%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET027^3 : 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 : n017.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 09:31:00 AM UTC 2026
% Result : Theorem 1.69s 1.30s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 476 ( 107 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 716 ( 7 ~; 35 |; 13 &; 605 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 7 con; 0-3 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 201 ( 145 ^; 56 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
member: $i > $i > mworld > $o ).
thf(func_def_15,type,
subset: $i > $i > mworld > $o ).
thf(func_def_16,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_30,type,
sK0: mworld > mworld ).
thf(func_def_34,type,
sK2: $i > $i > $i ).
thf(f155,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f88,f142]) ).
thf(f142,plain,
( $false
= ( subset @ sK4 @ sK5 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $false
= ( subset @ sK4 @ sK5 @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f132,f89]) ).
thf(f89,plain,
( ( subset @ sK3 @ sK4 @ mactual )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( subset @ sK3 @ sK4 @ mactual )
& ( subset @ sK4 @ sK5 @ mactual ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( ( subset @ sK3 @ sK4 @ mactual )
& ( subset @ sK4 @ sK5 @ mactual ) )
=> ( subset @ sK3 @ sK5 @ mactual ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( subset @ sK3 @ sK4 @ mactual )
& ( subset @ sK4 @ Y0 @ mactual ) )
=> ( subset @ sK3 @ Y0 @ mactual ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ sK3 @ sK4 @ mactual )
& ( subset @ sK4 @ Y0 @ mactual ) )
=> ( subset @ sK3 @ Y0 @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ sK3 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
=> ( subset @ sK3 @ Y1 @ mactual ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ sK3 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) )
=> ( subset @ sK3 @ Y1 @ mactual ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y2 @ mactual ) )
=> ( subset @ Y0 @ Y2 @ mactual ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y2 @ mactual ) )
=> ( subset @ Y0 @ Y2 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f53,f51,f55,f55,f55,f49,f54]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mand_def) ).
thf(f49,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,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.CoCRwbaNh1/DTF2THF_12929.p',mimplies_def) ).
thf(f55,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mforall_di_def) ).
thf(f51,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,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.CoCRwbaNh1/DTF2THF_12929.p',mlocal_def) ).
thf(f53,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( subset @ X3 @ X6 ) @ ( subset @ X6 @ X7 ) ) @ ( subset @ X3 @ X7 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f14,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X7: $i] : ( mimplies @ ( mand @ ( subset @ X3 @ X6 ) @ ( subset @ X6 @ X7 ) ) @ ( subset @ X3 @ X7 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',prove_transitivity_of_subset) ).
thf(f132,plain,
! [X0: $i] :
( ( $false
= ( subset @ sK3 @ X0 @ mactual ) )
| ( ( subset @ X0 @ sK5 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK5 @ mactual )
= $false )
| ( $false
= ( subset @ sK3 @ X0 @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f123,f86]) ).
thf(f86,plain,
( ( subset @ sK3 @ sK5 @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f123,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false )
| ( ( subset @ X2 @ X1 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 @ mactual )
= $false )
| ( $true = $false )
| ( ( subset @ X0 @ X2 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X2 @ X1 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X0 @ X2 @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f112,f75]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( member @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual ) )
| ( $true
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 @ mactual ) )
| ( ( ( member @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual )
=> ( member @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 @ mactual ) )
| ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 @ mactual ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) )
= ( subset @ X1 @ X2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f56,f51,f55,f55,f48,f55,f49]) ).
thf(f48,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,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.CoCRwbaNh1/DTF2THF_12929.p',mequiv_def) ).
thf(f56,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X6: $i] :
( mequiv @ ( subset @ X3 @ X6 )
@ ( mforall_di
@ ^ [X7: $i] : ( mimplies @ ( member @ X7 @ X3 ) @ ( member @ X7 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',subset_defn) ).
thf(f112,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( member @ ( sK2 @ X0 @ X1 ) @ X3 @ mactual ) )
| ( ( subset @ X2 @ X1 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X3 @ X2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( member @ ( sK2 @ X0 @ X1 ) @ X3 @ mactual ) )
| ( ( subset @ X2 @ X1 @ mactual )
= $false )
| ( $true = $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X3 @ X2 @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f96,f78]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( member @ X3 @ X2 @ mactual ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) )
| ( $false
= ( member @ X3 @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( member @ X3 @ X1 @ mactual )
=> ( member @ X3 @ X2 @ mactual ) ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( subset @ X1 @ X2 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f96,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( member @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) )
| ( ( subset @ X2 @ X1 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( member @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true = $false )
| ( ( subset @ X2 @ X1 @ mactual )
= $false )
| ( $true
= ( subset @ X0 @ X1 @ mactual ) ) ),
inference(superposition,[status(thm)],[f78,f74]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( ( member @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual )
= $false )
| ( $true
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f88,plain,
( $true
= ( subset @ sK4 @ sK5 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET027^3 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n017.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:48:26 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SET027^3 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : TPTP problem SET027+1.p with axiomatized equality
% 0.30/0.45 % Version : [BP13] axioms.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.45 % Source : [TPTP]
% 0.30/0.45 % Names : SET027+1 [QMLTP]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.30/0.45 % Syntax : Number of formulae : 29 ( 11 unt; 15 typ; 10 def)
% 0.30/0.45 % Number of atoms : 44 ( 10 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 9 ( 3 avg)
% 0.30/0.45 % Number of connectives : 61 ( 1 ~; 1 |; 2 &; 54 @)
% 0.30/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 14 ( 3 avg)
% 0.30/0.45 % Number of types : 3 ( 1 usr)
% 0.30/0.45 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 36 ( 30 ^; 3 !; 3 ?; 36 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.45 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.30/0.45 % $modalities == $modal_system_D].
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(mworld,type,
% 0.30/0.45 mworld: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(mrel_type,type,
% 0.30/0.45 mrel: mworld > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mactual_type,type,
% 0.30/0.45 mactual: mworld ).
% 0.30/0.45
% 0.30/0.45 thf(mlocal_type,type,
% 0.30/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mlocal_def,definition,
% 0.30/0.45 ( mlocal
% 0.30/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mnot_type,type,
% 0.30/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mand_type,type,
% 0.30/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mor_type,type,
% 0.30/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mimplies_type,type,
% 0.30/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mequiv_type,type,
% 0.30/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mnot_def,definition,
% 0.30/0.45 ( mnot
% 0.30/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.45 ~ ( A @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mand_def,definition,
% 0.30/0.45 ( mand
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 & ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mor_def,definition,
% 0.30/0.45 ( mor
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 | ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mimplies_def,definition,
% 0.30/0.45 ( mimplies
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 => ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mequiv_def,definition,
% 0.30/0.45 ( mequiv
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 <=> ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mbox_type,type,
% 0.30/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mbox_def,definition,
% 0.30/0.45 ( mbox
% 0.30/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.45 ! [V: mworld] :
% 0.30/0.45 ( ( mrel @ W @ V )
% 0.30/0.45 => ( Phi @ V ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mdia_type,type,
% 0.30/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mdia_def,definition,
% 0.30/0.45 ( mdia
% 0.30/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.45 ? [V: mworld] :
% 0.30/0.45 ( ( mrel @ W @ V )
% 0.30/0.45 & ( Phi @ V ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mrel_serial,axiom,
% 0.30/0.45 ! [W: mworld] :
% 0.30/0.45 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.30/0.45
% 0.30/0.45 thf(mforall_di_type,type,
% 0.30/0.45 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mforall_di_def,definition,
% 0.30/0.45 ( mforall_di
% 0.30/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.45 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mexists_di_type,type,
% 0.30/0.45 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mexists_di_def,definition,
% 0.30/0.45 ( mexists_di
% 0.30/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.45 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(member_decl,type,
% 0.30/0.45 member: $i > $i > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(subset_decl,type,
% 0.30/0.45 subset: $i > $i > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(subset_defn,axiom,
% 0.30/0.45 ( mlocal
% 0.30/0.45 @ ( mforall_di
% 0.30/0.45 @ ^ [B: $i] :
% 0.30/0.45 ( mforall_di
% 0.30/0.45 @ ^ [C: $i] :
% 0.30/0.45 ( mequiv @ ( subset @ B @ C )
% 0.30/0.45 @ ( mforall_di
% 0.30/0.45 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reflexivity_of_subset,axiom,
% 0.30/0.45 ( mlocal
% 0.30/0.45 @ ( mforall_di
% 0.30/0.45 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(prove_transitivity_of_subset,conjecture,
% 0.30/0.45 ( mlocal
% 0.30/0.45 @ ( mforall_di
% 0.30/0.45 @ ^ [B: $i] :
% 0.30/0.45 ( mforall_di
% 0.30/0.45 @ ^ [C: $i] :
% 0.30/0.45 ( mforall_di
% 0.30/0.45 @ ^ [D: $i] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.53/1.26 ---- Embedded in THF ---
% 1.53/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.27 %%% Generated on Tue Feb 24 11:48:26 EST 2026
% 1.53/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.27 %%% Logic specification used:
% 1.53/1.27 %%% thf(spec, logic, $$dhol).
% 1.53/1.27
% 1.53/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2DTF12929.p
% See solution above
% 1.53/1.27 ------------------------
% 1.53/1.28 ---- Cleaned THF ---
% 1.53/1.28 thf(mworld,type,
% 1.53/1.28 mworld: $tType ).
% 1.53/1.28
% 1.53/1.28 thf(mrel_type,type,
% 1.53/1.28 mrel: mworld > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mactual_type,type,
% 1.53/1.28 mactual: mworld ).
% 1.53/1.28
% 1.53/1.28 thf(mlocal_type,type,
% 1.53/1.28 mlocal: ( mworld > $o ) > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mlocal_def,definition,
% 1.53/1.28 ( mlocal
% 1.53/1.28 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mnot_type,type,
% 1.53/1.28 mnot: ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mand_type,type,
% 1.53/1.28 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mor_type,type,
% 1.53/1.28 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mimplies_type,type,
% 1.53/1.28 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mequiv_type,type,
% 1.53/1.28 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mnot_def,definition,
% 1.53/1.28 ( mnot
% 1.53/1.28 = ( ^ [A: mworld > $o,W: mworld] :
% 1.53/1.28 ~ ( A @ W ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mand_def,definition,
% 1.53/1.28 ( mand
% 1.53/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.53/1.28 ( ( A @ W )
% 1.53/1.28 & ( B @ W ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mor_def,definition,
% 1.53/1.28 ( mor
% 1.53/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.53/1.28 ( ( A @ W )
% 1.53/1.28 | ( B @ W ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mimplies_def,definition,
% 1.53/1.28 ( mimplies
% 1.53/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.53/1.28 ( ( A @ W )
% 1.53/1.28 => ( B @ W ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mequiv_def,definition,
% 1.53/1.28 ( mequiv
% 1.53/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.53/1.28 ( ( A @ W )
% 1.53/1.28 <=> ( B @ W ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mbox_type,type,
% 1.53/1.28 mbox: ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mbox_def,definition,
% 1.53/1.28 ( mbox
% 1.53/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.53/1.28 ! [V: mworld] :
% 1.53/1.28 ( ( mrel @ W @ V )
% 1.53/1.28 => ( Phi @ V ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mdia_type,type,
% 1.53/1.28 mdia: ( mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mdia_def,definition,
% 1.53/1.28 ( mdia
% 1.53/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.53/1.28 ? [V: mworld] :
% 1.53/1.28 ( ( mrel @ W @ V )
% 1.53/1.28 & ( Phi @ V ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mrel_serial,axiom,
% 1.53/1.28 ! [W: mworld] :
% 1.53/1.28 ? [V: mworld] : ( mrel @ W @ V ) ).
% 1.53/1.28
% 1.53/1.28 thf(mforall_di_type,type,
% 1.53/1.28 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mforall_di_def,definition,
% 1.53/1.28 ( mforall_di
% 1.53/1.28 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.53/1.28 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(mexists_di_type,type,
% 1.53/1.28 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(mexists_di_def,definition,
% 1.53/1.28 ( mexists_di
% 1.53/1.28 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.53/1.28 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(member_decl,type,
% 1.53/1.28 member: $i > $i > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(subset_decl,type,
% 1.53/1.28 subset: $i > $i > mworld > $o ).
% 1.53/1.28
% 1.53/1.28 thf(subset_defn,axiom,
% 1.53/1.28 ( mlocal
% 1.53/1.28 @ ( mforall_di
% 1.53/1.28 @ ^ [B: $i] :
% 1.53/1.28 ( mforall_di
% 1.53/1.28 @ ^ [C: $i] :
% 1.53/1.28 ( mequiv @ ( subset @ B @ C )
% 1.53/1.28 @ ( mforall_di
% 1.53/1.28 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(reflexivity_of_subset,axiom,
% 1.53/1.28 ( mlocal
% 1.53/1.28 @ ( mforall_di
% 1.53/1.28 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 1.53/1.28
% 1.53/1.28 thf(prove_transitivity_of_subset,conjecture,
% 1.53/1.28 ( mlocal
% 1.53/1.28 @ ( mforall_di
% 1.53/1.28 @ ^ [B: $i] :
% 1.53/1.28 ( mforall_di
% 1.53/1.28 @ ^ [C: $i] :
% 1.53/1.28 ( mforall_di
% 1.53/1.28 @ ^ [D: $i] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ) ).
% 1.53/1.28 ------------------------
% 1.53/1.29 % (13234)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_12929 for (2999ds/2Mi)
% 1.53/1.29 % (13232)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_12929 for (2999ds/27Mi)
% 1.53/1.30 % (13234)Instruction limit reached!
% 1.53/1.30 % (13234)------------------------------
% 1.53/1.30 % (13234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (13234)Termination reason: Unknown
% 1.53/1.30 % (13234)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (13234)Memory used [KB]: 1023
% 1.53/1.30 % (13234)Time elapsed: 0.003 s
% 1.53/1.30 % (13234)Instructions burned: 4 (million)
% 1.53/1.30 % (13234)------------------------------
% 1.53/1.30 % (13234)------------------------------
% 1.69/1.30 % (13231)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_12929 for (2999ds/4Mi)
% 1.69/1.30 % (13230)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12929 for (2999ds/183Mi)
% 1.69/1.30 % (13233)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12929 for (2999ds/2Mi)
% 1.69/1.30 % (13235)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_12929 for (2999ds/275Mi)
% 1.69/1.30 % (13236)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12929 for (2999ds/18Mi)
% 1.69/1.30 % (13233)Instruction limit reached!
% 1.69/1.30 % (13233)------------------------------
% 1.69/1.30 % (13233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (13233)Termination reason: Unknown
% 1.69/1.30 % (13233)Termination phase: shuffling
% 1.69/1.30
% 1.69/1.30 % (13233)Memory used [KB]: 1023
% 1.69/1.30 % (13233)Time elapsed: 0.003 s
% 1.69/1.30 % (13233)Instructions burned: 2 (million)
% 1.69/1.30 % (13233)------------------------------
% 1.69/1.30 % (13233)------------------------------
% 1.69/1.30 % (13232)First to succeed.
% 1.69/1.30 % (13231)Instruction limit reached!
% 1.69/1.30 % (13231)------------------------------
% 1.69/1.30 % (13231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (13231)Termination reason: Unknown
% 1.69/1.30 % (13231)Termination phase: Property scanning
% 1.69/1.30
% 1.69/1.30 % (13231)Memory used [KB]: 1023
% 1.69/1.30 % (13231)Time elapsed: 0.004 s
% 1.69/1.30 % (13231)Instructions burned: 4 (million)
% 1.69/1.30 % (13231)------------------------------
% 1.69/1.30 % (13231)------------------------------
% 1.69/1.30 % (13235)Refutation not found, incomplete strategy
% 1.69/1.30 % (13235)------------------------------
% 1.69/1.30 % (13235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (13235)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.30
% 1.69/1.30
% 1.69/1.30 % (13235)Memory used [KB]: 5500
% 1.69/1.30 % (13235)Time elapsed: 0.004 s
% 1.69/1.30 % (13235)Instructions burned: 3 (million)
% 1.69/1.30 % (13235)------------------------------
% 1.69/1.30 % (13235)------------------------------
% 1.69/1.30 % (13232)Refutation found. Thanks to Tanya!
% 1.69/1.30 % SZS status Theorem for DTF2THF_12929
% 1.69/1.30 % SZS output start Proof for DTF2THF_12929
% 1.69/1.30 thf(type_def_5, type, mworld: $tType).
% 1.69/1.30 thf(func_def_0, type, mworld: $tType).
% 1.69/1.30 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.69/1.30 thf(func_def_2, type, mactual: mworld).
% 1.69/1.30 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.69/1.30 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.69/1.30 thf(func_def_14, type, member: $i > $i > mworld > $o).
% 1.69/1.30 thf(func_def_15, type, subset: $i > $i > mworld > $o).
% 1.69/1.30 thf(func_def_16, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.69/1.30 thf(func_def_30, type, sK0: mworld > mworld).
% 1.69/1.30 thf(func_def_34, type, sK2: $i > $i > $i).
% 1.69/1.30 thf(f155,plain,(
% 1.69/1.30 $false),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.69/1.30 thf(f149,plain,(
% 1.69/1.30 ($true = $false)),
% 1.69/1.30 inference(backward_demodulation,[status(thm)],[f88,f142])).
% 1.69/1.30 thf(f142,plain,(
% 1.69/1.30 ($false = (subset @ sK4 @ sK5 @ mactual))),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.69/1.30 thf(f137,plain,(
% 1.69/1.30 ($false = (subset @ sK4 @ sK5 @ mactual)) | ($true = $false)),
% 1.69/1.30 inference(superposition,[status(thm)],[f132,f89])).
% 1.69/1.30 thf(f89,plain,(
% 1.69/1.30 ((subset @ sK3 @ sK4 @ mactual) = $true)),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.69/1.30 thf(f87,plain,(
% 1.69/1.30 (((subset @ sK3 @ sK4 @ mactual) & (subset @ sK4 @ sK5 @ mactual)) = $true)),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.69/1.30 thf(f85,plain,(
% 1.69/1.30 ((((subset @ sK3 @ sK4 @ mactual) & (subset @ sK4 @ sK5 @ mactual)) => (subset @ sK3 @ sK5 @ mactual)) = $false)),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.69/1.30 thf(f84,plain,(
% 1.69/1.30 ($false = ((^[Y0 : $i]: (((subset @ sK3 @ sK4 @ mactual) & (subset @ sK4 @ Y0 @ mactual)) => (subset @ sK3 @ Y0 @ mactual))) @ sK5))),
% 1.69/1.30 inference(sigma_clausification,[status(thm)],[f83])).
% 1.69/1.30 thf(f83,plain,(
% 1.69/1.30 ((!! @ $i @ (^[Y0 : $i]: (((subset @ sK3 @ sK4 @ mactual) & (subset @ sK4 @ Y0 @ mactual)) => (subset @ sK3 @ Y0 @ mactual)))) = $false)),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.69/1.30 thf(f82,plain,(
% 1.69/1.30 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ sK3 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)) => (subset @ sK3 @ Y1 @ mactual))))) @ sK4) = $false)),
% 1.69/1.30 inference(sigma_clausification,[status(thm)],[f81])).
% 1.69/1.30 thf(f81,plain,(
% 1.69/1.30 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ sK3 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)) => (subset @ sK3 @ Y1 @ mactual)))))) = $false)),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.69/1.30 thf(f80,plain,(
% 1.69/1.30 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y2 @ mactual)) => (subset @ Y0 @ Y2 @ mactual))))))) @ sK3) = $false)),
% 1.69/1.30 inference(sigma_clausification,[status(thm)],[f79])).
% 1.69/1.30 thf(f79,plain,(
% 1.69/1.30 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y2 @ mactual)) => (subset @ Y0 @ Y2 @ mactual)))))))))),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.69/1.30 thf(f61,plain,(
% 1.69/1.30 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) & (Y4 @ Y5))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))) != $true)),
% 1.69/1.30 inference(definition_unfolding,[status(thm)],[f53,f51,f55,f55,f55,f49,f54])).
% 1.69/1.30 thf(f54,plain,(
% 1.69/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f31])).
% 1.69/1.30 thf(f31,plain,(
% 1.69/1.30 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f30])).
% 1.69/1.30 thf(f30,plain,(
% 1.69/1.30 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.69/1.30 inference(rectify,[status(thm)],[f3])).
% 1.69/1.30 thf(f3,axiom,(
% 1.69/1.30 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mand_def)).
% 1.69/1.30 thf(f49,plain,(
% 1.69/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f18])).
% 1.69/1.30 thf(f18,plain,(
% 1.69/1.30 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f17])).
% 1.69/1.30 thf(f17,plain,(
% 1.69/1.30 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f5])).
% 1.69/1.30 thf(f5,axiom,(
% 1.69/1.30 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mimplies_def)).
% 1.69/1.30 thf(f55,plain,(
% 1.69/1.30 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f41])).
% 1.69/1.30 thf(f41,plain,(
% 1.69/1.30 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f40])).
% 1.69/1.30 thf(f40,plain,(
% 1.69/1.30 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f10])).
% 1.69/1.30 thf(f10,axiom,(
% 1.69/1.30 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mforall_di_def)).
% 1.69/1.30 thf(f51,plain,(
% 1.69/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f25])).
% 1.69/1.30 thf(f25,plain,(
% 1.69/1.30 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f1])).
% 1.69/1.30 thf(f1,axiom,(
% 1.69/1.30 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mlocal_def)).
% 1.69/1.30 thf(f53,plain,(
% 1.69/1.30 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f44])).
% 1.69/1.30 thf(f44,plain,(
% 1.69/1.30 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 1.69/1.30 inference(flattening,[status(thm)],[f22])).
% 1.69/1.30 thf(f22,plain,(
% 1.69/1.30 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y2)) @ (subset @ Y0 @ Y2))))))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f21])).
% 1.69/1.30 thf(f21,plain,(
% 1.69/1.30 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mimplies @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X2)) @ (subset @ X0 @ X2)))))))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f15])).
% 1.69/1.30 thf(f15,negated_conjecture,(
% 1.69/1.30 ~(mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X7 : $i] : (mimplies @ (mand @ (subset @ X3 @ X6) @ (subset @ X6 @ X7)) @ (subset @ X3 @ X7)))))))))),
% 1.69/1.30 inference(negated_conjecture,[status(cth)],[f14])).
% 1.69/1.30 thf(f14,conjecture,(
% 1.69/1.30 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X7 : $i] : (mimplies @ (mand @ (subset @ X3 @ X6) @ (subset @ X6 @ X7)) @ (subset @ X3 @ X7)))))))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',prove_transitivity_of_subset)).
% 1.69/1.30 thf(f132,plain,(
% 1.69/1.30 ( ! [X0 : $i] : (($false = (subset @ sK3 @ X0 @ mactual)) | ((subset @ X0 @ sK5 @ mactual) = $false)) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.69/1.30 thf(f128,plain,(
% 1.69/1.30 ( ! [X0 : $i] : (((subset @ X0 @ sK5 @ mactual) = $false) | ($false = (subset @ sK3 @ X0 @ mactual)) | ($true = $false)) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f123,f86])).
% 1.69/1.30 thf(f86,plain,(
% 1.69/1.30 ((subset @ sK3 @ sK5 @ mactual) = $false)),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.69/1.30 thf(f123,plain,(
% 1.69/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X0 @ X2 @ mactual) = $false) | ((subset @ X2 @ X1 @ mactual) = $false)) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.69/1.30 thf(f122,plain,(
% 1.69/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1 @ mactual) = $false) | ($true = $false) | ((subset @ X0 @ X2 @ mactual) = $false) | ($true = (subset @ X0 @ X1 @ mactual))) )),
% 1.69/1.30 inference(duplicate_literal_removal,[status(thm)],[f118])).
% 1.69/1.30 thf(f118,plain,(
% 1.69/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X2 @ X1 @ mactual) = $false) | ($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X0 @ X2 @ mactual) = $false)) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f112,f75])).
% 1.69/1.30 thf(f75,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (member @ (sK2 @ X1 @ X2) @ X1 @ mactual)) | ($true = (subset @ X1 @ X2 @ mactual))) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.69/1.30 thf(f73,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2 @ mactual)) | (((member @ (sK2 @ X1 @ X2) @ X1 @ mactual) => (member @ (sK2 @ X1 @ X2) @ X2 @ mactual)) = $false)) )),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.69/1.30 thf(f72,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2 @ mactual)) | ($false = ((^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))) @ (sK2 @ X1 @ X2)))) )),
% 1.69/1.30 inference(sigma_clausification,[status(thm)],[f71])).
% 1.69/1.30 thf(f71,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2 @ mactual)) | ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual)))) = $false)) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.69/1.30 thf(f69,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual)))) = (subset @ X1 @ X2 @ mactual))) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.69/1.30 thf(f68,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2 @ mactual) = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))))) = $true)) )),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.69/1.30 thf(f67,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))))) @ X2))) )),
% 1.69/1.30 inference(pi_clausification,[status(thm)],[f66])).
% 1.69/1.30 thf(f66,plain,(
% 1.69/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual))))))))) )),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.69/1.30 thf(f65,plain,(
% 1.69/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))))))) @ X1))) )),
% 1.69/1.30 inference(pi_clausification,[status(thm)],[f64])).
% 1.69/1.30 thf(f64,plain,(
% 1.69/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual))))))))))),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.69/1.30 thf(f62,plain,(
% 1.69/1.30 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 1.69/1.30 inference(definition_unfolding,[status(thm)],[f56,f51,f55,f55,f48,f55,f49])).
% 1.69/1.30 thf(f48,plain,(
% 1.69/1.30 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.69/1.30 thf(f35,plain,(
% 1.69/1.30 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f34])).
% 1.69/1.30 thf(f34,plain,(
% 1.69/1.30 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f6])).
% 1.69/1.30 thf(f6,axiom,(
% 1.69/1.30 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',mequiv_def)).
% 1.69/1.30 thf(f56,plain,(
% 1.69/1.30 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 1.69/1.30 inference(cnf_transformation,[status(thm)],[f39])).
% 1.69/1.30 thf(f39,plain,(
% 1.69/1.30 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 1.69/1.30 inference(fool_elimination,[status(thm)],[f38])).
% 1.69/1.30 thf(f38,plain,(
% 1.69/1.30 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (subset @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 1.69/1.30 inference(rectify,[status(thm)],[f12])).
% 1.69/1.30 thf(f12,axiom,(
% 1.69/1.30 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X6 : $i] : (mequiv @ (subset @ X3 @ X6) @ (mforall_di @ (^[X7 : $i] : (mimplies @ (member @ X7 @ X3) @ (member @ X7 @ X6))))))))))),
% 1.69/1.30 file('/export/starexec/sandbox/tmp/tmp.CoCRwbaNh1/DTF2THF_12929.p',subset_defn)).
% 1.69/1.30 thf(f112,plain,(
% 1.69/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (member @ (sK2 @ X0 @ X1) @ X3 @ mactual)) | ((subset @ X2 @ X1 @ mactual) = $false) | ($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X3 @ X2 @ mactual) = $false)) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.69/1.30 thf(f105,plain,(
% 1.69/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (member @ (sK2 @ X0 @ X1) @ X3 @ mactual)) | ((subset @ X2 @ X1 @ mactual) = $false) | ($true = $false) | ($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X3 @ X2 @ mactual) = $false)) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f96,f78])).
% 1.69/1.30 thf(f78,plain,(
% 1.69/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (member @ X3 @ X2 @ mactual)) | ($false = (subset @ X1 @ X2 @ mactual)) | ($false = (member @ X3 @ X1 @ mactual))) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 1.69/1.30 thf(f77,plain,(
% 1.69/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((member @ X3 @ X1 @ mactual) => (member @ X3 @ X2 @ mactual))) | ($false = (subset @ X1 @ X2 @ mactual))) )),
% 1.69/1.30 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.69/1.30 thf(f76,plain,(
% 1.69/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (subset @ X1 @ X2 @ mactual)) | ($true = ((^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))) @ X3))) )),
% 1.69/1.30 inference(pi_clausification,[status(thm)],[f70])).
% 1.69/1.30 thf(f70,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))))) | ($false = (subset @ X1 @ X2 @ mactual))) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.69/1.30 thf(f96,plain,(
% 1.69/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((member @ (sK2 @ X0 @ X1) @ X2 @ mactual) = $false) | ($true = (subset @ X0 @ X1 @ mactual)) | ((subset @ X2 @ X1 @ mactual) = $false)) )),
% 1.69/1.30 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.69/1.30 thf(f95,plain,(
% 1.69/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((member @ (sK2 @ X0 @ X1) @ X2 @ mactual) = $false) | ($true = $false) | ((subset @ X2 @ X1 @ mactual) = $false) | ($true = (subset @ X0 @ X1 @ mactual))) )),
% 1.69/1.30 inference(superposition,[status(thm)],[f78,f74])).
% 1.69/1.30 thf(f74,plain,(
% 1.69/1.30 ( ! [X2 : $i,X1 : $i] : (((member @ (sK2 @ X1 @ X2) @ X2 @ mactual) = $false) | ($true = (subset @ X1 @ X2 @ mactual))) )),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.69/1.30 thf(f88,plain,(
% 1.69/1.30 ($true = (subset @ sK4 @ sK5 @ mactual))),
% 1.69/1.30 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.69/1.30 % SZS output end Proof for DTF2THF_12929
% 1.69/1.30 % (13232)------------------------------
% 1.69/1.30 % (13232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.30 % (13232)Termination reason: Refutation
% 1.69/1.30
% 1.69/1.30 % (13232)Memory used [KB]: 5628
% 1.69/1.30 % (13232)Time elapsed: 0.010 s
% 1.69/1.30 % (13232)Instructions burned: 22 (million)
% 1.69/1.30 % (13232)------------------------------
% 1.69/1.30 % (13232)------------------------------
% 1.69/1.30 % (13229)Success in time 0.019 s
%------------------------------------------------------------------------------