%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET574^20 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 09:31:47 AM UTC 2026
% Result : Theorem 0.31s 1.35s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 645 ( 131 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 948 ( 7 ~; 50 |; 45 &; 757 @)
% ( 2 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 8 con; 0-3 aty)
% ( 24 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 194 ( 159 ^; 33 !; 2 ?; 194 :)
% 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,
intersect: $i > $i > mworld > $o ).
thf(func_def_16,type,
member: $i > $i > mworld > $o ).
thf(func_def_17,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_31,type,
sK0: mworld > $i ).
thf(func_def_38,type,
sK5: $i > $i > $i ).
thf(f187,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f186]) ).
thf(f186,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f89,f183]) ).
thf(f183,plain,
( ( member @ sK2 @ sK3 @ mactual )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true = $false )
| ( ( member @ sK2 @ sK3 @ mactual )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f169,f78]) ).
thf(f78,plain,
( ( eiw_di @ sK2 @ mactual )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( eiw_di @ sK2 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK2 @ Y1 @ mactual )
& ( member @ sK2 @ Y0 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: $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 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f56,f70,f69,f69,f69,f58,f55]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mand_def) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,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/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mimplies_def) ).
thf(f69,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] :
( ( eiw_di @ X5 @ X2 )
=> ( X1 @ X5 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mforall_di_def) ).
thf(f70,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mlocal_def) ).
thf(f56,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f40]) ).
thf(f40,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( member @ X3 @ X6 ) @ ( member @ X3 @ X7 ) ) @ ( intersect @ X6 @ X7 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( member @ X3 @ X6 ) @ ( member @ X3 @ X7 ) ) @ ( intersect @ X6 @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',prove_th13) ).
thf(f169,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( member @ sK2 @ sK3 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true = $false )
| ( ( member @ sK2 @ sK3 @ mactual )
= $false )
| ( ( eiw_di @ sK2 @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f90,f137]) ).
thf(f137,plain,
! [X0: $i] :
( ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( ( member @ X0 @ sK3 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $true = $false )
| ( ( member @ X0 @ sK3 @ mactual )
= $false )
| ( ( member @ X0 @ sK4 @ mactual )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f135,f82]) ).
thf(f82,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( eiw_di @ sK3 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK2 @ Y0 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
=> ( intersect @ sK3 @ Y0 @ mactual ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK2 @ Y1 @ mactual )
& ( member @ sK2 @ Y0 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK2 @ Y1 @ mactual )
& ( member @ sK2 @ Y0 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f135,plain,
! [X0: $i] :
( ( ( member @ X0 @ sK3 @ mactual )
= $false )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
! [X0: $i] :
( ( ( member @ X0 @ sK3 @ mactual )
= $false )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $true = $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f128,f86]) ).
thf(f86,plain,
( $true
= ( eiw_di @ sK4 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( eiw_di @ sK4 @ mactual )
=> ( ( ( member @ sK2 @ sK4 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
=> ( intersect @ sK3 @ sK4 @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK2 @ Y0 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
=> ( intersect @ sK3 @ Y0 @ mactual ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK2 @ Y0 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
=> ( intersect @ sK3 @ Y0 @ mactual ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f128,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ mactual )
= $false )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( ( member @ X0 @ sK3 @ mactual )
= $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
! [X0: $i] :
( ( ( member @ X0 @ sK3 @ mactual )
= $false )
| ( ( member @ X0 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( $true = $false )
| ( ( eiw_di @ X0 @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f112,f87]) ).
thf(f87,plain,
( ( intersect @ sK3 @ sK4 @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( ( member @ sK2 @ sK4 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
=> ( intersect @ sK3 @ sK4 @ mactual ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( member @ X3 @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X3 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( member @ X3 @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( eiw_di @ X3 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ( member @ X3 @ X2 @ mactual )
& ( member @ X3 @ X1 @ mactual ) )
= $false )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ( eiw_di @ X3 @ mactual )
& ( member @ X3 @ X2 @ mactual )
& ( member @ X3 @ X1 @ mactual ) )
= $false )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) )
@ X3 )
= $false )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) ) )
= $false )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) ) )
= ( intersect @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( ( ( eiw_di @ X2 @ mactual )
=> ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X2 @ mactual )
& ( member @ Y0 @ X1 @ mactual ) ) ) ) )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ X1 @ mactual ) ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ X1 @ mactual ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual )
& ( member @ Y1 @ X1 @ mactual ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y1 @ mactual )
& ( member @ Y2 @ Y0 @ mactual ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( intersect @ Y0 @ Y1 )
@ ( ^ [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] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f65,f70,f69,f69,f67,f64,f55]) ).
thf(f64,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X5: $i] :
( ( X1 @ X5 @ X2 )
& ( eiw_di @ X5 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mexists_di_def) ).
thf(f67,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mequiv_def) ).
thf(f65,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_di
@ ^ [X2: $i] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mequiv @ ( intersect @ X3 @ X6 )
@ ( mexists_di
@ ^ [X7: $i] : ( mand @ ( member @ X7 @ X3 ) @ ( member @ X7 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',intersect_defn) ).
thf(f90,plain,
( $true
= ( member @ sK2 @ sK4 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( member @ sK2 @ sK4 @ mactual )
& ( member @ sK2 @ sK3 @ mactual ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f89,plain,
( ( member @ sK2 @ sK3 @ mactual )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET574^20 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n007.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:58:38 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SET574^20 : TPTP v9.2.1. Released v8.1.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : TPTP problem SET574+3.p with axiomatized equality
% 0.27/0.46 % Version : [BP13] axioms.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.27/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.27/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.27/0.46 % Source : [TPTP]
% 0.27/0.46 % Names : SET574+1 [QMLTP]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.27/0.46 % Syntax : Number of formulae : 32 ( 12 unt; 16 typ; 10 def)
% 0.27/0.46 % Number of atoms : 53 ( 10 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 9 ( 3 avg)
% 0.27/0.46 % Number of connectives : 82 ( 1 ~; 1 |; 4 &; 71 @)
% 0.27/0.46 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 14 ( 4 avg)
% 0.27/0.46 % Number of types : 3 ( 1 usr)
% 0.27/0.46 % Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.27/0.46 % Number of variables : 41 ( 31 ^; 7 !; 3 ?; 41 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.27/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.27/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.27/0.46 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.27/0.46 % $modalities == $modal_system_T].
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(mworld,type,
% 0.27/0.46 mworld: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(mrel_type,type,
% 0.27/0.46 mrel: mworld > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mactual_type,type,
% 0.27/0.46 mactual: mworld ).
% 0.27/0.46
% 0.27/0.46 thf(mlocal_type,type,
% 0.27/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mlocal_def,definition,
% 0.27/0.46 ( mlocal
% 0.27/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mnot_type,type,
% 0.27/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mand_type,type,
% 0.27/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mor_type,type,
% 0.27/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mimplies_type,type,
% 0.27/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mequiv_type,type,
% 0.27/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mnot_def,definition,
% 0.27/0.46 ( mnot
% 0.27/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.27/0.46 ~ ( A @ W ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mand_def,definition,
% 0.27/0.46 ( mand
% 0.27/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.46 ( ( A @ W )
% 0.27/0.46 & ( B @ W ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mor_def,definition,
% 0.27/0.46 ( mor
% 0.27/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.46 ( ( A @ W )
% 0.27/0.46 | ( B @ W ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mimplies_def,definition,
% 0.27/0.46 ( mimplies
% 0.27/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.46 ( ( A @ W )
% 0.27/0.46 => ( B @ W ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mequiv_def,definition,
% 0.27/0.46 ( mequiv
% 0.27/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.46 ( ( A @ W )
% 0.27/0.46 <=> ( B @ W ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mbox_type,type,
% 0.27/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mbox_def,definition,
% 0.27/0.46 ( mbox
% 0.27/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.46 ! [V: mworld] :
% 0.27/0.46 ( ( mrel @ W @ V )
% 0.27/0.46 => ( Phi @ V ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mdia_type,type,
% 0.27/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mdia_def,definition,
% 0.27/0.46 ( mdia
% 0.27/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.46 ? [V: mworld] :
% 0.27/0.46 ( ( mrel @ W @ V )
% 0.27/0.46 & ( Phi @ V ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mrel_reflexive,axiom,
% 0.27/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.27/0.46
% 0.27/0.46 thf(eiw_di_type,type,
% 0.27/0.46 eiw_di: $i > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(eiw_di_nonempty,axiom,
% 0.27/0.46 ! [W: mworld] :
% 0.27/0.46 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.27/0.46
% 0.27/0.46 thf(eiw_di_decr,axiom,
% 0.27/0.46 ! [W: mworld,V: mworld,X: $i] :
% 0.27/0.46 ( ( ( eiw_di @ X @ W )
% 0.27/0.46 & ( mrel @ V @ W ) )
% 0.27/0.46 => ( eiw_di @ X @ V ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(mforall_di_type,type,
% 0.27/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.46
% 0.27/0.46 thf(mforall_di_def,definition,
% 0.27/0.47 ( mforall_di
% 0.27/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.47 ! [X: $i] :
% 0.27/0.47 ( ( eiw_di @ X @ W )
% 0.27/0.47 => ( A @ X @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mexists_di_type,type,
% 0.27/0.47 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mexists_di_def,definition,
% 0.27/0.47 ( mexists_di
% 0.27/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.47 ? [X: $i] :
% 0.27/0.47 ( ( eiw_di @ X @ W )
% 0.27/0.47 & ( A @ X @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(intersect_decl,type,
% 0.27/0.47 intersect: $i > $i > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(member_decl,type,
% 0.27/0.47 member: $i > $i > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(intersect_defn,axiom,
% 0.27/0.47 ( mlocal
% 0.27/0.47 @ ( mforall_di
% 0.27/0.47 @ ^ [B: $i] :
% 0.27/0.47 ( mforall_di
% 0.27/0.47 @ ^ [C: $i] :
% 0.27/0.47 ( mequiv @ ( intersect @ B @ C )
% 0.27/0.47 @ ( mexists_di
% 0.27/0.47 @ ^ [D: $i] : ( mand @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symmetry_of_intersect,axiom,
% 0.27/0.47 ( mlocal
% 0.27/0.47 @ ( mforall_di
% 0.27/0.47 @ ^ [B: $i] :
% 0.27/0.47 ( mforall_di
% 0.27/0.47 @ ^ [C: $i] : ( mimplies @ ( intersect @ B @ C ) @ ( intersect @ C @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(prove_th13,conjecture,
% 0.27/0.47 ( mlocal
% 0.27/0.47 @ ( mforall_di
% 0.27/0.47 @ ^ [B: $i] :
% 0.27/0.47 ( mforall_di
% 0.27/0.47 @ ^ [C: $i] :
% 0.27/0.47 ( mforall_di
% 0.27/0.47 @ ^ [D: $i] : ( mimplies @ ( mand @ ( member @ B @ C ) @ ( member @ B @ D ) ) @ ( intersect @ C @ D ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 11:58:39 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2DTF28360.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(mworld,type,
% 0.31/1.31 mworld: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_type,type,
% 0.31/1.31 mrel: mworld > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mactual_type,type,
% 0.31/1.31 mactual: mworld ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_type,type,
% 0.31/1.31 mlocal: ( mworld > $o ) > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_def,definition,
% 0.31/1.31 ( mlocal
% 0.31/1.31 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_type,type,
% 0.31/1.31 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mand_type,type,
% 0.31/1.31 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mor_type,type,
% 0.31/1.31 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_type,type,
% 0.31/1.31 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_type,type,
% 0.31/1.31 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_def,definition,
% 0.31/1.31 ( mnot
% 0.31/1.31 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/1.31 ~ ( A @ W ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mand_def,definition,
% 0.31/1.31 ( mand
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 & ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mor_def,definition,
% 0.31/1.31 ( mor
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 | ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_def,definition,
% 0.31/1.31 ( mimplies
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 => ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_def,definition,
% 0.31/1.31 ( mequiv
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 <=> ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_type,type,
% 0.31/1.31 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_def,definition,
% 0.31/1.31 ( mbox
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ! [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 => ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_type,type,
% 0.31/1.31 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_def,definition,
% 0.31/1.31 ( mdia
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ? [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 & ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_reflexive,axiom,
% 0.31/1.31 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_type,type,
% 0.31/1.31 eiw_di: $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_nonempty,axiom,
% 0.31/1.31 ! [W: mworld] :
% 0.31/1.31 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_decr,axiom,
% 0.31/1.31 ! [W: mworld,V: mworld,X: $i] :
% 0.31/1.31 ( ( ( eiw_di @ X @ W )
% 0.31/1.31 & ( mrel @ V @ W ) )
% 0.31/1.31 => ( eiw_di @ X @ V ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_type,type,
% 0.31/1.31 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_def,definition,
% 0.31/1.31 ( mforall_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ! [X: $i] :
% 0.31/1.31 ( ( eiw_di @ X @ W )
% 0.31/1.31 => ( A @ X @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_type,type,
% 0.31/1.31 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_def,definition,
% 0.31/1.31 ( mexists_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ? [X: $i] :
% 0.31/1.31 ( ( eiw_di @ X @ W )
% 0.31/1.31 & ( A @ X @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(intersect_decl,type,
% 0.31/1.31 intersect: $i > $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(member_decl,type,
% 0.31/1.31 member: $i > $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(intersect_defn,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] :
% 0.31/1.31 ( mequiv @ ( intersect @ B @ C )
% 0.31/1.31 @ ( mexists_di
% 0.31/1.31 @ ^ [D: $i] : ( mand @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(symmetry_of_intersect,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( intersect @ B @ C ) @ ( intersect @ C @ B ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(prove_th13,conjecture,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [D: $i] : ( mimplies @ ( mand @ ( member @ B @ C ) @ ( member @ B @ D ) ) @ ( intersect @ C @ D ) ) ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.33 % (28652)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_28360 for (2999ds/2Mi)
% 0.31/1.33 % (28651)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28360 for (2999ds/2Mi)
% 0.31/1.33 % (28651)Instruction limit reached!
% 0.31/1.33 % (28651)------------------------------
% 0.31/1.33 % (28651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (28651)Termination reason: Unknown
% 0.31/1.33 % (28651)Termination phase: Property scanning
% 0.31/1.33
% 0.31/1.33 % (28651)Memory used [KB]: 1023
% 0.31/1.33 % (28651)Time elapsed: 0.002 s
% 0.31/1.33 % (28651)Instructions burned: 3 (million)
% 0.31/1.33 % (28651)------------------------------
% 0.31/1.33 % (28651)------------------------------
% 0.31/1.33 % (28652)Instruction limit reached!
% 0.31/1.33 % (28652)------------------------------
% 0.31/1.33 % (28652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (28652)Termination reason: Unknown
% 0.31/1.33 % (28652)Termination phase: Property scanning
% 0.31/1.33
% 0.31/1.33 % (28652)Memory used [KB]: 1023
% 0.31/1.33 % (28652)Time elapsed: 0.003 s
% 0.31/1.33 % (28652)Instructions burned: 4 (million)
% 0.31/1.33 % (28652)------------------------------
% 0.31/1.33 % (28652)------------------------------
% 0.31/1.34 % (28650)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_28360 for (2999ds/27Mi)
% 0.31/1.34 % (28648)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28360 for (2999ds/183Mi)
% 0.31/1.34 % (28649)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_28360 for (2999ds/4Mi)
% 0.31/1.34 % (28653)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_28360 for (2999ds/275Mi)
% 0.31/1.34 % (28654)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28360 for (2999ds/18Mi)
% 0.31/1.34 % (28649)Instruction limit reached!
% 0.31/1.34 % (28649)------------------------------
% 0.31/1.34 % (28649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (28649)Termination reason: Unknown
% 0.31/1.34 % (28649)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34 % (28649)Memory used [KB]: 1023
% 0.31/1.34 % (28649)Time elapsed: 0.004 s
% 0.31/1.34 % (28649)Instructions burned: 4 (million)
% 0.31/1.34 % (28649)------------------------------
% 0.31/1.34 % (28649)------------------------------
% 0.31/1.34 % (28656)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_28360 for (2999ds/37Mi)
% 0.31/1.34 % (28653)Refutation not found, incomplete strategy
% 0.31/1.34 % (28653)------------------------------
% 0.31/1.34 % (28653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (28653)Termination reason: Refutation not found, incomplete strategy
% 0.31/1.34
% 0.31/1.34
% 0.31/1.34 % (28653)Memory used [KB]: 5500
% 0.31/1.34 % (28653)Time elapsed: 0.005 s
% 0.31/1.34 % (28653)Instructions burned: 5 (million)
% 0.31/1.34 % (28653)------------------------------
% 0.31/1.34 % (28653)------------------------------
% 0.31/1.34 % (28655)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28360 for (2999ds/3Mi)
% 0.31/1.34 % (28655)Instruction limit reached!
% 0.31/1.34 % (28655)------------------------------
% 0.31/1.34 % (28655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (28655)Termination reason: Unknown
% 0.31/1.34 % (28655)Termination phase: Function definition elimination
% 0.31/1.34
% 0.31/1.34 % (28655)Memory used [KB]: 1023
% 0.31/1.34 % (28655)Time elapsed: 0.003 s
% 0.31/1.34 % (28655)Instructions burned: 4 (million)
% 0.31/1.34 % (28655)------------------------------
% 0.31/1.34 % (28655)------------------------------
% 0.31/1.35 % (28654)Instruction limit reached!
% 0.31/1.35 % (28654)------------------------------
% 0.31/1.35 % (28654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (28654)Termination reason: Unknown
% 0.31/1.35 % (28654)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (28654)Memory used [KB]: 5628
% 0.31/1.35 % (28654)Time elapsed: 0.013 s
% 0.31/1.35 % (28654)Instructions burned: 18 (million)
% 0.31/1.35 % (28654)------------------------------
% 0.31/1.35 % (28654)------------------------------
% 0.31/1.35 % (28650)First to succeed.
% 0.31/1.35 % (28656)Instruction limit reached!
% 0.31/1.35 % (28656)------------------------------
% 0.31/1.35 % (28656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (28656)Termination reason: Unknown
% 0.31/1.35 % (28656)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (28656)Memory used [KB]: 5756
% 0.31/1.35 % (28656)Time elapsed: 0.013 s
% 0.31/1.35 % (28656)Instructions burned: 39 (million)
% 0.31/1.35 % (28656)------------------------------
% 0.31/1.35 % (28656)------------------------------
% 0.31/1.35 % (28659)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_28360 for (2999ds/1041Mi)
% 0.31/1.35 % (28648)Also succeeded, but the first one will report.
% 0.31/1.35 % (28650)Refutation found. Thanks to Tanya!
% 0.31/1.35 % SZS status Theorem for DTF2THF_28360
% 0.31/1.35 % SZS output start Proof for DTF2THF_28360
% 0.31/1.35 thf(type_def_5, type, mworld: $tType).
% 0.31/1.35 thf(func_def_0, type, mworld: $tType).
% 0.31/1.35 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.31/1.35 thf(func_def_2, type, mactual: mworld).
% 0.31/1.35 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.31/1.35 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 0.31/1.35 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.35 thf(func_def_15, type, intersect: $i > $i > mworld > $o).
% 0.31/1.35 thf(func_def_16, type, member: $i > $i > mworld > $o).
% 0.31/1.35 thf(func_def_17, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.31/1.35 thf(func_def_31, type, sK0: mworld > $i).
% 0.31/1.35 thf(func_def_38, type, sK5: $i > $i > $i).
% 0.31/1.35 thf(f187,plain,(
% 0.31/1.35 $false),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f186])).
% 0.31/1.35 thf(f186,plain,(
% 0.31/1.35 ($true = $false)),
% 0.31/1.35 inference(backward_demodulation,[status(thm)],[f89,f183])).
% 0.31/1.35 thf(f183,plain,(
% 0.31/1.35 ((member @ sK2 @ sK3 @ mactual) = $false)),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 0.31/1.35 thf(f182,plain,(
% 0.31/1.35 ($true = $false) | ((member @ sK2 @ sK3 @ mactual) = $false)),
% 0.31/1.35 inference(forward_demodulation,[status(thm)],[f169,f78])).
% 0.31/1.35 thf(f78,plain,(
% 0.31/1.35 ((eiw_di @ sK2 @ mactual) = $true)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.31/1.35 thf(f76,plain,(
% 0.31/1.35 (((eiw_di @ sK2 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((member @ sK2 @ Y1 @ mactual) & (member @ sK2 @ Y0 @ mactual)) => (intersect @ Y0 @ Y1 @ mactual))))))))) = $false)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f75])).
% 0.31/1.35 thf(f75,plain,(
% 0.31/1.35 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => (((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual)) => (intersect @ Y1 @ Y2 @ mactual)))))))))) @ sK2) = $false)),
% 0.31/1.35 inference(sigma_clausification,[status(thm)],[f74])).
% 0.31/1.35 thf(f74,plain,(
% 0.31/1.35 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) => (((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual)) => (intersect @ Y1 @ Y2 @ mactual))))))))))) != $true)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f71])).
% 0.31/1.35 thf(f71,plain,(
% 0.31/1.35 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $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))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)) @ (intersect @ Y1 @ Y2))))))))) != $true)),
% 0.31/1.35 inference(definition_unfolding,[status(thm)],[f56,f70,f69,f69,f69,f58,f55])).
% 0.31/1.35 thf(f55,plain,(
% 0.31/1.35 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f42])).
% 0.31/1.35 thf(f42,plain,(
% 0.31/1.35 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f41])).
% 0.31/1.35 thf(f41,plain,(
% 0.31/1.35 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 0.31/1.35 inference(rectify,[status(thm)],[f3])).
% 0.31/1.35 thf(f3,axiom,(
% 0.31/1.35 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mand_def)).
% 0.31/1.35 thf(f58,plain,(
% 0.31/1.35 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.35 thf(f30,plain,(
% 0.31/1.35 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f29])).
% 0.31/1.35 thf(f29,plain,(
% 0.31/1.35 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f5])).
% 0.31/1.35 thf(f5,axiom,(
% 0.31/1.35 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mimplies_def)).
% 0.31/1.35 thf(f69,plain,(
% 0.31/1.35 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f24])).
% 0.31/1.35 thf(f24,plain,(
% 0.31/1.35 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f23])).
% 0.31/1.35 thf(f23,plain,(
% 0.31/1.35 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f12])).
% 0.31/1.35 thf(f12,axiom,(
% 0.31/1.35 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mforall_di_def)).
% 0.31/1.35 thf(f70,plain,(
% 0.31/1.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f43])).
% 0.31/1.35 thf(f43,plain,(
% 0.31/1.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f1])).
% 0.31/1.35 thf(f1,axiom,(
% 0.31/1.35 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mlocal_def)).
% 0.31/1.35 thf(f56,plain,(
% 0.31/1.35 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)) @ (intersect @ Y1 @ Y2))))))))) != $true)),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f50])).
% 0.31/1.35 thf(f50,plain,(
% 0.31/1.35 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)) @ (intersect @ Y1 @ Y2))))))))) != $true)),
% 0.31/1.35 inference(flattening,[status(thm)],[f40])).
% 0.31/1.35 thf(f40,plain,(
% 0.31/1.35 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)) @ (intersect @ Y1 @ Y2))))))))) = $true)),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f39])).
% 0.31/1.35 thf(f39,plain,(
% 0.31/1.35 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mimplies @ (mand @ (member @ X0 @ X1) @ (member @ X0 @ X2)) @ (intersect @ X1 @ X2)))))))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f17])).
% 0.31/1.35 thf(f17,negated_conjecture,(
% 0.31/1.35 ~(mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X7 : $i] : (mimplies @ (mand @ (member @ X3 @ X6) @ (member @ X3 @ X7)) @ (intersect @ X6 @ X7)))))))))),
% 0.31/1.35 inference(negated_conjecture,[status(cth)],[f16])).
% 0.31/1.35 thf(f16,conjecture,(
% 0.31/1.35 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X7 : $i] : (mimplies @ (mand @ (member @ X3 @ X6) @ (member @ X3 @ X7)) @ (intersect @ X6 @ X7)))))))))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',prove_th13)).
% 0.31/1.35 thf(f169,plain,(
% 0.31/1.35 ((eiw_di @ sK2 @ mactual) = $false) | ((member @ sK2 @ sK3 @ mactual) = $false)),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 0.31/1.35 thf(f165,plain,(
% 0.31/1.35 ($true = $false) | ((member @ sK2 @ sK3 @ mactual) = $false) | ((eiw_di @ sK2 @ mactual) = $false)),
% 0.31/1.35 inference(superposition,[status(thm)],[f90,f137])).
% 0.31/1.35 thf(f137,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((member @ X0 @ sK4 @ mactual) = $false) | ((eiw_di @ X0 @ mactual) = $false) | ((member @ X0 @ sK3 @ mactual) = $false)) )),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 0.31/1.35 thf(f136,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((eiw_di @ X0 @ mactual) = $false) | ($true = $false) | ((member @ X0 @ sK3 @ mactual) = $false) | ((member @ X0 @ sK4 @ mactual) = $false)) )),
% 0.31/1.35 inference(forward_demodulation,[status(thm)],[f135,f82])).
% 0.31/1.35 thf(f82,plain,(
% 0.31/1.35 ($true = (eiw_di @ sK3 @ mactual))),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 0.31/1.35 thf(f80,plain,(
% 0.31/1.35 (((eiw_di @ sK3 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((member @ sK2 @ Y0 @ mactual) & (member @ sK2 @ sK3 @ mactual)) => (intersect @ sK3 @ Y0 @ mactual)))))) = $false)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f79])).
% 0.31/1.35 thf(f79,plain,(
% 0.31/1.35 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((member @ sK2 @ Y1 @ mactual) & (member @ sK2 @ Y0 @ mactual)) => (intersect @ Y0 @ Y1 @ mactual))))))) @ sK3) = $false)),
% 0.31/1.35 inference(sigma_clausification,[status(thm)],[f77])).
% 0.31/1.35 thf(f77,plain,(
% 0.31/1.35 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((member @ sK2 @ Y1 @ mactual) & (member @ sK2 @ Y0 @ mactual)) => (intersect @ Y0 @ Y1 @ mactual)))))))) = $false)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.31/1.35 thf(f135,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((member @ X0 @ sK3 @ mactual) = $false) | ((member @ X0 @ sK4 @ mactual) = $false) | ((eiw_di @ sK3 @ mactual) = $false) | ((eiw_di @ X0 @ mactual) = $false)) )),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 0.31/1.35 thf(f134,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((member @ X0 @ sK3 @ mactual) = $false) | ((member @ X0 @ sK4 @ mactual) = $false) | ((eiw_di @ X0 @ mactual) = $false) | ($true = $false) | ((eiw_di @ sK3 @ mactual) = $false)) )),
% 0.31/1.35 inference(forward_demodulation,[status(thm)],[f128,f86])).
% 0.31/1.35 thf(f86,plain,(
% 0.31/1.35 ($true = (eiw_di @ sK4 @ mactual))),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 0.31/1.35 thf(f84,plain,(
% 0.31/1.35 (((eiw_di @ sK4 @ mactual) => (((member @ sK2 @ sK4 @ mactual) & (member @ sK2 @ sK3 @ mactual)) => (intersect @ sK3 @ sK4 @ mactual))) = $false)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f83])).
% 0.31/1.35 thf(f83,plain,(
% 0.31/1.35 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((member @ sK2 @ Y0 @ mactual) & (member @ sK2 @ sK3 @ mactual)) => (intersect @ sK3 @ Y0 @ mactual)))) @ sK4) = $false)),
% 0.31/1.35 inference(sigma_clausification,[status(thm)],[f81])).
% 0.31/1.35 thf(f81,plain,(
% 0.31/1.35 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((member @ sK2 @ Y0 @ mactual) & (member @ sK2 @ sK3 @ mactual)) => (intersect @ sK3 @ Y0 @ mactual))))) = $false)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 0.31/1.35 thf(f128,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((eiw_di @ X0 @ mactual) = $false) | ((member @ X0 @ sK4 @ mactual) = $false) | ((eiw_di @ sK4 @ mactual) = $false) | ((member @ X0 @ sK3 @ mactual) = $false) | ((eiw_di @ sK3 @ mactual) = $false)) )),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 0.31/1.35 thf(f124,plain,(
% 0.31/1.35 ( ! [X0 : $i] : (((member @ X0 @ sK3 @ mactual) = $false) | ((member @ X0 @ sK4 @ mactual) = $false) | ((eiw_di @ sK3 @ mactual) = $false) | ((eiw_di @ sK4 @ mactual) = $false) | ($true = $false) | ((eiw_di @ X0 @ mactual) = $false)) )),
% 0.31/1.35 inference(superposition,[status(thm)],[f112,f87])).
% 0.31/1.35 thf(f87,plain,(
% 0.31/1.35 ((intersect @ sK3 @ sK4 @ mactual) = $false)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 0.31/1.35 thf(f85,plain,(
% 0.31/1.35 ((((member @ sK2 @ sK4 @ mactual) & (member @ sK2 @ sK3 @ mactual)) => (intersect @ sK3 @ sK4 @ mactual)) = $false)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 0.31/1.35 thf(f112,plain,(
% 0.31/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (intersect @ X1 @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false) | ((member @ X3 @ X2 @ mactual) = $false) | ((eiw_di @ X3 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false) | ((member @ X3 @ X1 @ mactual) = $false)) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 0.31/1.35 thf(f111,plain,(
% 0.31/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((eiw_di @ X3 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false) | (((member @ X3 @ X2 @ mactual) & (member @ X3 @ X1 @ mactual)) = $false) | ($true = (intersect @ X1 @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 0.31/1.35 thf(f110,plain,(
% 0.31/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | (((eiw_di @ X3 @ mactual) & ((member @ X3 @ X2 @ mactual) & (member @ X3 @ X1 @ mactual))) = $false) | ($true = (intersect @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f109])).
% 0.31/1.35 thf(f109,plain,(
% 0.31/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & ((member @ Y0 @ X2 @ mactual) & (member @ Y0 @ X1 @ mactual)))) @ X3) = $false) | ($true = (intersect @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.35 inference(pi_clausification,[status(thm)],[f108])).
% 0.31/1.35 thf(f108,plain,(
% 0.31/1.35 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & ((member @ Y0 @ X2 @ mactual) & (member @ Y0 @ X1 @ mactual))))) = $false) | ($true = (intersect @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 0.31/1.35 thf(f106,plain,(
% 0.31/1.35 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & ((member @ Y0 @ X2 @ mactual) & (member @ Y0 @ X1 @ mactual))))) = (intersect @ X1 @ X2 @ mactual))) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 0.31/1.35 thf(f105,plain,(
% 0.31/1.35 ( ! [X2 : $i,X1 : $i] : (($true = ((intersect @ X1 @ X2 @ mactual) = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & ((member @ Y0 @ X2 @ mactual) & (member @ Y0 @ X1 @ mactual))))))) | ((eiw_di @ X1 @ mactual) = $false) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 0.31/1.35 thf(f104,plain,(
% 0.31/1.35 ( ! [X2 : $i,X1 : $i] : ((((eiw_di @ X2 @ mactual) => ((intersect @ X1 @ X2 @ mactual) = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & ((member @ Y0 @ X2 @ mactual) & (member @ Y0 @ X1 @ mactual))))))) = $true) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f103])).
% 0.31/1.35 thf(f103,plain,(
% 0.31/1.35 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((intersect @ X1 @ Y0 @ mactual) = (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) & ((member @ Y1 @ Y0 @ mactual) & (member @ Y1 @ X1 @ mactual)))))))) @ X2))) )),
% 0.31/1.35 inference(pi_clausification,[status(thm)],[f102])).
% 0.31/1.35 thf(f102,plain,(
% 0.31/1.35 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((intersect @ X1 @ Y0 @ mactual) = (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) & ((member @ Y1 @ Y0 @ mactual) & (member @ Y1 @ X1 @ mactual))))))))) = $true)) )),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 0.31/1.35 thf(f101,plain,(
% 0.31/1.35 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((intersect @ X1 @ Y0 @ mactual) = (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) & ((member @ Y1 @ Y0 @ mactual) & (member @ Y1 @ X1 @ mactual)))))))))))) )),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f100])).
% 0.31/1.35 thf(f100,plain,(
% 0.31/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((intersect @ Y0 @ Y1 @ mactual) = (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) & ((member @ Y2 @ Y1 @ mactual) & (member @ Y2 @ Y0 @ mactual))))))))))) @ X1) = $true)) )),
% 0.31/1.35 inference(pi_clausification,[status(thm)],[f99])).
% 0.31/1.35 thf(f99,plain,(
% 0.31/1.35 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((intersect @ Y0 @ Y1 @ mactual) = (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ mactual) & ((member @ Y2 @ Y1 @ mactual) & (member @ Y2 @ Y0 @ mactual)))))))))))) = $true)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f73])).
% 0.31/1.35 thf(f73,plain,(
% 0.31/1.35 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (intersect @ Y0 @ Y1) @ ((^[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]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 0.31/1.35 inference(definition_unfolding,[status(thm)],[f65,f70,f69,f69,f67,f64,f55])).
% 0.31/1.35 thf(f64,plain,(
% 0.31/1.35 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f20])).
% 0.31/1.35 thf(f20,plain,(
% 0.31/1.35 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f19])).
% 0.31/1.35 thf(f19,plain,(
% 0.31/1.35 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f13])).
% 0.31/1.35 thf(f13,axiom,(
% 0.31/1.35 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : ((X1 @ X5 @ X2) & (eiw_di @ X5 @ X2)))))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mexists_di_def)).
% 0.31/1.35 thf(f67,plain,(
% 0.31/1.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f26])).
% 0.31/1.35 thf(f26,plain,(
% 0.31/1.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f25])).
% 0.31/1.35 thf(f25,plain,(
% 0.31/1.35 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 0.31/1.35 inference(rectify,[status(thm)],[f6])).
% 0.31/1.35 thf(f6,axiom,(
% 0.31/1.35 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))) = mequiv)),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',mequiv_def)).
% 0.31/1.35 thf(f65,plain,(
% 0.31/1.35 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (intersect @ Y0 @ Y1) @ (mexists_di @ (^[Y2 : $i]: (mand @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f38])).
% 0.31/1.35 thf(f38,plain,(
% 0.31/1.35 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (intersect @ Y0 @ Y1) @ (mexists_di @ (^[Y2 : $i]: (mand @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f37])).
% 0.31/1.35 thf(f37,plain,(
% 0.31/1.35 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (intersect @ X0 @ X1) @ (mexists_di @ (^[X2 : $i] : (mand @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f14])).
% 0.31/1.35 thf(f14,axiom,(
% 0.31/1.35 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (intersect @ X3 @ X6) @ (mexists_di @ (^[X7 : $i] : (mand @ (member @ X7 @ X3) @ (member @ X7 @ X6))))))))))),
% 0.31/1.35 file('/export/starexec/sandbox2/tmp/tmp.XnWc0R4icq/DTF2THF_28360.p',intersect_defn)).
% 0.31/1.35 thf(f90,plain,(
% 0.31/1.35 ($true = (member @ sK2 @ sK4 @ mactual))),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 0.31/1.35 thf(f88,plain,(
% 0.31/1.35 (((member @ sK2 @ sK4 @ mactual) & (member @ sK2 @ sK3 @ mactual)) = $true)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 0.31/1.35 thf(f89,plain,(
% 0.31/1.35 ((member @ sK2 @ sK3 @ mactual) = $true)),
% 0.31/1.35 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 0.31/1.35 % SZS output end Proof for DTF2THF_28360
% 0.31/1.35 % (28650)------------------------------
% 0.31/1.35 % (28650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (28650)Termination reason: Refutation
% 0.31/1.35
% 0.31/1.35 % (28650)Memory used [KB]: 5756
% 0.31/1.35 % (28650)Time elapsed: 0.018 s
% 0.31/1.35 % (28650)Instructions burned: 25 (million)
% 0.31/1.35 % (28650)------------------------------
% 0.31/1.35 % (28650)------------------------------
% 0.31/1.35 % (28647)Success in time 0.031 s
%------------------------------------------------------------------------------