 1.70/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((element @ X3 @ X2 @ mactual) = $true) | ((element @ X3 @ X1 @ mactual) = $false) | ((set_equal @ X1 @ X2 @ mactual) = $false)) )),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.70/1.37 thf(f472,plain,(
% 1.70/1.37 ~spl0_1 | ~spl0_4),
% 1.70/1.37 inference(avatar_contradiction_clause,[status(thm)],[f471])).
% 1.70/1.37 thf(f471,plain,(
% 1.70/1.37 $false | (~spl0_1 | ~spl0_4)),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f465])).
% 1.70/1.37 thf(f465,plain,(
% 1.70/1.37 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.70/1.37 inference(superposition,[status(thm)],[f82,f95])).
% 1.70/1.37 thf(f82,plain,(
% 1.70/1.37 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ~spl0_1),
% 1.70/1.37 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.70/1.37 thf(f80,definition,(
% 1.70/1.37 spl0_1 <=> ((set_equal @ sK2 @ sK1 @ mactual) = $true)),
% 1.70/1.37 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.70/1.37 thf(f462,plain,(
% 1.70/1.37 spl0_4 | ~spl0_3),
% 1.70/1.37 inference(avatar_split_clause,[status(thm)],[f457,f89,f93])).
% 1.70/1.37 thf(f457,plain,(
% 1.70/1.37 ((set_equal @ sK2 @ sK1 @ mactual) = $false) | ~spl0_3),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f453])).
% 1.70/1.37 thf(f453,plain,(
% 1.70/1.37 ($false = $true) | ((set_equal @ sK2 @ sK1 @ mactual) = $false) | ~spl0_3),
% 1.70/1.37 inference(superposition,[status(thm)],[f450,f91])).
% 1.70/1.37 thf(f91,plain,(
% 1.70/1.37 ($false = (set_equal @ sK1 @ sK2 @ mactual)) | ~spl0_3),
% 1.70/1.37 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.70/1.37 thf(f102,plain,(
% 1.70/1.37 ~spl0_2 | ~spl0_3),
% 1.70/1.37 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.70/1.37 thf(f101,plain,(
% 1.70/1.37 $false | (~spl0_2 | ~spl0_3)),
% 1.70/1.37 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.70/1.37 thf(f98,plain,(
% 1.70/1.37 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.70/1.37 inference(superposition,[status(thm)],[f86,f91])).
% 1.70/1.37 thf(f86,plain,(
% 1.70/1.37 ($true = (set_equal @ sK1 @ sK2 @ mactual)) | ~spl0_2),
% 1.70/1.37 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.70/1.37 thf(f84,definition,(
% 1.70/1.37 spl0_2 <=> ($true = (set_equal @ sK1 @ sK2 @ mactual))),
% 1.70/1.37 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.70/1.37 thf(f96,plain,(
% 1.70/1.37 spl0_3 | spl0_4),
% 1.70/1.37 inference(avatar_split_clause,[status(thm)],[f60,f93,f89])).
% 1.70/1.37 thf(f60,plain,(
% 1.70/1.37 ($false = (set_equal @ sK1 @ sK2 @ mactual)) | ((set_equal @ sK2 @ sK1 @ mactual) = $false)),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.70/1.37 thf(f58,plain,(
% 1.70/1.37 ((set_equal @ sK2 @ sK1 @ mactual) != (set_equal @ sK1 @ sK2 @ mactual))),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.70/1.37 thf(f57,plain,(
% 1.70/1.37 (((set_equal @ sK2 @ sK1 @ mactual) = (set_equal @ sK1 @ sK2 @ mactual)) = $false)),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.70/1.37 thf(f56,plain,(
% 1.70/1.37 (((^[Y0 : $i]: ((set_equal @ Y0 @ sK1 @ mactual) = (set_equal @ sK1 @ Y0 @ mactual))) @ sK2) = $false)),
% 1.70/1.37 inference(sigma_clausification,[status(thm)],[f55])).
% 1.70/1.37 thf(f55,plain,(
% 1.70/1.37 ((!! @ $i @ (^[Y0 : $i]: ((set_equal @ Y0 @ sK1 @ mactual) = (set_equal @ sK1 @ Y0 @ mactual)))) = $false)),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.70/1.37 thf(f54,plain,(
% 1.70/1.37 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y1 @ Y0 @ mactual) = (set_equal @ Y0 @ Y1 @ mactual))))) @ sK1))),
% 1.70/1.37 inference(sigma_clausification,[status(thm)],[f53])).
% 1.70/1.37 thf(f53,plain,(
% 1.70/1.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((set_equal @ Y1 @ Y0 @ mactual) = (set_equal @ Y0 @ Y1 @ mactual)))))))),
% 1.70/1.37 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.70/1.37 thf(f52,plain,(
% 1.70/1.37 (((^[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]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))) != $true)),
% 1.70/1.37 inference(definition_unfolding,[status(thm)],[f48,f44,f49,f49,f41])).
% 1.70/1.37 thf(f48,plain,(
% 1.70/1.37 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 1.70/1.37 inference(cnf_transformation,[status(thm)],[f38])).
% 1.70/1.37 thf(f38,plain,(
% 1.70/1.37 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 1.70/1.37 inference(flattening,[status(thm)],[f19])).
% 1.70/1.37 thf(f19,plain,(
% 1.70/1.37 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (set_equal @ Y0 @ Y1) @ (set_equal @ Y1 @ Y0))))))))),
% 1.70/1.37 inference(fool_elimination,[status(thm)],[f18])).
% 1.70/1.37 thf(f18,plain,(
% 1.70/1.37 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (set_equal @ X0 @ X1) @ (set_equal @ X1 @ X0)))))))),
% 1.70/1.37 inference(rectify,[status(thm)],[f13])).
% 1.70/1.37 thf(f13,negated_conjecture,(
% 1.70/1.37 ~(mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 1.70/1.37 inference(negated_conjecture,[status(cth)],[f12])).
% 1.70/1.37 thf(f12,conjecture,(
% 1.70/1.37 (mlocal @ (mforall_di @ (^[X5 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (set_equal @ X5 @ X6) @ (set_equal @ X6 @ X5)))))))),
% 1.70/1.37 file('/export/starexec/sandbox/tmp/tmp.5qRh4fW88Z/DTF2THF_10334.p',pel43)).
% 1.70/1.37 thf(f87,plain,(
% 1.70/1.37 spl0_1 | spl0_2),
% 1.70/1.37 inference(avatar_split_clause,[status(thm)],[f59,f84,f80])).
% 1.70/1.37 thf(f59,plain,(
% 1.70/1.37 ((set_equal @ sK2 @ sK1 @ mactual) = $true) | ($true = (set_equal @ sK1 @ sK2 @ mactual))),
% 1.70/1.37 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.70/1.37 % SZS output end Proof for DTF2THF_10334
% 1.70/1.37 % (10614)------------------------------
% 1.70/1.37 % (10614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (10614)Termination reason: Refutation
% 1.70/1.37
% 1.70/1.37 % (10614)Memory used [KB]: 5884
% 1.70/1.37 % (10614)Time elapsed: 0.043 s
% 1.70/1.37 % (10614)Instructions burned: 67 (million)
% 1.70/1.37 % (10614)------------------------------
% 1.70/1.37 % (10614)------------------------------
% 1.70/1.37 % (10613)Success in time 0.052 s
%------------------------------------------------------------------------------