%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU563^2 : 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 : n006.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 09:35:17 AM UTC 2026
% Result : Theorem 1.53s 1.28s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 53 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 167 ( 25 ~; 8 |; 9 &; 97 @)
% ( 3 <=>; 21 =>; 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 : 13 ( 9 usr; 9 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 38 ( 15 ^; 17 !; 6 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_15,type,
sK1: $i > $i > $i ).
thf(f65,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
$true != $true,
inference(superposition,[status(thm)],[f48,f58]) ).
thf(f58,plain,
( ( in @ sK6 @ emptyset )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
= ( ( in @ sK6 @ emptyset )
=> ( in @ sK6 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( in @ Y0 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( in @ Y0 @ sK4 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ emptyset
@ sK4 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f38,f33]) ).
thf(f33,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( subset
= ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subset
= ( ^ [X1: $i,X2: $i] :
! [X0: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',subset) ).
thf(f38,plain,
( ( subset @ emptyset @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( ( subset @ emptyset @ sK4 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f29]) ).
thf(f29,plain,
( ? [X0: $i] :
( $true
!= ( subset @ emptyset @ X0 ) )
=> ( ( subset @ emptyset @ sK4 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ? [X0: $i] :
( $true
!= ( subset @ emptyset @ X0 ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i] :
( $true
!= ( subset @ emptyset @ X0 ) )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( emptysetimpfalse = $true )
=> ( ( subsetI2 = $true )
=> ! [X0: $i] :
( $true
= ( subset @ emptyset @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( emptysetimpfalse
=> ( subsetI2
=> ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( emptysetimpfalse
=> ( subsetI2
=> ! [X1: $i] : ( subset @ emptyset @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( emptysetimpfalse
=> ( subsetI2
=> ! [X1: $i] : ( subset @ emptyset @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',emptysetsubset) ).
thf(f48,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f31,f40]) ).
thf(f40,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f31,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( emptysetimpfalse = $true )
| ( ( in @ sK0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
=> ( ( in @ sK0 @ emptyset )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> $false ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',emptysetimpfalse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU563^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:27:00 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 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 : SEU563^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.27/0.46 % Version : Especial > Reduced > Especial.
% 0.27/0.46 % English : (! A:i.subset emptyset A)
% 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 : ZFC065l [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 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 9 ( 3 unt; 5 typ; 3 def)
% 0.27/0.46 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 3 ( 4 avg)
% 0.27/0.46 % Number of connectives : 20 ( 0 ~; 0 |; 0 &; 14 @)
% 0.27/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 6 ( 2 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=392
% 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(emptysetimpfalse_type,type,
% 0.27/0.46 emptysetimpfalse: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetimpfalse,definition,
% 0.27/0.46 ( emptysetimpfalse
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => $false ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subset_type,type,
% 0.27/0.46 subset: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(subset,definition,
% 0.27/0.46 ( subset
% 0.27/0.46 = ( ^ [A: $i,B: $i] :
% 0.27/0.46 ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI2_type,type,
% 0.27/0.46 subsetI2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI2,definition,
% 0.27/0.46 ( subsetI2
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) )
% 0.27/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetsubset,conjecture,
% 0.27/0.46 ( emptysetimpfalse
% 0.27/0.46 => ( subsetI2
% 0.27/0.46 => ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.53/1.24 ---- Embedded in THF ---
% 1.53/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.24 %%% Generated on Tue Feb 24 12:27:01 EST 2026
% 1.53/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.24 %%% Logic specification used:
% 1.53/1.24 %%% thf(spec, logic, $$dhol).
% 1.53/1.24
% 1.53/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2DTF26022.p
% See solution above
% 1.53/1.24 ------------------------
% 1.53/1.25 ---- Cleaned THF ---
% 1.53/1.26 thf(in_type,type,
% 1.53/1.26 in: $i > $i > $o ).
% 1.53/1.26
% 1.53/1.26 thf(emptyset_type,type,
% 1.53/1.26 emptyset: $i ).
% 1.53/1.26
% 1.53/1.26 thf(emptysetimpfalse_type,type,
% 1.53/1.26 emptysetimpfalse: $o ).
% 1.53/1.26
% 1.53/1.26 thf(emptysetimpfalse,definition,
% 1.53/1.26 ( emptysetimpfalse
% 1.53/1.26 = ( ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ emptyset )
% 1.53/1.26 => $false ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(subset_type,type,
% 1.53/1.26 subset: $i > $i > $o ).
% 1.53/1.26
% 1.53/1.26 thf(subset,definition,
% 1.53/1.26 ( subset
% 1.53/1.26 = ( ^ [A: $i,B: $i] :
% 1.53/1.26 ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ A )
% 1.53/1.26 => ( in @ Xx @ B ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(subsetI2_type,type,
% 1.53/1.26 subsetI2: $o ).
% 1.53/1.26
% 1.53/1.26 thf(subsetI2,definition,
% 1.53/1.26 ( subsetI2
% 1.53/1.26 = ( ! [A: $i,B: $i] :
% 1.53/1.26 ( ! [Xx: $i] :
% 1.53/1.26 ( ( in @ Xx @ A )
% 1.53/1.26 => ( in @ Xx @ B ) )
% 1.53/1.26 => ( subset @ A @ B ) ) ) ) ).
% 1.53/1.26
% 1.53/1.26 thf(emptysetsubset,conjecture,
% 1.53/1.26 ( emptysetimpfalse
% 1.53/1.26 => ( subsetI2
% 1.53/1.26 => ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 1.53/1.26 ------------------------
% 1.53/1.28 % (26216)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_26022 for (2999ds/2Mi)
% 1.53/1.28 % (26218)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26022 for (2999ds/18Mi)
% 1.53/1.28 % (26216)Instruction limit reached!
% 1.53/1.28 % (26216)------------------------------
% 1.53/1.28 % (26216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (26216)Termination reason: Unknown
% 1.53/1.28 % (26216)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (26216)Memory used [KB]: 5500
% 1.53/1.28 % (26216)Time elapsed: 0.003 s
% 1.53/1.28 % (26216)Instructions burned: 3 (million)
% 1.53/1.28 % (26216)------------------------------
% 1.53/1.28 % (26216)------------------------------
% 1.53/1.28 % (26214)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_26022 for (2999ds/27Mi)
% 1.53/1.28 % (26218)First to succeed.
% 1.53/1.28 % (26215)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26022 for (2999ds/2Mi)
% 1.53/1.28 % (26214)Also succeeded, but the first one will report.
% 1.53/1.28 % (26218)Refutation found. Thanks to Tanya!
% 1.53/1.28 % SZS status Theorem for DTF2THF_26022
% 1.53/1.28 % SZS output start Proof for DTF2THF_26022
% 1.53/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.53/1.28 thf(func_def_4, type, subset: $i > $i > $o).
% 1.53/1.28 thf(func_def_15, type, sK1: $i > $i > $i).
% 1.53/1.28 thf(f65,plain,(
% 1.53/1.28 $false),
% 1.53/1.28 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.53/1.28 thf(f64,plain,(
% 1.53/1.28 ($true != $true)),
% 1.53/1.28 inference(superposition,[status(thm)],[f48,f58])).
% 1.53/1.28 thf(f58,plain,(
% 1.53/1.28 ((in @ sK6 @ emptyset) = $true)),
% 1.53/1.28 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.53/1.28 thf(f56,plain,(
% 1.53/1.28 ($false = ((in @ sK6 @ emptyset) => (in @ sK6 @ sK4)))),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.53/1.28 thf(f55,plain,(
% 1.53/1.28 (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (in @ Y0 @ sK4))) @ sK6) = $false)),
% 1.53/1.28 inference(sigma_clausification,[status(thm)],[f54])).
% 1.53/1.28 thf(f54,plain,(
% 1.53/1.28 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (in @ Y0 @ sK4)))) != $true)),
% 1.53/1.28 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.53/1.28 thf(f47,plain,(
% 1.53/1.28 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))) @ emptyset @ sK4) != $true)),
% 1.53/1.28 inference(definition_unfolding,[status(thm)],[f38,f33])).
% 1.53/1.28 thf(f33,plain,(
% 1.53/1.28 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.53/1.28 thf(f14,plain,(
% 1.53/1.28 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.53/1.28 inference(fool_elimination,[status(thm)],[f13])).
% 1.53/1.28 thf(f13,plain,(
% 1.53/1.28 (subset = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))))),
% 1.53/1.28 inference(rectify,[status(thm)],[f2])).
% 1.53/1.28 thf(f2,axiom,(
% 1.53/1.28 (subset = (^[X1 : $i, X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X1) => (in @ X0 @ X2)))))),
% 1.53/1.28 file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',subset)).
% 1.53/1.28 thf(f38,plain,(
% 1.53/1.28 ((subset @ emptyset @ sK4) != $true)),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f30])).
% 1.53/1.28 thf(f30,plain,(
% 1.53/1.28 (emptysetimpfalse = $true) & (subsetI2 = $true) & ((subset @ emptyset @ sK4) != $true)),
% 1.53/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f29])).
% 1.53/1.28 thf(f29,plain,(
% 1.53/1.28 ? [X0 : $i] : ($true != (subset @ emptyset @ X0)) => ((subset @ emptyset @ sK4) != $true)),
% 1.53/1.28 introduced(definition,[],[choice_axiom])).
% 1.53/1.28 thf(f19,plain,(
% 1.53/1.28 (emptysetimpfalse = $true) & (subsetI2 = $true) & ? [X0 : $i] : ($true != (subset @ emptyset @ X0))),
% 1.53/1.28 inference(flattening,[status(thm)],[f18])).
% 1.53/1.28 thf(f18,plain,(
% 1.53/1.28 (? [X0 : $i] : ($true != (subset @ emptyset @ X0)) & (subsetI2 = $true)) & (emptysetimpfalse = $true)),
% 1.53/1.28 inference(ennf_transformation,[status(thm)],[f10])).
% 1.53/1.28 thf(f10,plain,(
% 1.53/1.28 ~((emptysetimpfalse = $true) => ((subsetI2 = $true) => ! [X0 : $i] : ($true = (subset @ emptyset @ X0))))),
% 1.53/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.53/1.28 thf(f9,plain,(
% 1.53/1.28 ~(emptysetimpfalse => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0)))),
% 1.53/1.28 inference(rectify,[status(thm)],[f5])).
% 1.53/1.28 thf(f5,negated_conjecture,(
% 1.53/1.28 ~(emptysetimpfalse => (subsetI2 => ! [X1 : $i] : (subset @ emptyset @ X1)))),
% 1.53/1.28 inference(negated_conjecture,[status(cth)],[f4])).
% 1.53/1.28 thf(f4,conjecture,(
% 1.53/1.28 emptysetimpfalse => (subsetI2 => ! [X1 : $i] : (subset @ emptyset @ X1))),
% 1.53/1.28 file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',emptysetsubset)).
% 1.53/1.28 thf(f48,plain,(
% 1.53/1.28 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true)) )),
% 1.53/1.28 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.53/1.28 thf(f42,plain,(
% 1.53/1.28 ( ! [X1 : $i] : (($true != $true) | ((in @ X1 @ emptyset) != $true)) )),
% 1.53/1.28 inference(definition_unfolding,[status(thm)],[f31,f40])).
% 1.53/1.28 thf(f40,plain,(
% 1.53/1.28 (emptysetimpfalse = $true)),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f30])).
% 1.53/1.28 thf(f31,plain,(
% 1.53/1.28 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true)) )),
% 1.53/1.28 inference(cnf_transformation,[status(thm)],[f23])).
% 1.53/1.28 thf(f23,plain,(
% 1.53/1.28 ((emptysetimpfalse = $true) | ((in @ sK0 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.53/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22])).
% 1.53/1.28 thf(f22,plain,(
% 1.53/1.28 ? [X0 : $i] : ((in @ X0 @ emptyset) = $true) => ((in @ sK0 @ emptyset) = $true)),
% 1.53/1.28 introduced(definition,[],[choice_axiom])).
% 1.53/1.28 thf(f21,plain,(
% 1.53/1.28 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.53/1.28 inference(rectify,[status(thm)],[f20])).
% 1.53/1.28 thf(f20,plain,(
% 1.53/1.28 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.53/1.28 inference(nnf_transformation,[status(thm)],[f16])).
% 1.53/1.28 thf(f16,plain,(
% 1.53/1.28 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.53/1.28 inference(flattening,[status(thm)],[f15])).
% 1.53/1.28 thf(f15,plain,(
% 1.53/1.28 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true)),
% 1.53/1.28 inference(true_and_false_elimination,[status(thm)],[f8])).
% 1.53/1.28 thf(f8,plain,(
% 1.53/1.28 (emptysetimpfalse = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => $false)),
% 1.53/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.53/1.28 thf(f7,plain,(
% 1.53/1.28 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 1.53/1.28 inference(rectify,[status(thm)],[f1])).
% 1.53/1.28 thf(f1,axiom,(
% 1.53/1.28 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 1.53/1.28 file('/export/starexec/sandbox/tmp/tmp.683CnwDC6m/DTF2THF_26022.p',emptysetimpfalse)).
% 1.53/1.28 % SZS output end Proof for DTF2THF_26022
% 1.53/1.28 % (26218)------------------------------
% 1.53/1.28 % (26218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (26218)Termination reason: Refutation
% 1.53/1.28
% 1.53/1.28 % (26218)Memory used [KB]: 5500
% 1.53/1.28 % (26218)Time elapsed: 0.005 s
% 1.53/1.28 % (26218)Instructions burned: 3 (million)
% 1.53/1.28 % (26218)------------------------------
% 1.53/1.28 % (26218)------------------------------
% 1.53/1.28 % (26211)Success in time 0.02 s
%------------------------------------------------------------------------------