%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU503^2 : 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 : n003.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 09:34:58 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 32 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 119 ( 19 ~; 10 |; 2 &; 64 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 8 con; 0-2 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 11 ^; 21 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f38,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f31,f37]) ).
thf(f37,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl1_1 ),
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f4,f24]) ).
thf(f24,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl1_1
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f4,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f31,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(backward_demodulation,[status(thm)],[f13,f27]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl1_2
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f13,plain,
( $true
= ( in @ sK0 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( emptysetE = $true )
& ( $true
= ( in @ sK0 @ emptyset ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
=> ( $true
= ( in @ sK0 @ emptyset ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( emptysetE = $true )
& ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( emptysetE
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( emptysetE
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( emptysetE
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.ETkbyg7X6D/DTF2THF_1683.p',notinemptyset) ).
thf(f28,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f26,f23]) ).
thf(f21,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true = X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $o,X1: $i] :
( ( $true
= ( ^ [Y0: $o] : Y0
@ X2 ) )
| ( ( in @ X1 @ emptyset )
= $false ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( $true
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
| ( ( in @ X1 @ emptyset )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
= $true ),
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,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f14]) ).
thf(f14,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,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.ETkbyg7X6D/DTF2THF_1683.p',emptysetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU503^2 : 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
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:24:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU503^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.27/0.46 % Version : Especial > Reduced > Especial.
% 0.27/0.46 % English : (! x:i.~(in x emptyset))
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC005l [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 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
% 0.27/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.27/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.27/0.46 % Number of connectives : 7 ( 1 ~; 0 |; 0 &; 4 @)
% 0.27/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 6 ( 4 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=434
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyset_type,type,
% 0.27/0.46 emptyset: $i ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE_type,type,
% 0.27/0.46 emptysetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE,definition,
% 0.27/0.46 ( emptysetE
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notinemptyset,conjecture,
% 0.27/0.46 ( emptysetE
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ emptyset ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.44/1.27 ---- Embedded in THF ---
% 1.44/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.27 %%% Generated on Tue Feb 24 12:24:41 EST 2026
% 1.44/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.27 %%% Logic specification used:
% 1.44/1.27 %%% thf(spec, logic, $$dhol).
% 1.44/1.27
% 1.44/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ETkbyg7X6D/DTF2DTF1683.p
% See solution above
% 1.44/1.27 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.28 thf(in_type,type,
% 1.44/1.28 in: $i > $i > $o ).
% 1.44/1.28
% 1.44/1.28 thf(emptyset_type,type,
% 1.44/1.28 emptyset: $i ).
% 1.44/1.28
% 1.44/1.28 thf(emptysetE_type,type,
% 1.44/1.28 emptysetE: $o ).
% 1.44/1.28
% 1.44/1.28 thf(emptysetE,definition,
% 1.44/1.28 ( emptysetE
% 1.44/1.28 = ( ! [Xx: $i] :
% 1.44/1.28 ( ( in @ Xx @ emptyset )
% 1.44/1.28 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.44/1.28
% 1.44/1.28 thf(notinemptyset,conjecture,
% 1.44/1.28 ( emptysetE
% 1.44/1.28 => ! [Xx: $i] :
% 1.44/1.28 ~ ( in @ Xx @ emptyset ) ) ).
% 1.44/1.28 ------------------------
% 1.61/1.30 % (1983)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_1683 for (2999ds/2Mi)
% 1.61/1.30 % (1981)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_1683 for (2999ds/27Mi)
% 1.61/1.30 % (1983)Instruction limit reached!
% 1.61/1.30 % (1983)------------------------------
% 1.61/1.30 % (1983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (1983)Termination reason: Unknown
% 1.61/1.30 % (1983)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (1983)Memory used [KB]: 5500
% 1.61/1.30 % (1983)Time elapsed: 0.003 s
% 1.61/1.30 % (1983)Instructions burned: 3 (million)
% 1.61/1.30 % (1983)------------------------------
% 1.61/1.30 % (1983)------------------------------
% 1.61/1.30 % (1981)First to succeed.
% 1.61/1.30 % (1981)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_1683
% 1.61/1.30 % SZS output start Proof for DTF2THF_1683
% 1.61/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.61/1.30 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.30 thf(f38,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(avatar_sat_refutation,[status(thm)],[f28,f31,f37])).
% 1.61/1.30 thf(f37,plain,(
% 1.61/1.30 ~spl1_1),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.61/1.30 thf(f36,plain,(
% 1.61/1.30 $false | ~spl1_1),
% 1.61/1.30 inference(equality_resolution,[status(thm)],[f33])).
% 1.61/1.30 thf(f33,plain,(
% 1.61/1.30 ( ! [X0 : $o] : (($false != X0)) ) | ~spl1_1),
% 1.61/1.30 inference(superposition,[status(thm)],[f4,f24])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ( ! [X2 : $o] : (($true = X2)) ) | ~spl1_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.61/1.30 thf(f23,definition,(
% 1.61/1.30 spl1_1 <=> ! [X2 : $o] : ($true = X2)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.61/1.30 thf(f4,plain,(
% 1.61/1.30 ($true != $false)),
% 1.61/1.30 introduced(definition,[],[fool_axiom])).
% 1.61/1.30 thf(f31,plain,(
% 1.61/1.30 ~spl1_2),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.61/1.30 thf(f30,plain,(
% 1.61/1.30 $false | ~spl1_2),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 ($true = $false) | ~spl1_2),
% 1.61/1.30 inference(backward_demodulation,[status(thm)],[f13,f27])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) ) | ~spl1_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.61/1.30 thf(f26,definition,(
% 1.61/1.30 spl1_2 <=> ! [X1 : $i] : ((in @ X1 @ emptyset) = $false)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ($true = (in @ sK0 @ emptyset))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 (emptysetE = $true) & ($true = (in @ sK0 @ emptyset))),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ? [X0 : $i] : ((in @ X0 @ emptyset) = $true) => ($true = (in @ sK0 @ emptyset))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 (emptysetE = $true) & ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ~((emptysetE = $true) => ! [X0 : $i] : ((in @ X0 @ emptyset) != $true))),
% 1.61/1.30 inference(flattening,[status(thm)],[f8])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ~((emptysetE = $true) => ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.61/1.30 thf(f7,plain,(
% 1.61/1.30 ~(emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.61/1.30 inference(rectify,[status(thm)],[f3])).
% 1.61/1.30 thf(f3,negated_conjecture,(
% 1.61/1.30 ~(emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.61/1.30 thf(f2,conjecture,(
% 1.61/1.30 emptysetE => ! [X0 : $i] : ~(in @ X0 @ emptyset)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.ETkbyg7X6D/DTF2THF_1683.p',notinemptyset)).
% 1.61/1.30 thf(f28,plain,(
% 1.61/1.30 spl1_1 | spl1_2),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f21,f26,f23])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ emptyset) = $false) | ($true = X2)) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.61/1.30 thf(f20,plain,(
% 1.61/1.30 ( ! [X2 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: (Y0)) @ X2)) | ((in @ X1 @ emptyset) = $false)) )),
% 1.61/1.30 inference(pi_clausification,[status(thm)],[f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (Y0)))) | ((in @ X1 @ emptyset) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ( ! [X1 : $i] : ((((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 1.61/1.30 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1))) )),
% 1.61/1.30 inference(pi_clausification,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.61/1.30 inference(definition_unfolding,[status(thm)],[f15,f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 (emptysetE = $true)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.30 thf(f15,plain,(
% 1.61/1.30 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.30 thf(f6,plain,(
% 1.61/1.30 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,plain,(
% 1.61/1.30 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.61/1.30 inference(rectify,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.ETkbyg7X6D/DTF2THF_1683.p',emptysetE)).
% 1.61/1.30 % SZS output end Proof for DTF2THF_1683
% 1.61/1.30 % (1981)------------------------------
% 1.61/1.30 % (1981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (1981)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (1981)Memory used [KB]: 5500
% 1.61/1.30 % (1981)Time elapsed: 0.003 s
% 1.61/1.30 % (1981)Instructions burned: 1 (million)
% 1.61/1.30 % (1981)------------------------------
% 1.61/1.30 % (1981)------------------------------
% 1.61/1.30 % (1978)Success in time 0.013 s
%------------------------------------------------------------------------------