%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU511^2 : 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 : n029.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 09:35:00 AM UTC 2026
% Result : Theorem 1.62s 1.46s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 22 unt; 0 typ; 2 def)
% Number of atoms : 199 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 147 ( 25 ~; 10 |; 6 &; 78 @)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 9 con; 0-2 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 45 ( 15 ^; 20 !; 10 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f42,f46]) ).
thf(f46,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(forward_demodulation,[status(thm)],[f43,f32]) ).
thf(f32,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl2_1
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f43,plain,
( ( in @ sK1 @ emptyset )
= $true ),
inference(forward_demodulation,[status(thm)],[f17,f24]) ).
thf(f24,plain,
emptyset = sK0,
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( emptyset = sK0 )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( emptyset != sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f18,f16]) ).
thf(f16,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( nonempty
= ( ^ [X0: $i] : ( emptyset != X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',nonempty) ).
thf(f18,plain,
( $true
!= ( nonempty @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( emptysetE = $true )
& ( $true
!= ( nonempty @ sK0 ) )
& ( $true
= ( in @ sK1 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13,f12]) ).
thf(f12,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) ) )
=> ( ( $true
!= ( nonempty @ sK0 ) )
& ? [X1: $i] :
( ( in @ X1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X1: $i] :
( ( in @ X1 @ sK0 )
= $true )
=> ( $true
= ( in @ sK1 @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( emptysetE = $true )
& ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i] :
( ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) )
=> ( ( nonempty @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( emptysetE
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( emptysetE
=> ! [X2: $i] :
( ? [X0: $i] : ( in @ X0 @ X2 )
=> ( nonempty @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( emptysetE
=> ! [X2: $i] :
( ? [X0: $i] : ( in @ X0 @ X2 )
=> ( nonempty @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',nonemptyI1) ).
thf(f17,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f42,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f5,f35]) ).
thf(f35,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl2_2
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f5,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f36,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f34,f31]) ).
thf(f29,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true = X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true
= ( ^ [Y0: $o] : Y0
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( ( !! @ $o
@ ^ [Y0: $o] : Y0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f15]) ).
thf(f15,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',emptysetE) ).
thf(f19,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU511^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.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 12:25:14 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
% 0.26/0.50 ---- Original DTF file ---
% 0.26/0.50 thf(spec,logic,$$dhol).
% 0.26/0.50 %------------------------------------------------------------------------------
% 0.26/0.50 % File : SEU511^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.50 % Domain : Set Theory
% 0.26/0.50 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.26/0.50 % Version : Especial > Reduced > Especial.
% 0.26/0.50 % English : (! A:i.(? x:i.in x A) -> nonempty A)
% 0.26/0.50
% 0.26/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.50 % Source : [Bro08]
% 0.26/0.50 % Names : ZFC013l [Bro08]
% 0.26/0.50
% 0.26/0.50 % Status : Theorem
% 0.26/0.50 % Rating : 0.00 v9.0.0, 0.10 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
% 0.26/0.50 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.26/0.50 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.26/0.50 % Maximal formula atoms : 3 ( 3 avg)
% 0.26/0.50 % Number of connectives : 9 ( 1 ~; 0 |; 0 &; 5 @)
% 0.26/0.50 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.26/0.50 % Maximal formula depth : 7 ( 3 avg)
% 0.26/0.50 % Number of types : 2 ( 0 usr)
% 0.26/0.50 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.26/0.50 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.26/0.50 % Number of variables : 5 ( 1 ^; 3 !; 1 ?; 5 :)
% 0.26/0.50 % SPC : TH0_THM_EQU_NAR
% 0.26/0.50
% 0.26/0.50 % Comments : http://mathgate.info/detsetitem.php?id=431
% 0.26/0.50 %------------------------------------------------------------------------------
% 0.26/0.50 thf(in_type,type,
% 0.26/0.50 in: $i > $i > $o ).
% 0.26/0.50
% 0.26/0.50 thf(emptyset_type,type,
% 0.26/0.50 emptyset: $i ).
% 0.26/0.50
% 0.26/0.50 thf(emptysetE_type,type,
% 0.26/0.50 emptysetE: $o ).
% 0.26/0.50
% 0.26/0.50 thf(emptysetE,definition,
% 0.26/0.50 ( emptysetE
% 0.26/0.50 = ( ! [Xx: $i] :
% 0.26/0.50 ( ( in @ Xx @ emptyset )
% 0.26/0.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.26/0.50
% 0.26/0.50 thf(nonempty_type,type,
% 0.26/0.50 nonempty: $i > $o ).
% 0.26/0.50
% 0.26/0.50 thf(nonempty,definition,
% 0.26/0.50 ( nonempty
% 0.26/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.26/0.50
% 0.26/0.50 thf(nonemptyI1,conjecture,
% 0.26/0.50 ( emptysetE
% 0.26/0.50 => ! [A: $i] :
% 0.26/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.26/0.50 => ( nonempty @ A ) ) ) ).
% 0.26/0.50
% 0.26/0.50 %------------------------------------------------------------------------------
% 0.26/0.50 ------------------------
% 1.62/1.43 ---- Embedded in THF ---
% 1.62/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.43 %%% Generated on Tue Feb 24 12:25:15 EST 2026
% 1.62/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.43 %%% Logic specification used:
% 1.62/1.43 %%% thf(spec, logic, $$dhol).
% 1.62/1.43
% 1.62/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2DTF28719.p
% See solution above
% 1.62/1.43 ------------------------
% 1.62/1.44 ---- Cleaned THF ---
% 1.62/1.44 thf(in_type,type,
% 1.62/1.44 in: $i > $i > $o ).
% 1.62/1.44
% 1.62/1.44 thf(emptyset_type,type,
% 1.62/1.44 emptyset: $i ).
% 1.62/1.44
% 1.62/1.44 thf(emptysetE_type,type,
% 1.62/1.44 emptysetE: $o ).
% 1.62/1.44
% 1.62/1.44 thf(emptysetE,definition,
% 1.62/1.44 ( emptysetE
% 1.62/1.44 = ( ! [Xx: $i] :
% 1.62/1.44 ( ( in @ Xx @ emptyset )
% 1.62/1.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.62/1.44
% 1.62/1.44 thf(nonempty_type,type,
% 1.62/1.44 nonempty: $i > $o ).
% 1.62/1.44
% 1.62/1.44 thf(nonempty,definition,
% 1.62/1.44 ( nonempty
% 1.62/1.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.62/1.44
% 1.62/1.44 thf(nonemptyI1,conjecture,
% 1.62/1.44 ( emptysetE
% 1.62/1.44 => ! [A: $i] :
% 1.62/1.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.62/1.44 => ( nonempty @ A ) ) ) ).
% 1.62/1.44 ------------------------
% 1.62/1.46 % (28861)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28719 for (3000ds/2Mi)
% 1.62/1.46 % (28860)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_28719 for (3000ds/27Mi)
% 1.62/1.46 % (28858)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28719 for (3000ds/183Mi)
% 1.62/1.46 % (28862)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_28719 for (3000ds/2Mi)
% 1.62/1.46 % (28863)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_28719 for (3000ds/275Mi)
% 1.62/1.46 % (28859)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_28719 for (3000ds/4Mi)
% 1.62/1.46 % (28864)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28719 for (3000ds/18Mi)
% 1.62/1.46 % (28861)Instruction limit reached!
% 1.62/1.46 % (28861)------------------------------
% 1.62/1.46 % (28861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (28861)Termination reason: Unknown
% 1.62/1.46 % (28861)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (28861)Memory used [KB]: 5373
% 1.62/1.46 % (28861)Time elapsed: 0.003 s
% 1.62/1.46 % (28861)Instructions burned: 2 (million)
% 1.62/1.46 % (28861)------------------------------
% 1.62/1.46 % (28861)------------------------------
% 1.62/1.46 % (28862)Instruction limit reached!
% 1.62/1.46 % (28862)------------------------------
% 1.62/1.46 % (28862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (28862)Termination reason: Unknown
% 1.62/1.46 % (28862)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (28862)Memory used [KB]: 5500
% 1.62/1.46 % (28862)Time elapsed: 0.003 s
% 1.62/1.46 % (28862)Instructions burned: 2 (million)
% 1.62/1.46 % (28862)------------------------------
% 1.62/1.46 % (28862)------------------------------
% 1.62/1.46 % (28863)Refutation not found, incomplete strategy
% 1.62/1.46 % (28863)------------------------------
% 1.62/1.46 % (28863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (28863)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.46
% 1.62/1.46
% 1.62/1.46 % (28863)Memory used [KB]: 5500
% 1.62/1.46 % (28863)Time elapsed: 0.003 s
% 1.62/1.46 % (28863)Instructions burned: 2 (million)
% 1.62/1.46 % (28863)------------------------------
% 1.62/1.46 % (28863)------------------------------
% 1.62/1.46 % (28860)First to succeed.
% 1.62/1.46 % (28858)Also succeeded, but the first one will report.
% 1.62/1.46 % (28860)Refutation found. Thanks to Tanya!
% 1.62/1.46 % SZS status Theorem for DTF2THF_28719
% 1.62/1.46 % SZS output start Proof for DTF2THF_28719
% 1.62/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.62/1.46 thf(func_def_4, type, nonempty: $i > $o).
% 1.62/1.46 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.46 thf(f47,plain,(
% 1.62/1.46 $false),
% 1.62/1.46 inference(avatar_sat_refutation,[status(thm)],[f36,f42,f46])).
% 1.62/1.46 thf(f46,plain,(
% 1.62/1.46 ~spl2_1),
% 1.62/1.46 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.62/1.46 thf(f45,plain,(
% 1.62/1.46 $false | ~spl2_1),
% 1.62/1.46 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.62/1.46 thf(f44,plain,(
% 1.62/1.46 ($true = $false) | ~spl2_1),
% 1.62/1.46 inference(forward_demodulation,[status(thm)],[f43,f32])).
% 1.62/1.46 thf(f32,plain,(
% 1.62/1.46 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) ) | ~spl2_1),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.62/1.46 thf(f31,definition,(
% 1.62/1.46 spl2_1 <=> ! [X1 : $i] : ((in @ X1 @ emptyset) = $false)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.62/1.46 thf(f43,plain,(
% 1.62/1.46 ((in @ sK1 @ emptyset) = $true)),
% 1.62/1.46 inference(forward_demodulation,[status(thm)],[f17,f24])).
% 1.62/1.46 thf(f24,plain,(
% 1.62/1.46 (emptyset = sK0)),
% 1.62/1.46 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.62/1.46 thf(f23,plain,(
% 1.62/1.46 ((emptyset = sK0) = $true)),
% 1.62/1.46 inference(not_proxy_clausification,[status(thm)],[f22])).
% 1.62/1.46 thf(f22,plain,(
% 1.62/1.46 ($true != (~ (emptyset = sK0)))),
% 1.62/1.46 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.62/1.46 thf(f21,plain,(
% 1.62/1.46 (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK0) != $true)),
% 1.62/1.46 inference(definition_unfolding,[status(thm)],[f18,f16])).
% 1.62/1.46 thf(f16,plain,(
% 1.62/1.46 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f6])).
% 1.62/1.46 thf(f6,plain,(
% 1.62/1.46 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f2])).
% 1.62/1.46 thf(f2,axiom,(
% 1.62/1.46 (nonempty = (^[X0 : $i] : ((emptyset != X0))))),
% 1.62/1.46 file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',nonempty)).
% 1.62/1.46 thf(f18,plain,(
% 1.62/1.46 ($true != (nonempty @ sK0))),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.46 thf(f14,plain,(
% 1.62/1.46 (emptysetE = $true) & (($true != (nonempty @ sK0)) & ($true = (in @ sK1 @ sK0)))),
% 1.62/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13,f12])).
% 1.62/1.46 thf(f12,plain,(
% 1.62/1.46 ? [X0 : $i] : (((nonempty @ X0) != $true) & ? [X1 : $i] : ($true = (in @ X1 @ X0))) => (($true != (nonempty @ sK0)) & ? [X1 : $i] : ((in @ X1 @ sK0) = $true))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f13,plain,(
% 1.62/1.46 ? [X1 : $i] : ((in @ X1 @ sK0) = $true) => ($true = (in @ sK1 @ sK0))),
% 1.62/1.46 introduced(definition,[],[choice_axiom])).
% 1.62/1.46 thf(f11,plain,(
% 1.62/1.46 (emptysetE = $true) & ? [X0 : $i] : (((nonempty @ X0) != $true) & ? [X1 : $i] : ($true = (in @ X1 @ X0)))),
% 1.62/1.46 inference(ennf_transformation,[status(thm)],[f8])).
% 1.62/1.46 thf(f8,plain,(
% 1.62/1.46 ~((emptysetE = $true) => ! [X0 : $i] : (? [X1 : $i] : ($true = (in @ X1 @ X0)) => ((nonempty @ X0) = $true)))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f7])).
% 1.62/1.46 thf(f7,plain,(
% 1.62/1.46 ~(emptysetE => ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 1.62/1.46 inference(rectify,[status(thm)],[f4])).
% 1.62/1.46 thf(f4,negated_conjecture,(
% 1.62/1.46 ~(emptysetE => ! [X2 : $i] : (? [X0 : $i] : (in @ X0 @ X2) => (nonempty @ X2)))),
% 1.62/1.46 inference(negated_conjecture,[status(cth)],[f3])).
% 1.62/1.46 thf(f3,conjecture,(
% 1.62/1.46 emptysetE => ! [X2 : $i] : (? [X0 : $i] : (in @ X0 @ X2) => (nonempty @ X2))),
% 1.62/1.46 file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',nonemptyI1)).
% 1.62/1.46 thf(f17,plain,(
% 1.62/1.46 ($true = (in @ sK1 @ sK0))),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.46 thf(f42,plain,(
% 1.62/1.46 ~spl2_2),
% 1.62/1.46 inference(avatar_contradiction_clause,[status(thm)],[f41])).
% 1.62/1.46 thf(f41,plain,(
% 1.62/1.46 $false | ~spl2_2),
% 1.62/1.46 inference(equality_resolution,[status(thm)],[f38])).
% 1.62/1.46 thf(f38,plain,(
% 1.62/1.46 ( ! [X0 : $o] : (($false != X0)) ) | ~spl2_2),
% 1.62/1.46 inference(superposition,[status(thm)],[f5,f35])).
% 1.62/1.46 thf(f35,plain,(
% 1.62/1.46 ( ! [X2 : $o] : (($true = X2)) ) | ~spl2_2),
% 1.62/1.46 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.62/1.46 thf(f34,definition,(
% 1.62/1.46 spl2_2 <=> ! [X2 : $o] : ($true = X2)),
% 1.62/1.46 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.62/1.46 thf(f5,plain,(
% 1.62/1.46 ($true != $false)),
% 1.62/1.46 introduced(definition,[],[fool_axiom])).
% 1.62/1.46 thf(f36,plain,(
% 1.62/1.46 spl2_1 | spl2_2),
% 1.62/1.46 inference(avatar_split_clause,[status(thm)],[f29,f34,f31])).
% 1.62/1.46 thf(f29,plain,(
% 1.62/1.46 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ emptyset) = $false) | ($true = X2)) )),
% 1.62/1.46 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.62/1.46 thf(f28,plain,(
% 1.62/1.46 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ emptyset) = $false) | ($true = ((^[Y0 : $o]: (Y0)) @ X2))) )),
% 1.62/1.46 inference(pi_clausification,[status(thm)],[f27])).
% 1.62/1.46 thf(f27,plain,(
% 1.62/1.46 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false) | ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $true)) )),
% 1.62/1.46 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.62/1.46 thf(f26,plain,(
% 1.62/1.46 ( ! [X1 : $i] : (($true = ((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))) )),
% 1.62/1.46 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.62/1.46 thf(f25,plain,(
% 1.62/1.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1) = $true)) )),
% 1.62/1.46 inference(pi_clausification,[status(thm)],[f20])).
% 1.62/1.46 thf(f20,plain,(
% 1.62/1.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) = $true)),
% 1.62/1.46 inference(definition_unfolding,[status(thm)],[f19,f15])).
% 1.62/1.46 thf(f15,plain,(
% 1.62/1.46 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.62/1.46 thf(f10,plain,(
% 1.62/1.46 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.62/1.46 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.46 thf(f9,plain,(
% 1.62/1.46 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.62/1.46 inference(rectify,[status(thm)],[f1])).
% 1.62/1.46 thf(f1,axiom,(
% 1.62/1.46 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.62/1.46 file('/export/starexec/sandbox/tmp/tmp.YLzYBW2VbW/DTF2THF_28719.p',emptysetE)).
% 1.62/1.46 thf(f19,plain,(
% 1.62/1.46 (emptysetE = $true)),
% 1.62/1.46 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.46 % SZS output end Proof for DTF2THF_28719
% 1.62/1.46 % (28860)------------------------------
% 1.62/1.46 % (28860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (28860)Termination reason: Refutation
% 1.62/1.46
% 1.62/1.46 % (28860)Memory used [KB]: 5500
% 1.62/1.46 % (28860)Time elapsed: 0.004 s
% 1.62/1.46 % (28860)Instructions burned: 2 (million)
% 1.62/1.46 % (28860)------------------------------
% 1.62/1.46 % (28860)------------------------------
% 1.62/1.46 % (28857)Success in time 0.018 s
%------------------------------------------------------------------------------