%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET044^23 : 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 : n026.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 09:31:03 AM UTC 2026
% Result : Theorem 1.81s 1.42s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 10
% Syntax : Number of formulae : 94 ( 41 unt; 0 typ; 3 def)
% Number of atoms : 747 ( 169 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 1023 ( 56 ~; 107 |; 18 &; 767 @)
% ( 5 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 9 con; 0-3 aty)
% ( 22 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 185 ( 149 ^; 34 !; 2 ?; 185 :)
% 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_15,type,
element: $i > $i > mworld > $o ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_34,type,
sK3: $i > $i ).
thf(f205,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f142,f151,f166,f204]) ).
thf(f204,plain,
( ~ spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f203]) ).
thf(f203,plain,
( $false
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f202,f140]) ).
thf(f140,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
!= $false )
| spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f139,definition,
( spl1_3
<=> ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f202,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f196,f136]) ).
thf(f136,plain,
( ( ( eiw_di @ sK2 @ mactual )
!= $false )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl1_2
<=> ( ( eiw_di @ sK2 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f196,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ( $true = $false )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(duplicate_literal_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ( $true = $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( $true = $false )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(superposition,[status(thm)],[f112,f190]) ).
thf(f190,plain,
( ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $true )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f189,f140]) ).
thf(f189,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $true )
| ~ spl1_1
| spl1_2
| spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f188,f136]) ).
thf(f188,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $true )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1
| spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f180]) ).
thf(f180,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( $true = $false )
| ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $true )
| ~ spl1_1
| spl1_3 ),
inference(superposition,[status(thm)],[f97,f176]) ).
thf(f176,plain,
( ( ( element @ ( sK3 @ sK2 ) @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1
| spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f174,f140]) ).
thf(f174,plain,
( ( ( element @ ( sK3 @ sK2 ) @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true = $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( ( element @ ( sK3 @ sK2 ) @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f133,f82]) ).
thf(f82,plain,
! [X1: $i] :
( ( $true
= ( element @ X1 @ sK2 @ mactual ) )
| ( ( element @ X1 @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X1 @ X1 @ mactual )
= ( element @ X1 @ sK2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: $i] :
( ( $true
= ( ( element @ X1 @ sK2 @ mactual )
= ( element @ X1 @ X1 @ mactual ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( ( element @ X1 @ sK2 @ mactual )
= ( element @ X1 @ X1 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK2 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK2 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK2 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) ) )
& ( eiw_di @ sK2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) )
& ( eiw_di @ Y0 @ mactual ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) )
& ( eiw_di @ Y0 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $true
!= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) )
& ( eiw_di @ Y0 @ mactual ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) )
& ( eiw_di @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ 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 ) )
@ ( element @ Y1 @ Y0 )
@ ( element @ Y1 @ Y1 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [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] :
( ( Y1 @ Y3 @ Y2 )
& ( eiw_di @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( element @ Y2 @ Y1 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f65,f56,f57,f61,f54,f62,f55,f54,f61,f54,f62,f55]) ).
thf(f55,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mnot_def) ).
thf(f62,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mequiv_def) ).
thf(f54,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X2 )
=> ( X1 @ X6 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mforall_di_def) ).
thf(f61,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ X2 )
& ( X1 @ X6 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mexists_di_def) ).
thf(f57,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mimplies_def) ).
thf(f56,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,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.4nSd79MMiN/DTF2THF_2441.p',mlocal_def) ).
thf(f65,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f43]) ).
thf(f43,plain,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( element @ X1 @ X0 ) @ ( element @ X1 @ X1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X4: $i] : ( mequiv @ ( element @ X4 @ X3 ) @ ( mnot @ ( element @ X4 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X6: $i] : ( mequiv @ ( element @ X6 @ X7 ) @ ( element @ X6 @ X6 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X9: $i] :
( mforall_di
@ ^ [X10: $i] : ( mequiv @ ( element @ X10 @ X9 ) @ ( mnot @ ( element @ X10 @ X8 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X7: $i] :
( mforall_di
@ ^ [X6: $i] : ( mequiv @ ( element @ X6 @ X7 ) @ ( element @ X6 @ X6 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X9: $i] :
( mforall_di
@ ^ [X10: $i] : ( mequiv @ ( element @ X10 @ X9 ) @ ( mnot @ ( element @ X10 @ X8 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',pel40) ).
thf(f133,plain,
( ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl1_1
<=> ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( element @ X2 @ ( sK3 @ X1 ) @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X2 @ X1 @ mactual )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( element @ X2 @ ( sK3 @ X1 ) @ mactual ) )
| ( ( ~ ( element @ X2 @ X1 @ mactual ) )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ~ ( element @ X2 @ X1 @ mactual ) )
= ( element @ X2 @ ( sK3 @ X1 ) @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $true
= ( ( element @ X2 @ ( sK3 @ X1 ) @ mactual )
= ( ~ ( element @ X2 @ X1 @ mactual ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ ( sK3 @ X1 ) @ mactual )
= ( ~ ( element @ X2 @ X1 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK3 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) )
@ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK3 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK3 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) ) )
& ( eiw_di @ ( sK3 @ X1 ) @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) )
& ( eiw_di @ Y0 @ mactual ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) )
& ( eiw_di @ Y0 @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) )
& ( eiw_di @ Y0 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) )
& ( eiw_di @ Y1 @ mactual ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) )
& ( eiw_di @ Y1 @ mactual ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) )
& ( eiw_di @ Y1 @ mactual ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f112,plain,
! [X0: $i] :
( ( ( element @ ( sK3 @ X0 ) @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ X0 ) @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( ( element @ ( sK3 @ X0 ) @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i] :
( ( ( element @ ( sK3 @ X0 ) @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ X0 ) @ mactual )
= $false )
| ( ( element @ ( sK3 @ X0 ) @ X0 @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f102]) ).
thf(f102,plain,
! [X0: $i] :
( ( ( element @ ( sK3 @ X0 ) @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ X0 ) @ mactual )
= $false )
| ( ( element @ ( sK3 @ X0 ) @ X0 @ mactual )
= $false )
| ( $true = $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ X0 ) @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f98,f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( $true
= ( element @ X1 @ X1 @ mactual ) )
| ( ( element @ X1 @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( ( element @ X2 @ ( sK3 @ X1 ) @ mactual )
= $false )
| ( ( element @ X2 @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( element @ X2 @ X1 @ mactual ) )
= $true )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X2 @ ( sK3 @ X1 ) @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f166,plain,
( spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
| spl1_2
| ~ spl1_3 ),
inference(subsumption_resolution,[status(thm)],[f160,f136]) ).
thf(f160,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( $true = $false )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f89,f141]) ).
thf(f141,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f89,plain,
! [X1: $i] :
( ( $true
= ( eiw_di @ ( sK3 @ X1 ) @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f151,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f150]) ).
thf(f150,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f75,f137]) ).
thf(f137,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f75,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f142,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f123,f139,f135,f131]) ).
thf(f123,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $false != $false )
| ( ( element @ ( sK3 @ sK2 ) @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ mactual )
= $false ) ),
inference(equality_factoring,[status(thm)],[f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET044^23 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n026.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 11:50:40 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SET044^23 : TPTP v9.2.1. Released v8.1.0.
% 0.17/0.39 % Domain : Set Theory
% 0.17/0.39 % Problem : TPTP problem SET044+1.p with axiomatized equality
% 0.17/0.39 % Version : [BP13] axioms.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.17/0.39 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.17/0.39 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.17/0.39 % Source : [TPTP]
% 0.17/0.39 % Names : SET044+1 [QMLTP]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.17/0.39 % Syntax : Number of formulae : 30 ( 12 unt; 15 typ; 10 def)
% 0.17/0.39 % Number of atoms : 47 ( 10 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 15 ( 3 avg)
% 0.17/0.39 % Number of connectives : 75 ( 1 ~; 1 |; 5 &; 62 @)
% 0.17/0.39 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 14 ( 3 avg)
% 0.17/0.39 % Number of types : 3 ( 1 usr)
% 0.17/0.39 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.17/0.39 % Number of variables : 41 ( 28 ^; 10 !; 3 ?; 41 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.17/0.39 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.17/0.39 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.17/0.39 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.17/0.39 % $modalities == $modal_system_S5].
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(mworld,type,
% 0.17/0.39 mworld: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(mrel_type,type,
% 0.17/0.39 mrel: mworld > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mactual_type,type,
% 0.17/0.39 mactual: mworld ).
% 0.17/0.39
% 0.17/0.39 thf(mlocal_type,type,
% 0.17/0.39 mlocal: ( mworld > $o ) > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mlocal_def,definition,
% 0.17/0.39 ( mlocal
% 0.17/0.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(mnot_type,type,
% 0.17/0.39 mnot: ( mworld > $o ) > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mand_type,type,
% 0.17/0.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mor_type,type,
% 0.17/0.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mimplies_type,type,
% 0.17/0.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mequiv_type,type,
% 0.17/0.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.39
% 0.17/0.39 thf(mnot_def,definition,
% 0.17/0.39 ( mnot
% 0.17/0.39 = ( ^ [A: mworld > $o,W: mworld] :
% 0.17/0.39 ~ ( A @ W ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(mand_def,definition,
% 0.17/0.39 ( mand
% 0.17/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.39 ( ( A @ W )
% 0.17/0.39 & ( B @ W ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(mor_def,definition,
% 0.17/0.39 ( mor
% 0.17/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.39 ( ( A @ W )
% 0.17/0.39 | ( B @ W ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(mimplies_def,definition,
% 0.17/0.39 ( mimplies
% 0.17/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.39 ( ( A @ W )
% 0.17/0.39 => ( B @ W ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(mequiv_def,definition,
% 0.17/0.39 ( mequiv
% 0.17/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.40 ( ( A @ W )
% 0.17/0.40 <=> ( B @ W ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(mbox_type,type,
% 0.17/0.40 mbox: ( mworld > $o ) > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(mbox_def,definition,
% 0.17/0.40 ( mbox
% 0.17/0.40 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.17/0.40 ! [V: mworld] :
% 0.17/0.40 ( ( mrel @ W @ V )
% 0.17/0.40 => ( Phi @ V ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(mdia_type,type,
% 0.17/0.40 mdia: ( mworld > $o ) > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(mdia_def,definition,
% 0.17/0.40 ( mdia
% 0.17/0.40 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.17/0.40 ? [V: mworld] :
% 0.17/0.40 ( ( mrel @ W @ V )
% 0.17/0.40 & ( Phi @ V ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(mrel_reflexive,axiom,
% 0.17/0.40 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.17/0.40
% 0.17/0.40 thf(mrel_euclidean,axiom,
% 0.17/0.40 ! [W: mworld,V: mworld,U: mworld] :
% 0.17/0.40 ( ( ( mrel @ W @ U )
% 0.17/0.40 & ( mrel @ W @ V ) )
% 0.17/0.40 => ( mrel @ U @ V ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(eiw_di_type,type,
% 0.17/0.40 eiw_di: $i > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(eiw_di_nonempty,axiom,
% 0.17/0.40 ! [W: mworld] :
% 0.17/0.40 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.17/0.40
% 0.17/0.40 thf(eiw_di_decr,axiom,
% 0.17/0.40 ! [W: mworld,V: mworld,X: $i] :
% 0.17/0.40 ( ( ( eiw_di @ X @ W )
% 0.17/0.40 & ( mrel @ V @ W ) )
% 0.17/0.40 => ( eiw_di @ X @ V ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(mforall_di_type,type,
% 0.17/0.40 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(mforall_di_def,definition,
% 0.17/0.40 ( mforall_di
% 0.17/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.17/0.40 ! [X: $i] :
% 0.17/0.40 ( ( eiw_di @ X @ W )
% 0.17/0.40 => ( A @ X @ W ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(mexists_di_type,type,
% 0.17/0.40 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(mexists_di_def,definition,
% 0.17/0.40 ( mexists_di
% 0.17/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.17/0.40 ? [X: $i] :
% 0.17/0.40 ( ( eiw_di @ X @ W )
% 0.17/0.40 & ( A @ X @ W ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(element_decl,type,
% 0.17/0.40 element: $i > $i > mworld > $o ).
% 0.17/0.40
% 0.17/0.40 thf(pel40,conjecture,
% 0.17/0.40 ( mlocal
% 0.17/0.40 @ ( mimplies
% 0.17/0.40 @ ( mexists_di
% 0.17/0.40 @ ^ [Y: $i] :
% 0.17/0.40 ( mforall_di
% 0.17/0.40 @ ^ [X: $i] : ( mequiv @ ( element @ X @ Y ) @ ( element @ X @ X ) ) ) )
% 0.17/0.40 @ ( mnot
% 0.17/0.40 @ ( mforall_di
% 0.17/0.40 @ ^ [X1: $i] :
% 0.17/0.40 ( mexists_di
% 0.17/0.40 @ ^ [Y1: $i] :
% 0.17/0.40 ( mforall_di
% 0.17/0.40 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ Y1 ) @ ( mnot @ ( element @ Z @ X1 ) ) ) ) ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.64/1.37 ---- Embedded in THF ---
% 1.64/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.37 %%% Generated on Tue Feb 24 11:50:41 EST 2026
% 1.64/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.37 %%% Logic specification used:
% 1.64/1.37 %%% thf(spec, logic, $$dhol).
% 1.64/1.37
% 1.64/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2DTF2441.p
% See solution above
% 1.64/1.37 ------------------------
% 1.64/1.38 ---- Cleaned THF ---
% 1.64/1.38 thf(mworld,type,
% 1.64/1.38 mworld: $tType ).
% 1.64/1.38
% 1.64/1.38 thf(mrel_type,type,
% 1.64/1.38 mrel: mworld > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mactual_type,type,
% 1.64/1.38 mactual: mworld ).
% 1.64/1.38
% 1.64/1.38 thf(mlocal_type,type,
% 1.64/1.38 mlocal: ( mworld > $o ) > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mlocal_def,definition,
% 1.64/1.38 ( mlocal
% 1.64/1.38 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mnot_type,type,
% 1.64/1.38 mnot: ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mand_type,type,
% 1.64/1.38 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mor_type,type,
% 1.64/1.38 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mimplies_type,type,
% 1.64/1.38 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mequiv_type,type,
% 1.64/1.38 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mnot_def,definition,
% 1.64/1.38 ( mnot
% 1.64/1.38 = ( ^ [A: mworld > $o,W: mworld] :
% 1.64/1.38 ~ ( A @ W ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mand_def,definition,
% 1.64/1.38 ( mand
% 1.64/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.64/1.38 ( ( A @ W )
% 1.64/1.38 & ( B @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mor_def,definition,
% 1.64/1.38 ( mor
% 1.64/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.64/1.38 ( ( A @ W )
% 1.64/1.38 | ( B @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mimplies_def,definition,
% 1.64/1.38 ( mimplies
% 1.64/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.64/1.38 ( ( A @ W )
% 1.64/1.38 => ( B @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mequiv_def,definition,
% 1.64/1.38 ( mequiv
% 1.64/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.64/1.38 ( ( A @ W )
% 1.64/1.38 <=> ( B @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mbox_type,type,
% 1.64/1.38 mbox: ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mbox_def,definition,
% 1.64/1.38 ( mbox
% 1.64/1.38 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.64/1.38 ! [V: mworld] :
% 1.64/1.38 ( ( mrel @ W @ V )
% 1.64/1.38 => ( Phi @ V ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mdia_type,type,
% 1.64/1.38 mdia: ( mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mdia_def,definition,
% 1.64/1.38 ( mdia
% 1.64/1.38 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.64/1.38 ? [V: mworld] :
% 1.64/1.38 ( ( mrel @ W @ V )
% 1.64/1.38 & ( Phi @ V ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mrel_reflexive,axiom,
% 1.64/1.38 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.64/1.38
% 1.64/1.38 thf(mrel_euclidean,axiom,
% 1.64/1.38 ! [W: mworld,V: mworld,U: mworld] :
% 1.64/1.38 ( ( ( mrel @ W @ U )
% 1.64/1.38 & ( mrel @ W @ V ) )
% 1.64/1.38 => ( mrel @ U @ V ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(eiw_di_type,type,
% 1.64/1.38 eiw_di: $i > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(eiw_di_nonempty,axiom,
% 1.64/1.38 ! [W: mworld] :
% 1.64/1.38 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.64/1.38
% 1.64/1.38 thf(eiw_di_decr,axiom,
% 1.64/1.38 ! [W: mworld,V: mworld,X: $i] :
% 1.64/1.38 ( ( ( eiw_di @ X @ W )
% 1.64/1.38 & ( mrel @ V @ W ) )
% 1.64/1.38 => ( eiw_di @ X @ V ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mforall_di_type,type,
% 1.64/1.38 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mforall_di_def,definition,
% 1.64/1.38 ( mforall_di
% 1.64/1.38 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.64/1.38 ! [X: $i] :
% 1.64/1.38 ( ( eiw_di @ X @ W )
% 1.64/1.38 => ( A @ X @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(mexists_di_type,type,
% 1.64/1.38 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(mexists_di_def,definition,
% 1.64/1.38 ( mexists_di
% 1.64/1.38 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.64/1.38 ? [X: $i] :
% 1.64/1.38 ( ( eiw_di @ X @ W )
% 1.64/1.38 & ( A @ X @ W ) ) ) ) ).
% 1.64/1.38
% 1.64/1.38 thf(element_decl,type,
% 1.64/1.38 element: $i > $i > mworld > $o ).
% 1.64/1.38
% 1.64/1.38 thf(pel40,conjecture,
% 1.64/1.38 ( mlocal
% 1.64/1.38 @ ( mimplies
% 1.64/1.38 @ ( mexists_di
% 1.64/1.38 @ ^ [Y: $i] :
% 1.64/1.38 ( mforall_di
% 1.64/1.38 @ ^ [X: $i] : ( mequiv @ ( element @ X @ Y ) @ ( element @ X @ X ) ) ) )
% 1.64/1.38 @ ( mnot
% 1.64/1.38 @ ( mforall_di
% 1.64/1.38 @ ^ [X1: $i] :
% 1.64/1.38 ( mexists_di
% 1.64/1.38 @ ^ [Y1: $i] :
% 1.64/1.38 ( mforall_di
% 1.64/1.38 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ Y1 ) @ ( mnot @ ( element @ Z @ X1 ) ) ) ) ) ) ) ) ) ).
% 1.64/1.38 ------------------------
% 1.81/1.40 % (2545)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_2441 for (2999ds/275Mi)
% 1.81/1.40 % (2544)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_2441 for (2999ds/2Mi)
% 1.81/1.40 % (2542)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_2441 for (2999ds/27Mi)
% 1.81/1.40 % (2543)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2441 for (2999ds/2Mi)
% 1.81/1.40 % (2541)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_2441 for (2999ds/4Mi)
% 1.81/1.40 % (2543)Instruction limit reached!
% 1.81/1.40 % (2543)------------------------------
% 1.81/1.40 % (2543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (2543)Termination reason: Unknown
% 1.81/1.40 % (2543)Termination phase: Property scanning
% 1.81/1.40
% 1.81/1.40 % (2544)Instruction limit reached!
% 1.81/1.40 % (2544)------------------------------
% 1.81/1.40 % (2544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (2544)Termination reason: Unknown
% 1.81/1.40 % (2544)Termination phase: Property scanning
% 1.81/1.40
% 1.81/1.40 % (2544)Memory used [KB]: 1023
% 1.81/1.40 % (2544)Time elapsed: 0.003 s
% 1.81/1.40 % (2544)Instructions burned: 3 (million)
% 1.81/1.40 % (2544)------------------------------
% 1.81/1.40 % (2544)------------------------------
% 1.81/1.40 % (2543)Memory used [KB]: 1023
% 1.81/1.40 % (2543)Time elapsed: 0.003 s
% 1.81/1.40 % (2543)Instructions burned: 3 (million)
% 1.81/1.40 % (2543)------------------------------
% 1.81/1.40 % (2543)------------------------------
% 1.81/1.40 % (2541)Instruction limit reached!
% 1.81/1.40 % (2541)------------------------------
% 1.81/1.40 % (2541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (2541)Termination reason: Unknown
% 1.81/1.40 % (2541)Termination phase: Function definition elimination
% 1.81/1.40
% 1.81/1.40 % (2541)Memory used [KB]: 1023
% 1.81/1.40 % (2541)Time elapsed: 0.003 s
% 1.81/1.40 % (2541)Instructions burned: 4 (million)
% 1.81/1.40 % (2541)------------------------------
% 1.81/1.40 % (2541)------------------------------
% 1.81/1.40 % (2546)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2441 for (2999ds/18Mi)
% 1.81/1.41 % (2540)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2441 for (2999ds/183Mi)
% 1.81/1.41 % (2545)Refutation not found, incomplete strategy
% 1.81/1.41 % (2545)------------------------------
% 1.81/1.41 % (2545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.41 % (2545)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.41
% 1.81/1.41
% 1.81/1.41 % (2545)Memory used [KB]: 5500
% 1.81/1.41 % (2545)Time elapsed: 0.004 s
% 1.81/1.41 % (2545)Instructions burned: 4 (million)
% 1.81/1.41 % (2545)------------------------------
% 1.81/1.41 % (2545)------------------------------
% 1.81/1.41 % (2542)Refutation not found, incomplete strategy
% 1.81/1.41 % (2542)------------------------------
% 1.81/1.41 % (2542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.41 % (2542)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.41
% 1.81/1.41
% 1.81/1.41 % (2542)Memory used [KB]: 5628
% 1.81/1.41 % (2542)Time elapsed: 0.011 s
% 1.81/1.41 % (2542)Instructions burned: 17 (million)
% 1.81/1.41 % (2542)------------------------------
% 1.81/1.41 % (2542)------------------------------
% 1.81/1.42 % (2546)Instruction limit reached!
% 1.81/1.42 % (2546)------------------------------
% 1.81/1.42 % (2546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (2546)Termination reason: Unknown
% 1.81/1.42 % (2546)Termination phase: Saturation
% 1.81/1.42
% 1.81/1.42 % (2546)Memory used [KB]: 5628
% 1.81/1.42 % (2546)Time elapsed: 0.013 s
% 1.81/1.42 % (2546)Instructions burned: 19 (million)
% 1.81/1.42 % (2546)------------------------------
% 1.81/1.42 % (2546)------------------------------
% 1.81/1.42 % (2540)First to succeed.
% 1.81/1.42 % (2548)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_2441 for (2999ds/37Mi)
% 1.81/1.42 % (2547)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2441 for (2999ds/3Mi)
% 1.81/1.42 % (2549)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_2441 for (2999ds/15Mi)
% 1.81/1.42 % (2547)Instruction limit reached!
% 1.81/1.42 % (2547)------------------------------
% 1.81/1.42 % (2547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (2547)Termination reason: Unknown
% 1.81/1.42 % (2547)Termination phase: Property scanning
% 1.81/1.42
% 1.81/1.42 % (2547)Memory used [KB]: 1023
% 1.81/1.42 % (2547)Time elapsed: 0.003 s
% 1.81/1.42 % (2547)Instructions burned: 3 (million)
% 1.81/1.42 % (2547)------------------------------
% 1.81/1.42 % (2547)------------------------------
% 1.81/1.42 % (2550)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_2441 for (2999ds/3Mi)
% 1.81/1.42 % (2540)Refutation found. Thanks to Tanya!
% 1.81/1.42 % SZS status Theorem for DTF2THF_2441
% 1.81/1.42 % SZS output start Proof for DTF2THF_2441
% 1.81/1.42 thf(type_def_5, type, mworld: $tType).
% 1.81/1.42 thf(func_def_0, type, mworld: $tType).
% 1.81/1.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.81/1.42 thf(func_def_2, type, mactual: mworld).
% 1.81/1.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.81/1.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.81/1.42 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.81/1.42 thf(func_def_15, type, element: $i > $i > mworld > $o).
% 1.81/1.42 thf(func_def_29, type, sK0: mworld > $i).
% 1.81/1.42 thf(func_def_34, type, sK3: $i > $i).
% 1.81/1.42 thf(f205,plain,(
% 1.81/1.42 $false),
% 1.81/1.42 inference(avatar_sat_refutation,[status(thm)],[f142,f151,f166,f204])).
% 1.81/1.42 thf(f204,plain,(
% 1.81/1.42 ~spl1_1 | spl1_2 | spl1_3),
% 1.81/1.42 inference(avatar_contradiction_clause,[status(thm)],[f203])).
% 1.81/1.42 thf(f203,plain,(
% 1.81/1.42 $false | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f202,f140])).
% 1.81/1.42 thf(f140,plain,(
% 1.81/1.42 ((eiw_di @ (sK3 @ sK2) @ mactual) != $false) | spl1_3),
% 1.81/1.42 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.81/1.42 thf(f139,definition,(
% 1.81/1.42 spl1_3 <=> ((eiw_di @ (sK3 @ sK2) @ mactual) = $false)),
% 1.81/1.42 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.81/1.42 thf(f202,plain,(
% 1.81/1.42 ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f196,f136])).
% 1.81/1.42 thf(f136,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) != $false) | spl1_2),
% 1.81/1.42 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.81/1.42 thf(f135,definition,(
% 1.81/1.42 spl1_2 <=> ((eiw_di @ sK2 @ mactual) = $false)),
% 1.81/1.42 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.81/1.42 thf(f196,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.81/1.42 thf(f195,plain,(
% 1.81/1.42 ($true = $false) | ((eiw_di @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(duplicate_literal_removal,[status(thm)],[f194])).
% 1.81/1.42 thf(f194,plain,(
% 1.81/1.42 ($true = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ($true = $false) | ((eiw_di @ sK2 @ mactual) = $false) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(superposition,[status(thm)],[f112,f190])).
% 1.81/1.42 thf(f190,plain,(
% 1.81/1.42 ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $true) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f189,f140])).
% 1.81/1.42 thf(f189,plain,(
% 1.81/1.42 ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $true) | (~spl1_1 | spl1_2 | spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f188,f136])).
% 1.81/1.42 thf(f188,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $true) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | (~spl1_1 | spl1_3)),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f180])).
% 1.81/1.42 thf(f180,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ($true = $false) | ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $true) | (~spl1_1 | spl1_3)),
% 1.81/1.42 inference(superposition,[status(thm)],[f97,f176])).
% 1.81/1.42 thf(f176,plain,(
% 1.81/1.42 ((element @ (sK3 @ sK2) @ (sK3 @ sK2) @ mactual) = $false) | (~spl1_1 | spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f174,f140])).
% 1.81/1.42 thf(f174,plain,(
% 1.81/1.42 ((element @ (sK3 @ sK2) @ (sK3 @ sK2) @ mactual) = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ~spl1_1),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.81/1.42 thf(f169,plain,(
% 1.81/1.42 ($true = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ((element @ (sK3 @ sK2) @ (sK3 @ sK2) @ mactual) = $false) | ~spl1_1),
% 1.81/1.42 inference(superposition,[status(thm)],[f133,f82])).
% 1.81/1.42 thf(f82,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = (element @ X1 @ sK2 @ mactual)) | ((element @ X1 @ X1 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.81/1.42 thf(f80,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ((element @ X1 @ X1 @ mactual) = (element @ X1 @ sK2 @ mactual))) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.81/1.42 thf(f79,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = ((element @ X1 @ sK2 @ mactual) = (element @ X1 @ X1 @ mactual))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.81/1.42 thf(f78,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => ((element @ X1 @ sK2 @ mactual) = (element @ X1 @ X1 @ mactual))))) )),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.81/1.42 thf(f77,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ sK2 @ mactual) = (element @ Y0 @ Y0 @ mactual)))) @ X1))) )),
% 1.81/1.42 inference(pi_clausification,[status(thm)],[f76])).
% 1.81/1.42 thf(f76,plain,(
% 1.81/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ sK2 @ mactual) = (element @ Y0 @ Y0 @ mactual))))))),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.81/1.42 thf(f74,plain,(
% 1.81/1.42 ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ sK2 @ mactual) = (element @ Y0 @ Y0 @ mactual))))) & (eiw_di @ sK2 @ mactual)))),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.81/1.42 thf(f73,plain,(
% 1.81/1.42 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ Y1 @ mactual))))) & (eiw_di @ Y0 @ mactual))) @ sK2))),
% 1.81/1.42 inference(sigma_clausification,[status(thm)],[f72])).
% 1.81/1.42 thf(f72,plain,(
% 1.81/1.42 ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ Y1 @ mactual))))) & (eiw_di @ Y0 @ mactual)))))),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.81/1.42 thf(f70,plain,(
% 1.81/1.42 ($true != ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (element @ Y1 @ Y1 @ mactual))))) & (eiw_di @ Y0 @ mactual)))) => (~ (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => ((element @ Y2 @ Y1 @ mactual) = (~ (element @ Y2 @ Y0 @ mactual)))))) & (eiw_di @ Y1 @ mactual))))))))))),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.81/1.42 thf(f69,plain,(
% 1.81/1.42 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ 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))))))) @ (element @ Y1 @ Y0) @ (element @ Y1 @ Y1)))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[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]: ((Y1 @ Y3 @ Y2) & (eiw_di @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) = (Y4 @ Y5))))))) @ (element @ Y2 @ Y1) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: (~ (Y3 @ Y4))))) @ (element @ Y2 @ Y0)))))))))))))),
% 1.81/1.42 inference(definition_unfolding,[status(thm)],[f65,f56,f57,f61,f54,f62,f55,f54,f61,f54,f62,f55])).
% 1.81/1.42 thf(f55,plain,(
% 1.81/1.42 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f26])).
% 1.81/1.42 thf(f26,plain,(
% 1.81/1.42 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f25])).
% 1.81/1.42 thf(f25,plain,(
% 1.81/1.42 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.81/1.42 inference(rectify,[status(thm)],[f2])).
% 1.81/1.42 thf(f2,axiom,(
% 1.81/1.42 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mnot_def)).
% 1.81/1.42 thf(f62,plain,(
% 1.81/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f32])).
% 1.81/1.42 thf(f32,plain,(
% 1.81/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f31])).
% 1.81/1.42 thf(f31,plain,(
% 1.81/1.42 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 1.81/1.42 inference(rectify,[status(thm)],[f6])).
% 1.81/1.42 thf(f6,axiom,(
% 1.81/1.42 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mequiv_def)).
% 1.81/1.42 thf(f54,plain,(
% 1.81/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f46])).
% 1.81/1.42 thf(f46,plain,(
% 1.81/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f45])).
% 1.81/1.42 thf(f45,plain,(
% 1.81/1.42 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.81/1.42 inference(rectify,[status(thm)],[f13])).
% 1.81/1.42 thf(f13,axiom,(
% 1.81/1.42 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : ((eiw_di @ X6 @ X2) => (X1 @ X6 @ X2)))) = mforall_di)),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mforall_di_def)).
% 1.81/1.42 thf(f61,plain,(
% 1.81/1.42 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f36])).
% 1.81/1.42 thf(f36,plain,(
% 1.81/1.42 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f35])).
% 1.81/1.42 thf(f35,plain,(
% 1.81/1.42 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((eiw_di @ X2 @ X1) & (X0 @ X2 @ X1)))))),
% 1.81/1.42 inference(rectify,[status(thm)],[f14])).
% 1.81/1.42 thf(f14,axiom,(
% 1.81/1.42 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((eiw_di @ X6 @ X2) & (X1 @ X6 @ X2)))))),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mexists_di_def)).
% 1.81/1.42 thf(f57,plain,(
% 1.81/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f28])).
% 1.81/1.42 thf(f28,plain,(
% 1.81/1.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f27])).
% 1.81/1.42 thf(f27,plain,(
% 1.81/1.42 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.81/1.42 inference(rectify,[status(thm)],[f5])).
% 1.81/1.42 thf(f5,axiom,(
% 1.81/1.42 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mimplies_def)).
% 1.81/1.42 thf(f56,plain,(
% 1.81/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.81/1.42 thf(f18,plain,(
% 1.81/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f1])).
% 1.81/1.42 thf(f1,axiom,(
% 1.81/1.42 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',mlocal_def)).
% 1.81/1.42 thf(f65,plain,(
% 1.81/1.42 ($true != (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (element @ Y1 @ Y0) @ (element @ Y1 @ Y1)))))) @ (mnot @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y1) @ (mnot @ (element @ Y2 @ Y0)))))))))))))),
% 1.81/1.42 inference(cnf_transformation,[status(thm)],[f47])).
% 1.81/1.42 thf(f47,plain,(
% 1.81/1.42 ($true != (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (element @ Y1 @ Y0) @ (element @ Y1 @ Y1)))))) @ (mnot @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y1) @ (mnot @ (element @ Y2 @ Y0)))))))))))))),
% 1.81/1.42 inference(flattening,[status(thm)],[f44])).
% 1.81/1.42 thf(f44,plain,(
% 1.81/1.42 ~($true = (mlocal @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (element @ Y1 @ Y0) @ (element @ Y1 @ Y1)))))) @ (mnot @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (element @ Y2 @ Y1) @ (mnot @ (element @ Y2 @ Y0)))))))))))))),
% 1.81/1.42 inference(fool_elimination,[status(thm)],[f43])).
% 1.81/1.42 thf(f43,plain,(
% 1.81/1.42 ~(mlocal @ (mimplies @ (mexists_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (element @ X1 @ X0) @ (element @ X1 @ X1)))))) @ (mnot @ (mforall_di @ (^[X2 : $i] : (mexists_di @ (^[X3 : $i] : (mforall_di @ (^[X4 : $i] : (mequiv @ (element @ X4 @ X3) @ (mnot @ (element @ X4 @ X2))))))))))))),
% 1.81/1.42 inference(rectify,[status(thm)],[f16])).
% 1.81/1.42 thf(f16,negated_conjecture,(
% 1.81/1.42 ~(mlocal @ (mimplies @ (mexists_di @ (^[X7 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (element @ X6 @ X7) @ (element @ X6 @ X6)))))) @ (mnot @ (mforall_di @ (^[X8 : $i] : (mexists_di @ (^[X9 : $i] : (mforall_di @ (^[X10 : $i] : (mequiv @ (element @ X10 @ X9) @ (mnot @ (element @ X10 @ X8))))))))))))),
% 1.81/1.42 inference(negated_conjecture,[status(cth)],[f15])).
% 1.81/1.42 thf(f15,conjecture,(
% 1.81/1.42 (mlocal @ (mimplies @ (mexists_di @ (^[X7 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (element @ X6 @ X7) @ (element @ X6 @ X6)))))) @ (mnot @ (mforall_di @ (^[X8 : $i] : (mexists_di @ (^[X9 : $i] : (mforall_di @ (^[X10 : $i] : (mequiv @ (element @ X10 @ X9) @ (mnot @ (element @ X10 @ X8))))))))))))),
% 1.81/1.42 file('/export/starexec/sandbox/tmp/tmp.4nSd79MMiN/DTF2THF_2441.p',pel40)).
% 1.81/1.42 thf(f133,plain,(
% 1.81/1.42 ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $false) | ~spl1_1),
% 1.81/1.42 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.81/1.42 thf(f131,definition,(
% 1.81/1.42 spl1_1 <=> ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $false)),
% 1.81/1.42 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.81/1.42 thf(f97,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (element @ X2 @ (sK3 @ X1) @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false) | ((element @ X2 @ X1 @ mactual) = $true)) )),
% 1.81/1.42 inference(not_proxy_clausification,[status(thm)],[f96])).
% 1.81/1.42 thf(f96,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (element @ X2 @ (sK3 @ X1) @ mactual)) | ((~ (element @ X2 @ X1 @ mactual)) = $false) | ((eiw_di @ X1 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.81/1.42 thf(f94,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X2 @ mactual) = $false) | ((~ (element @ X2 @ X1 @ mactual)) = (element @ X2 @ (sK3 @ X1) @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.81/1.42 thf(f93,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X2 @ mactual) = $false) | ($true = ((element @ X2 @ (sK3 @ X1) @ mactual) = (~ (element @ X2 @ X1 @ mactual)))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.81/1.42 thf(f92,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = ((eiw_di @ X2 @ mactual) => ((element @ X2 @ (sK3 @ X1) @ mactual) = (~ (element @ X2 @ X1 @ mactual)))))) )),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.81/1.42 thf(f91,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ (sK3 @ X1) @ mactual) = (~ (element @ Y0 @ X1 @ mactual))))) @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(pi_clausification,[status(thm)],[f90])).
% 1.81/1.42 thf(f90,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ (sK3 @ X1) @ mactual) = (~ (element @ Y0 @ X1 @ mactual))))))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.81/1.42 thf(f88,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((element @ Y0 @ (sK3 @ X1) @ mactual) = (~ (element @ Y0 @ X1 @ mactual)))))) & (eiw_di @ (sK3 @ X1) @ mactual)))) )),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.81/1.42 thf(f87,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (~ (element @ Y1 @ X1 @ mactual)))))) & (eiw_di @ Y0 @ mactual))) @ (sK3 @ X1)))) )),
% 1.81/1.42 inference(sigma_clausification,[status(thm)],[f86])).
% 1.81/1.42 thf(f86,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (~ (element @ Y1 @ X1 @ mactual)))))) & (eiw_di @ Y0 @ mactual)))))) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.81/1.42 thf(f85,plain,(
% 1.81/1.42 ( ! [X1 : $i] : ((((eiw_di @ X1 @ mactual) => (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((element @ Y1 @ Y0 @ mactual) = (~ (element @ Y1 @ X1 @ mactual)))))) & (eiw_di @ Y0 @ mactual))))) = $true)) )),
% 1.81/1.42 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.81/1.42 thf(f84,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => ((element @ Y2 @ Y1 @ mactual) = (~ (element @ Y2 @ Y0 @ mactual)))))) & (eiw_di @ Y1 @ mactual)))))) @ X1))) )),
% 1.81/1.42 inference(pi_clausification,[status(thm)],[f83])).
% 1.81/1.42 thf(f83,plain,(
% 1.81/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => ((element @ Y2 @ Y1 @ mactual) = (~ (element @ Y2 @ Y0 @ mactual)))))) & (eiw_di @ Y1 @ mactual))))))))),
% 1.81/1.42 inference(not_proxy_clausification,[status(thm)],[f71])).
% 1.81/1.42 thf(f71,plain,(
% 1.81/1.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => ((element @ Y2 @ Y1 @ mactual) = (~ (element @ Y2 @ Y0 @ mactual)))))) & (eiw_di @ Y1 @ mactual)))))))) = $false)),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.81/1.42 thf(f112,plain,(
% 1.81/1.42 ( ! [X0 : $i] : (((element @ (sK3 @ X0) @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ X0) @ mactual) = $false) | ((eiw_di @ X0 @ mactual) = $false) | ((element @ (sK3 @ X0) @ X0 @ mactual) = $false)) )),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.81/1.42 thf(f111,plain,(
% 1.81/1.42 ( ! [X0 : $i] : (((element @ (sK3 @ X0) @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ X0) @ mactual) = $false) | ((element @ (sK3 @ X0) @ X0 @ mactual) = $false) | ((eiw_di @ X0 @ mactual) = $false) | ($true = $false)) )),
% 1.81/1.42 inference(duplicate_literal_removal,[status(thm)],[f102])).
% 1.81/1.42 thf(f102,plain,(
% 1.81/1.42 ( ! [X0 : $i] : (((element @ (sK3 @ X0) @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ X0) @ mactual) = $false) | ((element @ (sK3 @ X0) @ X0 @ mactual) = $false) | ($true = $false) | ((eiw_di @ X0 @ mactual) = $false) | ((eiw_di @ (sK3 @ X0) @ mactual) = $false)) )),
% 1.81/1.42 inference(superposition,[status(thm)],[f98,f81])).
% 1.81/1.42 thf(f81,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = (element @ X1 @ X1 @ mactual)) | ((element @ X1 @ sK2 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.81/1.42 thf(f98,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (((element @ X2 @ (sK3 @ X1) @ mactual) = $false) | ((element @ X2 @ X1 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.81/1.42 inference(not_proxy_clausification,[status(thm)],[f95])).
% 1.81/1.42 thf(f95,plain,(
% 1.81/1.42 ( ! [X2 : $i,X1 : $i] : (((~ (element @ X2 @ X1 @ mactual)) = $true) | ((eiw_di @ X2 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false) | ((element @ X2 @ (sK3 @ X1) @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.81/1.42 thf(f166,plain,(
% 1.81/1.42 spl1_2 | ~spl1_3),
% 1.81/1.42 inference(avatar_contradiction_clause,[status(thm)],[f165])).
% 1.81/1.42 thf(f165,plain,(
% 1.81/1.42 $false | (spl1_2 | ~spl1_3)),
% 1.81/1.42 inference(subsumption_resolution,[status(thm)],[f160,f136])).
% 1.81/1.42 thf(f160,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ~spl1_3),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.81/1.42 thf(f157,plain,(
% 1.81/1.42 ($true = $false) | ((eiw_di @ sK2 @ mactual) = $false) | ~spl1_3),
% 1.81/1.42 inference(superposition,[status(thm)],[f89,f141])).
% 1.81/1.42 thf(f141,plain,(
% 1.81/1.42 ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ~spl1_3),
% 1.81/1.42 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.81/1.42 thf(f89,plain,(
% 1.81/1.42 ( ! [X1 : $i] : (($true = (eiw_di @ (sK3 @ X1) @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 1.81/1.42 thf(f151,plain,(
% 1.81/1.42 ~spl1_2),
% 1.81/1.42 inference(avatar_contradiction_clause,[status(thm)],[f150])).
% 1.81/1.42 thf(f150,plain,(
% 1.81/1.42 $false | ~spl1_2),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.81/1.42 thf(f145,plain,(
% 1.81/1.42 ($true = $false) | ~spl1_2),
% 1.81/1.42 inference(superposition,[status(thm)],[f75,f137])).
% 1.81/1.42 thf(f137,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ~spl1_2),
% 1.81/1.42 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.81/1.42 thf(f75,plain,(
% 1.81/1.42 ($true = (eiw_di @ sK2 @ mactual))),
% 1.81/1.42 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.81/1.42 thf(f142,plain,(
% 1.81/1.42 spl1_1 | spl1_2 | spl1_3),
% 1.81/1.42 inference(avatar_split_clause,[status(thm)],[f123,f139,f135,f131])).
% 1.81/1.42 thf(f123,plain,(
% 1.81/1.42 ((eiw_di @ (sK3 @ sK2) @ mactual) = $false) | ((eiw_di @ sK2 @ mactual) = $false) | ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $false)),
% 1.81/1.42 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.81/1.42 thf(f122,plain,(
% 1.81/1.42 ((eiw_di @ sK2 @ mactual) = $false) | ($false != $false) | ((element @ (sK3 @ sK2) @ sK2 @ mactual) = $false) | ((eiw_di @ (sK3 @ sK2) @ mactual) = $false)),
% 1.81/1.42 inference(equality_factoring,[status(thm)],[f112])).
% 1.81/1.42 % SZS output end Proof for DTF2THF_2441
% 1.81/1.42 % (2540)------------------------------
% 1.81/1.42 % (2540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (2540)Termination reason: Refutation
% 1.81/1.42
% 1.81/1.42 % (2540)Memory used [KB]: 5756
% 1.81/1.42 % (2540)Time elapsed: 0.018 s
% 1.81/1.42 % (2540)Instructions burned: 20 (million)
% 1.81/1.42 % (2540)------------------------------
% 1.81/1.42 % (2540)------------------------------
% 1.81/1.42 % (2539)Success in time 0.027 s
%------------------------------------------------------------------------------