%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU519^2 : 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 : n023.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 09:35:03 AM UTC 2026
% Result : Theorem 1.64s 1.46s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 409 ( 117 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 351 ( 60 ~; 42 |; 28 &; 193 @)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 79 ( 0 ^; 58 !; 21 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_8,type,
sK0: $i > $i > $i ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f58,f65]) ).
thf(f65,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true != $true )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f37,f50]) ).
thf(f50,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl6_1
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f37,plain,
( ( in @ emptyset @ ( powerset @ sK5 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( in @ emptyset @ ( powerset @ sK5 ) )
!= $true )
& ( powersetI = $true )
& ( emptysetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f13,f26]) ).
thf(f26,plain,
( ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $true )
=> ( ( in @ emptyset @ ( powerset @ sK5 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $true )
& ( powersetI = $true )
& ( emptysetE = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
!= $true )
& ( powersetI = $true )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( emptysetE = $true )
=> ( ( powersetI = $true )
=> ! [X0: $i] :
( ( in @ emptyset @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( emptysetE
=> ( powersetI
=> ! [X0: $i] : ( in @ emptyset @ ( powerset @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [X2: $i] : ( in @ emptyset @ ( powerset @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( emptysetE
=> ( powersetI
=> ! [X2: $i] : ( in @ emptyset @ ( powerset @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2THF_14527.p',emptyinPowerset) ).
thf(f58,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f56,f53]) ).
thf(f53,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl6_2
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f56,plain,
( ( in @ ( sK0 @ sK5 @ emptyset ) @ emptyset )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( in @ ( sK0 @ sK5 @ emptyset ) @ emptyset )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f37,f46]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f30,f36]) ).
thf(f36,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f30,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ( ! [X5: $i] :
( ( ( in @ X5 @ sK2 )
= $true )
| ( ( in @ X5 @ sK1 )
!= $true ) )
& ( ( in @ sK1 @ ( powerset @ sK2 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18]) ).
thf(f18,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK0 @ X1 @ X0 ) @ X1 )
!= $true )
& ( ( in @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) )
& ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ sK2 )
= $true )
| ( ( in @ X5 @ sK1 )
!= $true ) )
& ( ( in @ sK1 @ ( powerset @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
!= $true ) )
& ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( powersetI
= ( ! [X2: $i,X3: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X3 )
=> ( in @ X0 @ X2 ) )
=> ( in @ X3 @ ( powerset @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2THF_14527.p',powersetI) ).
thf(f54,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f45,f52,f49]) ).
thf(f45,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( $true != $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f34,f35]) ).
thf(f35,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f34,plain,
! [X0: $i,X1: $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true = X1 )
| ( emptysetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ( ( ( in @ sK3 @ emptyset )
= $true )
& ( sK4 != $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f22,f24,f23]) ).
thf(f23,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ emptyset )
= $true )
& ? [X3: $o] : ( $true != X3 ) )
=> ( ( ( in @ sK3 @ emptyset )
= $true )
& ? [X3: $o] : ( $true != X3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X3: $o] : ( $true != X3 )
=> ( sK4 != $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X2: $i] :
( ( ( in @ X2 @ emptyset )
= $true )
& ? [X3: $o] : ( $true != X3 ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,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.h54HfvHfx3/DTF2THF_14527.p',emptysetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU519^2 : 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 : n023.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 12:26:04 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU519^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Preliminary Notions - Power Sets and Unions
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! A:i.in emptyset (powerset A))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC021l [Bro08]
% 0.19/0.47 % : ZFC022l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % 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
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.47 % Number of atoms : 11 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.47 % Number of connectives : 17 ( 0 ~; 0 |; 0 &; 12 @)
% 0.19/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 6 ( 3 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : http://mathgate.info/detsetitem.php?id=389
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(in_type,type,
% 0.19/0.48 in: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(emptyset_type,type,
% 0.19/0.48 emptyset: $i ).
% 0.19/0.48
% 0.19/0.48 thf(powerset_type,type,
% 0.19/0.48 powerset: $i > $i ).
% 0.19/0.48
% 0.19/0.48 thf(emptysetE_type,type,
% 0.19/0.48 emptysetE: $o ).
% 0.19/0.48
% 0.19/0.48 thf(emptysetE,definition,
% 0.19/0.48 ( emptysetE
% 0.19/0.48 = ( ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ emptyset )
% 0.19/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(powersetI_type,type,
% 0.19/0.48 powersetI: $o ).
% 0.19/0.48
% 0.19/0.48 thf(powersetI,definition,
% 0.19/0.48 ( powersetI
% 0.19/0.48 = ( ! [A: $i,B: $i] :
% 0.19/0.48 ( ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ B )
% 0.19/0.48 => ( in @ Xx @ A ) )
% 0.19/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(emptyinPowerset,conjecture,
% 0.19/0.48 ( emptysetE
% 0.19/0.48 => ( powersetI
% 0.19/0.48 => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.64/1.42 ---- Embedded in THF ---
% 1.64/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.42 %%% Generated on Tue Feb 24 12:26:05 EST 2026
% 1.64/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.42 %%% Logic specification used:
% 1.64/1.42 %%% thf(spec, logic, $$dhol).
% 1.64/1.42
% 1.64/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2DTF14527.p
% See solution above
% 1.64/1.42 ------------------------
% 1.64/1.43 ---- Cleaned THF ---
% 1.64/1.43 thf(in_type,type,
% 1.64/1.43 in: $i > $i > $o ).
% 1.64/1.43
% 1.64/1.43 thf(emptyset_type,type,
% 1.64/1.43 emptyset: $i ).
% 1.64/1.43
% 1.64/1.43 thf(powerset_type,type,
% 1.64/1.43 powerset: $i > $i ).
% 1.64/1.43
% 1.64/1.43 thf(emptysetE_type,type,
% 1.64/1.43 emptysetE: $o ).
% 1.64/1.43
% 1.64/1.43 thf(emptysetE,definition,
% 1.64/1.43 ( emptysetE
% 1.64/1.43 = ( ! [Xx: $i] :
% 1.64/1.43 ( ( in @ Xx @ emptyset )
% 1.64/1.43 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.64/1.43
% 1.64/1.43 thf(powersetI_type,type,
% 1.64/1.43 powersetI: $o ).
% 1.64/1.43
% 1.64/1.43 thf(powersetI,definition,
% 1.64/1.43 ( powersetI
% 1.64/1.43 = ( ! [A: $i,B: $i] :
% 1.64/1.43 ( ! [Xx: $i] :
% 1.64/1.43 ( ( in @ Xx @ B )
% 1.64/1.43 => ( in @ Xx @ A ) )
% 1.64/1.43 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.64/1.43
% 1.64/1.43 thf(emptyinPowerset,conjecture,
% 1.64/1.43 ( emptysetE
% 1.64/1.43 => ( powersetI
% 1.64/1.43 => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.64/1.43 ------------------------
% 1.64/1.45 % (14628)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14527 for (3000ds/2Mi)
% 1.64/1.45 % (14625)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14527 for (3000ds/183Mi)
% 1.64/1.45 % (14626)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_14527 for (3000ds/4Mi)
% 1.64/1.45 % (14627)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_14527 for (3000ds/27Mi)
% 1.64/1.45 % (14629)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_14527 for (3000ds/2Mi)
% 1.64/1.45 % (14630)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_14527 for (3000ds/275Mi)
% 1.64/1.45 % (14631)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14527 for (3000ds/18Mi)
% 1.64/1.45 % (14628)Instruction limit reached!
% 1.64/1.45 % (14628)------------------------------
% 1.64/1.45 % (14628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (14628)Termination reason: Unknown
% 1.64/1.45 % (14628)Termination phase: Saturation
% 1.64/1.45
% 1.64/1.45 % (14629)Instruction limit reached!
% 1.64/1.45 % (14629)------------------------------
% 1.64/1.45 % (14629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (14629)Termination reason: Unknown
% 1.64/1.45 % (14629)Termination phase: Saturation
% 1.64/1.45
% 1.64/1.45 % (14629)Memory used [KB]: 5500
% 1.64/1.45 % (14629)Time elapsed: 0.003 s
% 1.64/1.45 % (14629)Instructions burned: 2 (million)
% 1.64/1.45 % (14629)------------------------------
% 1.64/1.45 % (14629)------------------------------
% 1.64/1.45 % (14628)Memory used [KB]: 5500
% 1.64/1.45 % (14628)Time elapsed: 0.003 s
% 1.64/1.45 % (14628)Instructions burned: 3 (million)
% 1.64/1.45 % (14628)------------------------------
% 1.64/1.45 % (14628)------------------------------
% 1.64/1.45 % (14626)Instruction limit reached!
% 1.64/1.45 % (14626)------------------------------
% 1.64/1.45 % (14626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (14626)Termination reason: Unknown
% 1.64/1.45 % (14626)Termination phase: Saturation
% 1.64/1.45
% 1.64/1.45 % (14626)Memory used [KB]: 5500
% 1.64/1.45 % (14626)Time elapsed: 0.004 s
% 1.64/1.45 % (14626)Instructions burned: 4 (million)
% 1.64/1.45 % (14626)------------------------------
% 1.64/1.45 % (14626)------------------------------
% 1.64/1.45 % (14631)First to succeed.
% 1.64/1.46 % (14625)Also succeeded, but the first one will report.
% 1.64/1.46 % (14631)Refutation found. Thanks to Tanya!
% 1.64/1.46 % SZS status Theorem for DTF2THF_14527
% 1.64/1.46 % SZS output start Proof for DTF2THF_14527
% 1.64/1.46 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.46 thf(func_def_2, type, powerset: $i > $i).
% 1.64/1.46 thf(func_def_8, type, sK0: $i > $i > $i).
% 1.64/1.46 thf(f66,plain,(
% 1.64/1.46 $false),
% 1.64/1.46 inference(avatar_sat_refutation,[status(thm)],[f54,f58,f65])).
% 1.64/1.46 thf(f65,plain,(
% 1.64/1.46 ~spl6_1),
% 1.64/1.46 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.64/1.46 thf(f64,plain,(
% 1.64/1.46 $false | ~spl6_1),
% 1.64/1.46 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.64/1.46 thf(f61,plain,(
% 1.64/1.46 ($true != $true) | ~spl6_1),
% 1.64/1.46 inference(superposition,[status(thm)],[f37,f50])).
% 1.64/1.46 thf(f50,plain,(
% 1.64/1.46 ( ! [X1 : $o] : (($true = X1)) ) | ~spl6_1),
% 1.64/1.46 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.64/1.46 thf(f49,definition,(
% 1.64/1.46 spl6_1 <=> ! [X1 : $o] : ($true = X1)),
% 1.64/1.46 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.64/1.46 thf(f37,plain,(
% 1.64/1.46 ((in @ emptyset @ (powerset @ sK5)) != $true)),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.46 thf(f27,plain,(
% 1.64/1.46 ((in @ emptyset @ (powerset @ sK5)) != $true) & (powersetI = $true) & (emptysetE = $true)),
% 1.64/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f13,f26])).
% 1.64/1.46 thf(f26,plain,(
% 1.64/1.46 ? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $true) => ((in @ emptyset @ (powerset @ sK5)) != $true)),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f13,plain,(
% 1.64/1.46 ? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $true) & (powersetI = $true) & (emptysetE = $true)),
% 1.64/1.46 inference(flattening,[status(thm)],[f12])).
% 1.64/1.46 thf(f12,plain,(
% 1.64/1.46 (? [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) != $true) & (powersetI = $true)) & (emptysetE = $true)),
% 1.64/1.46 inference(ennf_transformation,[status(thm)],[f7])).
% 1.64/1.46 thf(f7,plain,(
% 1.64/1.46 ~((emptysetE = $true) => ((powersetI = $true) => ! [X0 : $i] : ((in @ emptyset @ (powerset @ X0)) = $true)))),
% 1.64/1.46 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.46 thf(f6,plain,(
% 1.64/1.46 ~(emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))),
% 1.64/1.46 inference(rectify,[status(thm)],[f4])).
% 1.64/1.46 thf(f4,negated_conjecture,(
% 1.64/1.46 ~(emptysetE => (powersetI => ! [X2 : $i] : (in @ emptyset @ (powerset @ X2))))),
% 1.64/1.46 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.46 thf(f3,conjecture,(
% 1.64/1.46 emptysetE => (powersetI => ! [X2 : $i] : (in @ emptyset @ (powerset @ X2)))),
% 1.64/1.46 file('/export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2THF_14527.p',emptyinPowerset)).
% 1.64/1.46 thf(f58,plain,(
% 1.64/1.46 ~spl6_2),
% 1.64/1.46 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.64/1.46 thf(f57,plain,(
% 1.64/1.46 $false | ~spl6_2),
% 1.64/1.46 inference(subsumption_resolution,[status(thm)],[f56,f53])).
% 1.64/1.46 thf(f53,plain,(
% 1.64/1.46 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true)) ) | ~spl6_2),
% 1.64/1.46 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.64/1.46 thf(f52,definition,(
% 1.64/1.46 spl6_2 <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.64/1.46 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.64/1.46 thf(f56,plain,(
% 1.64/1.46 ((in @ (sK0 @ sK5 @ emptyset) @ emptyset) = $true)),
% 1.64/1.46 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.64/1.46 thf(f55,plain,(
% 1.64/1.46 ((in @ (sK0 @ sK5 @ emptyset) @ emptyset) = $true) | ($true != $true)),
% 1.64/1.46 inference(superposition,[status(thm)],[f37,f46])).
% 1.64/1.46 thf(f46,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) | ((in @ (sK0 @ X1 @ X0) @ X0) = $true)) )),
% 1.64/1.46 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.64/1.46 thf(f39,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) = $true) | ($true != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) )),
% 1.64/1.46 inference(definition_unfolding,[status(thm)],[f30,f36])).
% 1.64/1.46 thf(f36,plain,(
% 1.64/1.46 (powersetI = $true)),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.46 thf(f30,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) = $true) | ((in @ X0 @ (powerset @ X1)) = $true) | (powersetI != $true)) )),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.46 thf(f20,plain,(
% 1.64/1.46 (! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1) != $true) & ((in @ (sK0 @ X1 @ X0) @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | (! [X5 : $i] : (((in @ X5 @ sK2) = $true) | ((in @ X5 @ sK1) != $true)) & ((in @ sK1 @ (powerset @ sK2)) != $true)))),
% 1.64/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f19,f18])).
% 1.64/1.46 thf(f18,plain,(
% 1.64/1.46 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK0 @ X1 @ X0) @ X1) != $true) & ((in @ (sK0 @ X1 @ X0) @ X0) = $true)))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f19,plain,(
% 1.64/1.46 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) & ((in @ X3 @ (powerset @ X4)) != $true)) => (! [X5 : $i] : (((in @ X5 @ sK2) = $true) | ((in @ X5 @ sK1) != $true)) & ((in @ sK1 @ (powerset @ sK2)) != $true))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f17,plain,(
% 1.64/1.46 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) & ((in @ X3 @ (powerset @ X4)) != $true)))),
% 1.64/1.46 inference(rectify,[status(thm)],[f16])).
% 1.64/1.46 thf(f16,plain,(
% 1.64/1.46 (! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) & ((in @ X1 @ (powerset @ X0)) != $true)))),
% 1.64/1.46 inference(nnf_transformation,[status(thm)],[f15])).
% 1.64/1.46 thf(f15,plain,(
% 1.64/1.46 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI = $true)),
% 1.64/1.46 inference(ennf_transformation,[status(thm)],[f9])).
% 1.64/1.46 thf(f9,plain,(
% 1.64/1.46 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI = $true)),
% 1.64/1.46 inference(fool_elimination,[status(thm)],[f8])).
% 1.64/1.46 thf(f8,plain,(
% 1.64/1.46 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 1.64/1.46 inference(rectify,[status(thm)],[f2])).
% 1.64/1.46 thf(f2,axiom,(
% 1.64/1.46 (powersetI = ! [X2 : $i,X3 : $i] : (! [X0 : $i] : ((in @ X0 @ X3) => (in @ X0 @ X2)) => (in @ X3 @ (powerset @ X2))))),
% 1.64/1.46 file('/export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2THF_14527.p',powersetI)).
% 1.64/1.46 thf(f54,plain,(
% 1.64/1.46 spl6_1 | spl6_2),
% 1.64/1.46 inference(avatar_split_clause,[status(thm)],[f45,f52,f49])).
% 1.64/1.46 thf(f45,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ((in @ X0 @ emptyset) != $true)) )),
% 1.64/1.46 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.64/1.46 thf(f42,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ($true != $true) | ((in @ X0 @ emptyset) != $true)) )),
% 1.64/1.46 inference(definition_unfolding,[status(thm)],[f34,f35])).
% 1.64/1.46 thf(f35,plain,(
% 1.64/1.46 (emptysetE = $true)),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f27])).
% 1.64/1.46 thf(f34,plain,(
% 1.64/1.46 ( ! [X0 : $i,X1 : $o] : (((in @ X0 @ emptyset) != $true) | ($true = X1) | (emptysetE != $true)) )),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f25])).
% 1.64/1.46 thf(f25,plain,(
% 1.64/1.46 (! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | (((in @ sK3 @ emptyset) = $true) & (sK4 != $true)))),
% 1.64/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f22,f24,f23])).
% 1.64/1.46 thf(f23,plain,(
% 1.64/1.46 ? [X2 : $i] : (((in @ X2 @ emptyset) = $true) & ? [X3 : $o] : ($true != X3)) => (((in @ sK3 @ emptyset) = $true) & ? [X3 : $o] : ($true != X3))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f24,plain,(
% 1.64/1.46 ? [X3 : $o] : ($true != X3) => (sK4 != $true)),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 thf(f22,plain,(
% 1.64/1.46 (! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : (((in @ X2 @ emptyset) = $true) & ? [X3 : $o] : ($true != X3)))),
% 1.64/1.46 inference(rectify,[status(thm)],[f21])).
% 1.64/1.46 thf(f21,plain,(
% 1.64/1.46 (! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset) = $true) & ? [X1 : $o] : ($true != X1)))),
% 1.64/1.46 inference(nnf_transformation,[status(thm)],[f14])).
% 1.64/1.46 thf(f14,plain,(
% 1.64/1.46 ! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 1.64/1.46 inference(ennf_transformation,[status(thm)],[f11])).
% 1.64/1.46 thf(f11,plain,(
% 1.64/1.46 ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 1.64/1.46 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.46 thf(f10,plain,(
% 1.64/1.46 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.64/1.46 inference(rectify,[status(thm)],[f1])).
% 1.64/1.46 thf(f1,axiom,(
% 1.64/1.46 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.64/1.46 file('/export/starexec/sandbox/tmp/tmp.h54HfvHfx3/DTF2THF_14527.p',emptysetE)).
% 1.64/1.46 % SZS output end Proof for DTF2THF_14527
% 1.64/1.46 % (14631)------------------------------
% 1.64/1.46 % (14631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (14631)Termination reason: Refutation
% 1.64/1.46
% 1.64/1.46 % (14631)Memory used [KB]: 5500
% 1.64/1.46 % (14631)Time elapsed: 0.005 s
% 1.64/1.46 % (14631)Instructions burned: 4 (million)
% 1.64/1.46 % (14631)------------------------------
% 1.64/1.46 % (14631)------------------------------
% 1.64/1.46 % (14623)Success in time 0.019 s
%------------------------------------------------------------------------------