%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET924^1 : 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 : 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 09:32:21 AM UTC 2026
% Result : Theorem 1.76s 1.32s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 5 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 145 ( 5 ~; 0 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 20 ^; 0 !; 0 ?; 20 :)
% 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,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
in: $i > $i > mworld > $o ).
thf(func_def_16,type,
empty: $i > mworld > $o ).
thf(func_def_17,type,
singleton: $i > $i ).
thf(func_def_18,type,
set_difference: $i > $i > $i ).
thf(func_def_33,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f86,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f78,f83]) ).
thf(f83,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f56]) ).
thf(f56,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) @ ( mnot @ ( in @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gdLzT1MWJ9/DTF2THF_14572.p',l34_zfmisc_1) ).
thf(f78,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f74,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) @ ( mnot @ ( in @ X1 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f23,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) @ ( mnot @ ( in @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gdLzT1MWJ9/DTF2THF_14572.p',t67_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET924^1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:04:26 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SET924^1 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : TPTP problem SET924+1.p with axiomatized equality
% 0.30/0.46 % Version : [BP13] axioms.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.46 % Source : [TPTP]
% 0.30/0.46 % Names : SET924+1 [QMLTP]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0
% 0.30/0.46 % Syntax : Number of formulae : 42 ( 10 unt; 18 typ; 10 def)
% 0.30/0.46 % Number of atoms : 114 ( 10 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 9 ( 4 avg)
% 0.30/0.46 % Number of connectives : 177 ( 1 ~; 1 |; 2 &; 170 @)
% 0.30/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 14 ( 7 avg)
% 0.30/0.46 % Number of types : 3 ( 1 usr)
% 0.30/0.46 % Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 18 ( 17 usr; 1 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 57 ( 53 ^; 2 !; 2 ?; 57 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.30/0.46 % $modalities == $modal_system_K].
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(mworld,type,
% 0.30/0.46 mworld: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_type,type,
% 0.30/0.46 mrel: mworld > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mactual_type,type,
% 0.30/0.46 mactual: mworld ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_type,type,
% 0.30/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_def,definition,
% 0.30/0.46 ( mlocal
% 0.30/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_type,type,
% 0.30/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mand_type,type,
% 0.30/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mor_type,type,
% 0.30/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_type,type,
% 0.30/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_type,type,
% 0.30/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_def,definition,
% 0.30/0.46 ( mnot
% 0.30/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.46 ~ ( A @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mand_def,definition,
% 0.30/0.46 ( mand
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 & ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mor_def,definition,
% 0.30/0.46 ( mor
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 | ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_def,definition,
% 0.30/0.46 ( mimplies
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 => ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_def,definition,
% 0.30/0.46 ( mequiv
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 <=> ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_type,type,
% 0.30/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_def,definition,
% 0.30/0.46 ( mbox
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ! [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 => ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_type,type,
% 0.30/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_def,definition,
% 0.30/0.46 ( mdia
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ? [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 & ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mforall_di_type,type,
% 0.30/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mforall_di_def,definition,
% 0.30/0.46 ( mforall_di
% 0.30/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mexists_di_type,type,
% 0.30/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mexists_di_def,definition,
% 0.30/0.46 ( mexists_di
% 0.30/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(qmltpeq_decl,type,
% 0.30/0.46 qmltpeq: $i > $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(in_decl,type,
% 0.30/0.46 in: $i > $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(empty_decl,type,
% 0.30/0.46 empty: $i > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_decl,type,
% 0.30/0.46 singleton: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(set_difference_decl,type,
% 0.30/0.46 set_difference: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(reflexivity,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symmetry,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [X: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(transitivity,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [X: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [Y: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set_difference_substitution_1,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set_difference_substitution_2,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_substitution_1,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(empty_substitution_1,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in_substitution_1,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in_substitution_2,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(antisymmetry_r2_hidden,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(rc1_xboole_0,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mexists_di
% 0.30/0.46 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(rc2_xboole_0,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mexists_di
% 0.30/0.46 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(t67_zfmisc_1,conjecture,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(l34_zfmisc_1,axiom,
% 0.30/0.46 ( mlocal
% 0.30/0.46 @ ( mforall_di
% 0.30/0.46 @ ^ [A: $i] :
% 0.30/0.46 ( mforall_di
% 0.30/0.46 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.56/1.28 ---- Embedded in THF ---
% 1.56/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.28 %%% Generated on Tue Feb 24 12:04:27 EST 2026
% 1.56/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.28 %%% Logic specification used:
% 1.56/1.28 %%% thf(spec, logic, $$dhol).
% 1.56/1.28
% 1.56/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gdLzT1MWJ9/DTF2DTF14572.p
% See solution above
% 1.56/1.28 ------------------------
% 1.56/1.29 ---- Cleaned THF ---
% 1.56/1.29 thf(mworld,type,
% 1.56/1.29 mworld: $tType ).
% 1.56/1.29
% 1.56/1.29 thf(mrel_type,type,
% 1.56/1.29 mrel: mworld > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mactual_type,type,
% 1.56/1.29 mactual: mworld ).
% 1.56/1.29
% 1.56/1.29 thf(mlocal_type,type,
% 1.56/1.29 mlocal: ( mworld > $o ) > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mlocal_def,definition,
% 1.56/1.29 ( mlocal
% 1.56/1.29 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mnot_type,type,
% 1.56/1.29 mnot: ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mand_type,type,
% 1.56/1.29 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mor_type,type,
% 1.56/1.29 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mimplies_type,type,
% 1.56/1.29 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mequiv_type,type,
% 1.56/1.29 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mnot_def,definition,
% 1.56/1.29 ( mnot
% 1.56/1.29 = ( ^ [A: mworld > $o,W: mworld] :
% 1.56/1.29 ~ ( A @ W ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mand_def,definition,
% 1.56/1.29 ( mand
% 1.56/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.29 ( ( A @ W )
% 1.56/1.29 & ( B @ W ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mor_def,definition,
% 1.56/1.29 ( mor
% 1.56/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.29 ( ( A @ W )
% 1.56/1.29 | ( B @ W ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mimplies_def,definition,
% 1.56/1.29 ( mimplies
% 1.56/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.29 ( ( A @ W )
% 1.56/1.29 => ( B @ W ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mequiv_def,definition,
% 1.56/1.29 ( mequiv
% 1.56/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.56/1.29 ( ( A @ W )
% 1.56/1.29 <=> ( B @ W ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mbox_type,type,
% 1.56/1.29 mbox: ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mbox_def,definition,
% 1.56/1.29 ( mbox
% 1.56/1.29 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.56/1.29 ! [V: mworld] :
% 1.56/1.29 ( ( mrel @ W @ V )
% 1.56/1.29 => ( Phi @ V ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mdia_type,type,
% 1.56/1.29 mdia: ( mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mdia_def,definition,
% 1.56/1.29 ( mdia
% 1.56/1.29 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.56/1.29 ? [V: mworld] :
% 1.56/1.29 ( ( mrel @ W @ V )
% 1.56/1.29 & ( Phi @ V ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mforall_di_type,type,
% 1.56/1.29 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mforall_di_def,definition,
% 1.56/1.29 ( mforall_di
% 1.56/1.29 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.56/1.29 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(mexists_di_type,type,
% 1.56/1.29 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(mexists_di_def,definition,
% 1.56/1.29 ( mexists_di
% 1.56/1.29 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.56/1.29 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(qmltpeq_decl,type,
% 1.56/1.29 qmltpeq: $i > $i > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(in_decl,type,
% 1.56/1.29 in: $i > $i > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(empty_decl,type,
% 1.56/1.29 empty: $i > mworld > $o ).
% 1.56/1.29
% 1.56/1.29 thf(singleton_decl,type,
% 1.56/1.29 singleton: $i > $i ).
% 1.56/1.29
% 1.56/1.29 thf(set_difference_decl,type,
% 1.56/1.29 set_difference: $i > $i > $i ).
% 1.56/1.29
% 1.56/1.29 thf(reflexivity,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(symmetry,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [X: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(transitivity,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [X: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [Y: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(set_difference_substitution_1,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(set_difference_substitution_2,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(singleton_substitution_1,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(empty_substitution_1,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(in_substitution_1,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(in_substitution_2,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(antisymmetry_r2_hidden,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(rc1_xboole_0,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mexists_di
% 1.56/1.29 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(rc2_xboole_0,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mexists_di
% 1.56/1.29 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(t67_zfmisc_1,conjecture,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 1.56/1.29
% 1.56/1.29 thf(l34_zfmisc_1,axiom,
% 1.56/1.29 ( mlocal
% 1.56/1.29 @ ( mforall_di
% 1.56/1.29 @ ^ [A: $i] :
% 1.56/1.29 ( mforall_di
% 1.56/1.29 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 1.56/1.29 ------------------------
% 1.76/1.30 % (14850)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14572 for (2999ds/18Mi)
% 1.76/1.30 % (14844)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14572 for (2999ds/183Mi)
% 1.76/1.31 % (14850)Instruction limit reached!
% 1.76/1.31 % (14850)------------------------------
% 1.76/1.31 % (14850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (14850)Termination reason: Unknown
% 1.76/1.31 % (14850)Termination phase: Saturation
% 1.76/1.31
% 1.76/1.31 % (14850)Memory used [KB]: 5628
% 1.76/1.31 % (14850)Time elapsed: 0.006 s
% 1.76/1.31 % (14850)Instructions burned: 18 (million)
% 1.76/1.31 % (14850)------------------------------
% 1.76/1.31 % (14850)------------------------------
% 1.76/1.31 % (14845)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_14572 for (2999ds/4Mi)
% 1.76/1.31 % (14847)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14572 for (2999ds/2Mi)
% 1.76/1.31 % (14848)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_14572 for (2999ds/2Mi)
% 1.76/1.31 % (14846)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_14572 for (2999ds/27Mi)
% 1.76/1.31 % (14849)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_14572 for (2999ds/275Mi)
% 1.76/1.31 % (14847)Instruction limit reached!
% 1.76/1.31 % (14847)------------------------------
% 1.76/1.31 % (14847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (14847)Termination reason: Unknown
% 1.76/1.31 % (14847)Termination phase: shuffling
% 1.76/1.31
% 1.76/1.31 % (14847)Memory used [KB]: 1023
% 1.76/1.31 % (14847)Time elapsed: 0.003 s
% 1.76/1.31 % (14847)Instructions burned: 2 (million)
% 1.76/1.31 % (14847)------------------------------
% 1.76/1.31 % (14847)------------------------------
% 1.76/1.31 % (14848)Instruction limit reached!
% 1.76/1.31 % (14848)------------------------------
% 1.76/1.31 % (14848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (14848)Termination reason: Unknown
% 1.76/1.31 % (14848)Termination phase: shuffling
% 1.76/1.31
% 1.76/1.31 % (14848)Memory used [KB]: 1023
% 1.76/1.31 % (14848)Time elapsed: 0.003 s
% 1.76/1.31 % (14848)Instructions burned: 2 (million)
% 1.76/1.31 % (14848)------------------------------
% 1.76/1.31 % (14848)------------------------------
% 1.76/1.31 % (14845)Instruction limit reached!
% 1.76/1.31 % (14845)------------------------------
% 1.76/1.31 % (14845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.31 % (14845)Termination reason: Unknown
% 1.76/1.31 % (14845)Termination phase: Property scanning
% 1.76/1.31
% 1.76/1.31 % (14845)Memory used [KB]: 1023
% 1.76/1.31 % (14845)Time elapsed: 0.004 s
% 1.76/1.31 % (14845)Instructions burned: 4 (million)
% 1.76/1.31 % (14845)------------------------------
% 1.76/1.31 % (14845)------------------------------
% 1.76/1.32 % (14849)First to succeed.
% 1.76/1.32 % (14849)Refutation found. Thanks to Tanya!
% 1.76/1.32 % SZS status Theorem for DTF2THF_14572
% 1.76/1.32 % SZS output start Proof for DTF2THF_14572
% 1.76/1.32 thf(type_def_5, type, mworld: $tType).
% 1.76/1.32 thf(func_def_0, type, mworld: $tType).
% 1.76/1.32 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.76/1.32 thf(func_def_2, type, mactual: mworld).
% 1.76/1.32 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.76/1.32 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.76/1.32 thf(func_def_14, type, qmltpeq: $i > $i > mworld > $o).
% 1.76/1.32 thf(func_def_15, type, in: $i > $i > mworld > $o).
% 1.76/1.32 thf(func_def_16, type, empty: $i > mworld > $o).
% 1.76/1.32 thf(func_def_17, type, singleton: $i > $i).
% 1.76/1.32 thf(func_def_18, type, set_difference: $i > $i > $i).
% 1.76/1.32 thf(func_def_33, type, ph1: !>[X0: $tType]:(X0)).
% 1.76/1.32 thf(f86,plain,(
% 1.76/1.32 $false),
% 1.76/1.32 inference(subsumption_resolution,[status(thm)],[f78,f83])).
% 1.76/1.32 thf(f83,plain,(
% 1.76/1.32 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.76/1.32 inference(cnf_transformation,[status(thm)],[f57])).
% 1.76/1.32 thf(f57,plain,(
% 1.76/1.32 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.76/1.32 inference(fool_elimination,[status(thm)],[f56])).
% 1.76/1.32 thf(f56,plain,(
% 1.76/1.32 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 1.76/1.32 inference(rectify,[status(thm)],[f25])).
% 1.76/1.32 thf(f25,axiom,(
% 1.76/1.32 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 1.76/1.32 file('/export/starexec/sandbox2/tmp/tmp.gdLzT1MWJ9/DTF2THF_14572.p',l34_zfmisc_1)).
% 1.76/1.32 thf(f78,plain,(
% 1.76/1.32 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.76/1.32 inference(cnf_transformation,[status(thm)],[f74])).
% 1.76/1.32 thf(f74,plain,(
% 1.76/1.32 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.76/1.32 inference(flattening,[status(thm)],[f34])).
% 1.76/1.32 thf(f34,plain,(
% 1.76/1.32 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.76/1.32 inference(fool_elimination,[status(thm)],[f33])).
% 1.76/1.32 thf(f33,plain,(
% 1.76/1.32 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 1.76/1.32 inference(rectify,[status(thm)],[f24])).
% 1.76/1.32 thf(f24,negated_conjecture,(
% 1.76/1.32 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 1.76/1.32 inference(negated_conjecture,[status(cth)],[f23])).
% 1.76/1.32 thf(f23,conjecture,(
% 1.76/1.32 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 1.76/1.32 file('/export/starexec/sandbox2/tmp/tmp.gdLzT1MWJ9/DTF2THF_14572.p',t67_zfmisc_1)).
% 1.76/1.32 % SZS output end Proof for DTF2THF_14572
% 1.76/1.32 % (14849)------------------------------
% 1.76/1.32 % (14849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.32 % (14849)Termination reason: Refutation
% 1.76/1.32
% 1.76/1.32 % (14849)Memory used [KB]: 5500
% 1.76/1.32 % (14849)Time elapsed: 0.006 s
% 1.76/1.32 % (14849)Instructions burned: 7 (million)
% 1.76/1.32 % (14849)------------------------------
% 1.76/1.32 % (14849)------------------------------
% 1.76/1.32 % (14843)Success in time 0.022 s
%------------------------------------------------------------------------------