%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU535^2 : TPTP v9.2.1. Released v3.7.0.
% 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 09:35:08 AM UTC 2026
% Result : Theorem 1.52s 1.24s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 152 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 130 ( 17 ~; 10 |; 6 &; 70 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 8 con; 0-2 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 39 ( 11 ^; 24 !; 4 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_10,type,
sK0: $i > $o ).
thf(f38,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f31,f37]) ).
thf(f37,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f4,f24]) ).
thf(f24,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl2_1
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f4,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f31,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(backward_demodulation,[status(thm)],[f14,f27]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl2_2
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f14,plain,
( ( in @ sK1 @ emptyset )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( sK0 @ sK1 ) )
& ( ( in @ sK1 @ emptyset )
= $true )
& ( emptysetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ X1 ) )
& ( $true
= ( in @ X1 @ emptyset ) ) )
=> ( ( $true
!= ( sK0 @ sK1 ) )
& ( ( in @ sK1 @ emptyset )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ X1 ) )
& ( $true
= ( in @ X1 @ emptyset ) ) )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ emptyset ) )
=> ( $true
= ( X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( emptysetE
=> ! [X1: $i > $o,X0: $i] :
( ( in @ X0 @ emptyset )
=> ( X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( emptysetE
=> ! [X1: $i > $o,X0: $i] :
( ( in @ X0 @ emptyset )
=> ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nN7vDwXZCX/DTF2THF_8192.p',vacuousDall) ).
thf(f28,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f26,f23]) ).
thf(f21,plain,
! [X2: $o,X1: $i] :
( ( $true = X2 )
| ( ( in @ X1 @ emptyset )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( ( ^ [Y0: $o] : Y0
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
file('/export/starexec/sandbox/tmp/tmp.nN7vDwXZCX/DTF2THF_8192.p',emptysetE) ).
thf(f13,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU535^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:24:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SEU535^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Bounded Quantifier Laws
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! phi:i>o.! x:i.in x emptyset -> phi x)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC037l [Bro08]
% 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, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.30/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 8 ( 0 ~; 0 |; 0 &; 5 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=508
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall,conjecture,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 => ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.52/1.21 ---- Embedded in THF ---
% 1.52/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.21 %%% Generated on Tue Feb 24 12:24:56 EST 2026
% 1.52/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.21 %%% Logic specification used:
% 1.52/1.21 %%% thf(spec, logic, $$dhol).
% 1.52/1.21
% 1.52/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nN7vDwXZCX/DTF2DTF8192.p
% See solution above
% 1.52/1.21 ------------------------
% 1.52/1.22 ---- Cleaned THF ---
% 1.52/1.22 thf(in_type,type,
% 1.52/1.22 in: $i > $i > $o ).
% 1.52/1.22
% 1.52/1.22 thf(emptyset_type,type,
% 1.52/1.22 emptyset: $i ).
% 1.52/1.22
% 1.52/1.22 thf(emptysetE_type,type,
% 1.52/1.22 emptysetE: $o ).
% 1.52/1.22
% 1.52/1.22 thf(emptysetE,definition,
% 1.52/1.22 ( emptysetE
% 1.52/1.22 = ( ! [Xx: $i] :
% 1.52/1.22 ( ( in @ Xx @ emptyset )
% 1.52/1.22 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.52/1.22
% 1.52/1.22 thf(vacuousDall,conjecture,
% 1.52/1.22 ( emptysetE
% 1.52/1.22 => ! [Xphi: $i > $o,Xx: $i] :
% 1.52/1.22 ( ( in @ Xx @ emptyset )
% 1.52/1.22 => ( Xphi @ Xx ) ) ) ).
% 1.52/1.22 ------------------------
% 1.52/1.24 % (8384)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_8192 for (3000ds/4Mi)
% 1.52/1.24 % (8388)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_8192 for (3000ds/275Mi)
% 1.52/1.24 % (8384)First to succeed.
% 1.52/1.24 % (8388)Also succeeded, but the first one will report.
% 1.52/1.24 % (8384)Refutation found. Thanks to Tanya!
% 1.52/1.24 % SZS status Theorem for DTF2THF_8192
% 1.52/1.24 % SZS output start Proof for DTF2THF_8192
% 1.52/1.24 thf(func_def_0, type, in: $i > $i > $o).
% 1.52/1.24 thf(func_def_10, type, sK0: $i > $o).
% 1.52/1.24 thf(f38,plain,(
% 1.52/1.24 $false),
% 1.52/1.24 inference(avatar_sat_refutation,[status(thm)],[f28,f31,f37])).
% 1.52/1.24 thf(f37,plain,(
% 1.52/1.24 ~spl2_1),
% 1.52/1.24 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.52/1.24 thf(f36,plain,(
% 1.52/1.24 $false | ~spl2_1),
% 1.52/1.24 inference(equality_resolution,[status(thm)],[f35])).
% 1.52/1.24 thf(f35,plain,(
% 1.52/1.24 ( ! [X0 : $o] : (($false != X0)) ) | ~spl2_1),
% 1.52/1.24 inference(superposition,[status(thm)],[f4,f24])).
% 1.52/1.24 thf(f24,plain,(
% 1.52/1.24 ( ! [X2 : $o] : (($true = X2)) ) | ~spl2_1),
% 1.52/1.24 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.52/1.24 thf(f23,definition,(
% 1.52/1.24 spl2_1 <=> ! [X2 : $o] : ($true = X2)),
% 1.52/1.24 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.52/1.24 thf(f4,plain,(
% 1.52/1.24 ($true != $false)),
% 1.52/1.24 introduced(definition,[],[fool_axiom])).
% 1.52/1.24 thf(f31,plain,(
% 1.52/1.24 ~spl2_2),
% 1.52/1.24 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.52/1.24 thf(f30,plain,(
% 1.52/1.24 $false | ~spl2_2),
% 1.52/1.24 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.52/1.24 thf(f29,plain,(
% 1.52/1.24 ($true = $false) | ~spl2_2),
% 1.52/1.24 inference(backward_demodulation,[status(thm)],[f14,f27])).
% 1.52/1.24 thf(f27,plain,(
% 1.52/1.24 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) ) | ~spl2_2),
% 1.52/1.24 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.52/1.24 thf(f26,definition,(
% 1.52/1.24 spl2_2 <=> ! [X1 : $i] : ((in @ X1 @ emptyset) = $false)),
% 1.52/1.24 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.52/1.24 thf(f14,plain,(
% 1.52/1.24 ((in @ sK1 @ emptyset) = $true)),
% 1.52/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.52/1.24 thf(f11,plain,(
% 1.52/1.24 (($true != (sK0 @ sK1)) & ((in @ sK1 @ emptyset) = $true)) & (emptysetE = $true)),
% 1.52/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.52/1.24 thf(f10,plain,(
% 1.52/1.24 ? [X0 : $i > $o,X1 : $i] : (($true != (X0 @ X1)) & ($true = (in @ X1 @ emptyset))) => (($true != (sK0 @ sK1)) & ((in @ sK1 @ emptyset) = $true))),
% 1.52/1.24 introduced(definition,[],[choice_axiom])).
% 1.52/1.24 thf(f9,plain,(
% 1.52/1.24 ? [X0 : $i > $o,X1 : $i] : (($true != (X0 @ X1)) & ($true = (in @ X1 @ emptyset))) & (emptysetE = $true)),
% 1.52/1.24 inference(ennf_transformation,[status(thm)],[f6])).
% 1.52/1.24 thf(f6,plain,(
% 1.52/1.24 ~((emptysetE = $true) => ! [X0 : $i > $o,X1 : $i] : (($true = (in @ X1 @ emptyset)) => ($true = (X0 @ X1))))),
% 1.52/1.24 inference(fool_elimination,[status(thm)],[f5])).
% 1.52/1.24 thf(f5,plain,(
% 1.52/1.24 ~(emptysetE => ! [X0 : $i > $o,X1 : $i] : ((in @ X1 @ emptyset) => (X0 @ X1)))),
% 1.52/1.24 inference(rectify,[status(thm)],[f3])).
% 1.52/1.24 thf(f3,negated_conjecture,(
% 1.52/1.24 ~(emptysetE => ! [X1 : $i > $o,X0 : $i] : ((in @ X0 @ emptyset) => (X1 @ X0)))),
% 1.52/1.24 inference(negated_conjecture,[status(cth)],[f2])).
% 1.52/1.24 thf(f2,conjecture,(
% 1.52/1.24 emptysetE => ! [X1 : $i > $o,X0 : $i] : ((in @ X0 @ emptyset) => (X1 @ X0))),
% 1.52/1.24 file('/export/starexec/sandbox/tmp/tmp.nN7vDwXZCX/DTF2THF_8192.p',vacuousDall)).
% 1.52/1.24 thf(f28,plain,(
% 1.52/1.24 spl2_1 | spl2_2),
% 1.52/1.24 inference(avatar_split_clause,[status(thm)],[f21,f26,f23])).
% 1.52/1.24 thf(f21,plain,(
% 1.52/1.24 ( ! [X2 : $o,X1 : $i] : (($true = X2) | ((in @ X1 @ emptyset) = $false)) )),
% 1.52/1.24 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.52/1.24 thf(f20,plain,(
% 1.52/1.24 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ emptyset) = $false) | (((^[Y0 : $o]: (Y0)) @ X2) = $true)) )),
% 1.52/1.24 inference(pi_clausification,[status(thm)],[f19])).
% 1.52/1.24 thf(f19,plain,(
% 1.52/1.24 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false) | ($true = (!! @ $o @ (^[Y0 : $o]: (Y0))))) )),
% 1.52/1.24 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.52/1.24 thf(f18,plain,(
% 1.52/1.24 ( ! [X1 : $i] : (($true = ((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))) )),
% 1.52/1.24 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.52/1.24 thf(f17,plain,(
% 1.52/1.24 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1))) )),
% 1.52/1.24 inference(pi_clausification,[status(thm)],[f16])).
% 1.52/1.24 thf(f16,plain,(
% 1.52/1.24 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) = $true)),
% 1.52/1.24 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.52/1.24 thf(f12,plain,(
% 1.52/1.24 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.52/1.24 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.24 thf(f8,plain,(
% 1.52/1.24 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.52/1.24 inference(fool_elimination,[status(thm)],[f7])).
% 1.52/1.24 thf(f7,plain,(
% 1.52/1.24 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.52/1.24 inference(rectify,[status(thm)],[f1])).
% 1.52/1.24 thf(f1,axiom,(
% 1.52/1.24 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.52/1.24 file('/export/starexec/sandbox/tmp/tmp.nN7vDwXZCX/DTF2THF_8192.p',emptysetE)).
% 1.52/1.24 thf(f13,plain,(
% 1.52/1.24 (emptysetE = $true)),
% 1.52/1.24 inference(cnf_transformation,[status(thm)],[f11])).
% 1.52/1.24 % SZS output end Proof for DTF2THF_8192
% 1.52/1.24 % (8384)------------------------------
% 1.52/1.24 % (8384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.24 % (8384)Termination reason: Refutation
% 1.52/1.24
% 1.52/1.24 % (8384)Memory used [KB]: 5500
% 1.52/1.24 % (8384)Time elapsed: 0.003 s
% 1.52/1.24 % (8384)Instructions burned: 1 (million)
% 1.52/1.24 % (8384)------------------------------
% 1.52/1.24 % (8384)------------------------------
% 1.52/1.24 % (8382)Success in time 0.014 s
%------------------------------------------------------------------------------