%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU746^2 : 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 : n020.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 09:36:52 AM UTC 2026
% Result : Theorem 1.49s 1.26s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 466 ( 119 equ; 0 cnn)
% Maximal formula atoms : 18 ( 12 avg)
% Number of connectives : 543 ( 36 ~; 41 |; 51 &; 347 @)
% ( 3 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 12 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 18 ^; 44 !; 25 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f41,f46,f47,f53]) ).
thf(f53,plain,
( spl5_3
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f50,f34,f43]) ).
thf(f43,definition,
( spl5_3
<=> ( ( in @ sK4 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f34,definition,
( spl5_1
<=> ( $true
= ( in @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( in @ sK4 @ sK2 ) )
| ( ( in @ sK4 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( in @ sK4 @ sK1 )
= $true )
| ( $false = $true )
| ( $true
= ( in @ sK4 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f32,f15]) ).
thf(f15,plain,
( $true
= ( in @ sK4 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( binunionE = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK4 @ sK0 ) )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK4 @ sK2 ) ) )
& ( $true != sK3 )
& ( ( $true = sK3 )
| ( ( in @ sK4 @ sK1 )
!= $true ) )
& ( $true
= ( in @ sK4 @ ( binunion @ sK1 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $o,X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X4 @ ( binunion @ X1 @ X2 ) ) ) ) ) )
=> ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X4: $i,X3: $o] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK1 ) ) )
& ( $true
= ( in @ X4 @ ( binunion @ sK1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK0 ) )
= $true )
& ? [X4: $i,X3: $o] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK1 ) ) )
& ( $true
= ( in @ X4 @ ( binunion @ sK1 @ X2 ) ) ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ? [X4: $i,X3: $o] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK1 ) ) )
& ( ( in @ X4 @ ( binunion @ sK1 @ sK2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X4: $i,X3: $o] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ sK1 ) ) )
& ( ( in @ X4 @ ( binunion @ sK1 @ sK2 ) )
= $true ) )
=> ( ( $true
= ( in @ sK4 @ sK0 ) )
& ( ( $true = sK3 )
| ( $true
!= ( in @ sK4 @ sK2 ) ) )
& ( $true != sK3 )
& ( ( $true = sK3 )
| ( ( in @ sK4 @ sK1 )
!= $true ) )
& ( $true
= ( in @ sK4 @ ( binunion @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( binunionE = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $o,X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X4 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $o,X4: $i] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X2 ) ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X4 @ ( binunion @ X1 @ X2 ) ) )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( binunionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $o,X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( $true
= ( in @ X4 @ ( binunion @ X1 @ X2 ) ) )
=> ( ( ( $true
= ( in @ X4 @ X1 ) )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X4 @ X2 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ( ( ( in @ X2 @ X3 )
=> X5 )
=> ( ( ( in @ X2 @ X4 )
=> X5 )
=> X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X5: $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ( ( ( in @ X2 @ X3 )
=> X5 )
=> ( ( ( in @ X2 @ X4 )
=> X5 )
=> X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxDWzRysx/DTF2THF_9267.p',binunionTE) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( $true
= ( in @ X3 @ X1 ) )
| ( ( in @ X3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( ( ( in @ X3 @ X1 )
| ( in @ X3 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ X3 @ X1 )
| ( in @ X3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ Y0 @ X1 )
| ( in @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ Y0 @ X1 )
| ( in @ Y0 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ Y0 @ X1 ) )
=> ( ( in @ Y1 @ X1 )
| ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ Y0 @ X1 ) )
=> ( ( in @ Y1 @ X1 )
| ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ Y2 @ Y0 )
| ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ Y2 @ Y0 )
| ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f22]) ).
thf(f22,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f23,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ Y2 @ Y0 )
| ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ Y2 @ Y0 )
| ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ X0 @ X1 )
| ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionE
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxDWzRysx/DTF2THF_9267.p',binunionE) ).
thf(f47,plain,
~ spl5_2,
inference(avatar_split_clause,[status(thm)],[f17,f38]) ).
thf(f38,definition,
( spl5_2
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f17,plain,
$true != sK3,
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f46,plain,
( ~ spl5_3
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f16,f38,f43]) ).
thf(f16,plain,
( ( $true = sK3 )
| ( ( in @ sK4 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f41,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f38,f34]) ).
thf(f18,plain,
( ( $true = sK3 )
| ( $true
!= ( in @ sK4 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU746^2 : 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
% 0.15/0.34 % Computer : n020.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 12:32:27 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
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEU746^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Set Theory
% 0.26/0.47 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.26/0.47 % Version : Especial > Reduced > Especial.
% 0.26/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.26/0.47 % (! phi:o.! x:i.in x A -> in x (binunion X Y) ->
% 0.26/0.47 % (in x X -> phi) -> (in x Y -> phi) -> phi)))
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.47 % Source : [Bro08]
% 0.26/0.47 % Names : ZFC248l [Bro08]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % 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 v4.1.0, 0.00 v3.7.0
% 0.26/0.47 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.26/0.47 % Number of atoms : 12 ( 1 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 7 ( 6 avg)
% 0.26/0.47 % Number of connectives : 35 ( 0 ~; 1 |; 0 &; 24 @)
% 0.26/0.47 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 16 ( 9 avg)
% 0.26/0.47 % Number of types : 2 ( 0 usr)
% 0.26/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.26/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : http://mathgate.info/detsetitem.php?id=308
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(in_type,type,
% 0.26/0.47 in: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(powerset_type,type,
% 0.26/0.47 powerset: $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(binunion_type,type,
% 0.26/0.47 binunion: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(binunionE_type,type,
% 0.26/0.47 binunionE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionE,definition,
% 0.26/0.47 ( binunionE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionTE,conjecture,
% 0.26/0.47 ( binunionE
% 0.26/0.47 => ! [A: $i,X: $i] :
% 0.26/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.47 => ! [Y: $i] :
% 0.26/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.47 => ( ( ( in @ Xx @ X )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => ( ( ( in @ Xx @ Y )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => Xphi ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 12:32:28 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.EoxDWzRysx/DTF2DTF9267.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.24 ---- Cleaned THF ---
% 1.49/1.25 thf(in_type,type,
% 1.49/1.25 in: $i > $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(powerset_type,type,
% 1.49/1.25 powerset: $i > $i ).
% 1.49/1.25
% 1.49/1.25 thf(binunion_type,type,
% 1.49/1.25 binunion: $i > $i > $i ).
% 1.49/1.25
% 1.49/1.25 thf(binunionE_type,type,
% 1.49/1.25 binunionE: $o ).
% 1.49/1.25
% 1.49/1.25 thf(binunionE,definition,
% 1.49/1.25 ( binunionE
% 1.49/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.49/1.25 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.49/1.25 => ( ( in @ Xx @ A )
% 1.49/1.25 | ( in @ Xx @ B ) ) ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(binunionTE,conjecture,
% 1.49/1.25 ( binunionE
% 1.49/1.25 => ! [A: $i,X: $i] :
% 1.49/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.49/1.25 => ! [Y: $i] :
% 1.49/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.49/1.25 => ! [Xphi: $o,Xx: $i] :
% 1.49/1.25 ( ( in @ Xx @ A )
% 1.49/1.25 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.49/1.25 => ( ( ( in @ Xx @ X )
% 1.49/1.25 => Xphi )
% 1.49/1.25 => ( ( ( in @ Xx @ Y )
% 1.49/1.25 => Xphi )
% 1.49/1.25 => Xphi ) ) ) ) ) ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (9569)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_9267 for (2999ds/27Mi)
% 1.49/1.26 % (9568)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_9267 for (2999ds/4Mi)
% 1.49/1.26 % (9569)First to succeed.
% 1.49/1.26 % (9568)Instruction limit reached!
% 1.49/1.26 % (9568)------------------------------
% 1.49/1.26 % (9568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (9568)Termination reason: Unknown
% 1.49/1.26 % (9568)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (9568)Memory used [KB]: 5500
% 1.49/1.26 % (9568)Time elapsed: 0.003 s
% 1.49/1.26 % (9568)Instructions burned: 4 (million)
% 1.49/1.26 % (9568)------------------------------
% 1.49/1.26 % (9568)------------------------------
% 1.49/1.26 % (9569)Refutation found. Thanks to Tanya!
% 1.49/1.26 % SZS status Theorem for DTF2THF_9267
% 1.49/1.26 % SZS output start Proof for DTF2THF_9267
% 1.49/1.26 thf(func_def_0, type, in: $i > $i > $o).
% 1.49/1.26 thf(func_def_1, type, powerset: $i > $i).
% 1.49/1.26 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.49/1.26 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.26 thf(f54,plain,(
% 1.49/1.26 $false),
% 1.49/1.26 inference(avatar_sat_refutation,[status(thm)],[f41,f46,f47,f53])).
% 1.49/1.26 thf(f53,plain,(
% 1.49/1.26 spl5_3 | spl5_1),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f50,f34,f43])).
% 1.49/1.26 thf(f43,definition,(
% 1.49/1.26 spl5_3 <=> ((in @ sK4 @ sK1) = $true)),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.49/1.26 thf(f34,definition,(
% 1.49/1.26 spl5_1 <=> ($true = (in @ sK4 @ sK2))),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.49/1.26 thf(f50,plain,(
% 1.49/1.26 ($true = (in @ sK4 @ sK2)) | ((in @ sK4 @ sK1) = $true)),
% 1.49/1.26 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.49/1.26 thf(f48,plain,(
% 1.49/1.26 ((in @ sK4 @ sK1) = $true) | ($false = $true) | ($true = (in @ sK4 @ sK2))),
% 1.49/1.26 inference(superposition,[status(thm)],[f32,f15])).
% 1.49/1.26 thf(f15,plain,(
% 1.49/1.26 ($true = (in @ sK4 @ (binunion @ sK1 @ sK2)))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.26 thf(f14,plain,(
% 1.49/1.26 (binunionE = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & (($true = (in @ sK2 @ (powerset @ sK0))) & (($true = (in @ sK4 @ sK0)) & (($true = sK3) | ($true != (in @ sK4 @ sK2))) & ($true != sK3) & (($true = sK3) | ((in @ sK4 @ sK1) != $true)) & ($true = (in @ sK4 @ (binunion @ sK1 @ sK2))))))),
% 1.49/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f13,f12,f11])).
% 1.49/1.26 thf(f11,plain,(
% 1.49/1.26 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $o,X4 : $i] : (((in @ X4 @ X0) = $true) & (($true = X3) | ($true != (in @ X4 @ X2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ X1))) & ($true = (in @ X4 @ (binunion @ X1 @ X2)))))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X4 : $i,X3 : $o] : (($true = (in @ X4 @ sK0)) & (($true = X3) | ($true != (in @ X4 @ X2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ sK1))) & ($true = (in @ X4 @ (binunion @ sK1 @ X2))))))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f12,plain,(
% 1.49/1.26 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X4 : $i,X3 : $o] : (($true = (in @ X4 @ sK0)) & (($true = X3) | ($true != (in @ X4 @ X2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ sK1))) & ($true = (in @ X4 @ (binunion @ sK1 @ X2))))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X4 : $i,X3 : $o] : (($true = (in @ X4 @ sK0)) & (($true = X3) | ($true != (in @ X4 @ sK2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ sK1))) & ((in @ X4 @ (binunion @ sK1 @ sK2)) = $true)))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f13,plain,(
% 1.49/1.26 ? [X4 : $i,X3 : $o] : (($true = (in @ X4 @ sK0)) & (($true = X3) | ($true != (in @ X4 @ sK2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ sK1))) & ((in @ X4 @ (binunion @ sK1 @ sK2)) = $true)) => (($true = (in @ sK4 @ sK0)) & (($true = sK3) | ($true != (in @ sK4 @ sK2))) & ($true != sK3) & (($true = sK3) | ((in @ sK4 @ sK1) != $true)) & ($true = (in @ sK4 @ (binunion @ sK1 @ sK2))))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f10,plain,(
% 1.49/1.26 (binunionE = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $o,X4 : $i] : (((in @ X4 @ X0) = $true) & (($true = X3) | ($true != (in @ X4 @ X2))) & ($true != X3) & (($true = X3) | ($true != (in @ X4 @ X1))) & ($true = (in @ X4 @ (binunion @ X1 @ X2))))))),
% 1.49/1.26 inference(flattening,[status(thm)],[f9])).
% 1.49/1.26 thf(f9,plain,(
% 1.49/1.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $o,X4 : $i] : ((((($true != X3) & (($true = X3) | ($true != (in @ X4 @ X2)))) & (($true = X3) | ($true != (in @ X4 @ X1)))) & ($true = (in @ X4 @ (binunion @ X1 @ X2)))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionE = $true)),
% 1.49/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.26 thf(f6,plain,(
% 1.49/1.26 ~((binunionE = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $o,X4 : $i] : (((in @ X4 @ X0) = $true) => (($true = (in @ X4 @ (binunion @ X1 @ X2))) => ((($true = (in @ X4 @ X1)) => ($true = X3)) => ((($true = (in @ X4 @ X2)) => ($true = X3)) => ($true = X3))))))))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.26 thf(f5,plain,(
% 1.49/1.26 ~(binunionE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $o,X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binunion @ X1 @ X2)) => (((in @ X4 @ X1) => X3) => (((in @ X4 @ X2) => X3) => X3)))))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f3])).
% 1.49/1.26 thf(f3,negated_conjecture,(
% 1.49/1.26 ~(binunionE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $o,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ X3 @ X4)) => (((in @ X2 @ X3) => X5) => (((in @ X2 @ X4) => X5) => X5)))))))),
% 1.49/1.26 inference(negated_conjecture,[status(cth)],[f2])).
% 1.49/1.26 thf(f2,conjecture,(
% 1.49/1.26 binunionE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X5 : $o,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ X3 @ X4)) => (((in @ X2 @ X3) => X5) => (((in @ X2 @ X4) => X5) => X5))))))),
% 1.49/1.26 file('/export/starexec/sandbox/tmp/tmp.EoxDWzRysx/DTF2THF_9267.p',binunionTE)).
% 1.49/1.26 thf(f32,plain,(
% 1.49/1.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X2 @ X1)) = $false) | ($true = (in @ X3 @ X1)) | ((in @ X3 @ X2) = $true)) )),
% 1.49/1.26 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.49/1.26 thf(f31,plain,(
% 1.49/1.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X2 @ X1)) = $false) | (((in @ X3 @ X1) | (in @ X3 @ X2)) = $true)) )),
% 1.49/1.26 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.49/1.26 thf(f30,plain,(
% 1.49/1.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (binunion @ X2 @ X1)) => ((in @ X3 @ X1) | (in @ X3 @ X2))))) )),
% 1.49/1.26 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.49/1.26 thf(f29,plain,(
% 1.49/1.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (binunion @ X2 @ X1)) => ((in @ Y0 @ X1) | (in @ Y0 @ X2)))) @ X3))) )),
% 1.49/1.26 inference(pi_clausification,[status(thm)],[f28])).
% 1.49/1.26 thf(f28,plain,(
% 1.49/1.26 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binunion @ X2 @ X1)) => ((in @ Y0 @ X1) | (in @ Y0 @ X2))))) = $true)) )),
% 1.49/1.26 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.49/1.26 thf(f27,plain,(
% 1.49/1.26 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binunion @ Y0 @ X1)) => ((in @ Y1 @ X1) | (in @ Y1 @ Y0)))))) @ X2))) )),
% 1.49/1.26 inference(pi_clausification,[status(thm)],[f26])).
% 1.49/1.26 thf(f26,plain,(
% 1.49/1.26 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binunion @ Y0 @ X1)) => ((in @ Y1 @ X1) | (in @ Y1 @ Y0))))))) = $true)) )),
% 1.49/1.26 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.49/1.26 thf(f25,plain,(
% 1.49/1.26 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1)))))))) @ X1) = $true)) )),
% 1.49/1.26 inference(pi_clausification,[status(thm)],[f24])).
% 1.49/1.26 thf(f24,plain,(
% 1.49/1.26 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1))))))))))),
% 1.49/1.26 inference(definition_unfolding,[status(thm)],[f23,f22])).
% 1.49/1.26 thf(f22,plain,(
% 1.49/1.26 (binunionE = $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.26 thf(f23,plain,(
% 1.49/1.26 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1))))))))))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.26 thf(f8,plain,(
% 1.49/1.26 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y0) | (in @ Y2 @ Y1))))))))))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f7])).
% 1.49/1.26 thf(f7,plain,(
% 1.49/1.26 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binunion @ X1 @ X2)) => ((in @ X0 @ X1) | (in @ X0 @ X2))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f1])).
% 1.49/1.26 thf(f1,axiom,(
% 1.49/1.26 (binunionE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1))))),
% 1.49/1.26 file('/export/starexec/sandbox/tmp/tmp.EoxDWzRysx/DTF2THF_9267.p',binunionE)).
% 1.49/1.26 thf(f47,plain,(
% 1.49/1.26 ~spl5_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f17,f38])).
% 1.49/1.26 thf(f38,definition,(
% 1.49/1.26 spl5_2 <=> ($true = sK3)),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.49/1.26 thf(f17,plain,(
% 1.49/1.26 ($true != sK3)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.26 thf(f46,plain,(
% 1.49/1.26 ~spl5_3 | spl5_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f16,f38,f43])).
% 1.49/1.26 thf(f16,plain,(
% 1.49/1.26 ($true = sK3) | ((in @ sK4 @ sK1) != $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.26 thf(f41,plain,(
% 1.49/1.26 ~spl5_1 | spl5_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f18,f38,f34])).
% 1.49/1.26 thf(f18,plain,(
% 1.49/1.26 ($true = sK3) | ($true != (in @ sK4 @ sK2))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.26 % SZS output end Proof for DTF2THF_9267
% 1.49/1.26 % (9569)------------------------------
% 1.49/1.26 % (9569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (9569)Termination reason: Refutation
% 1.49/1.26
% 1.49/1.26 % (9569)Memory used [KB]: 5500
% 1.49/1.26 % (9569)Time elapsed: 0.004 s
% 1.49/1.26 % (9569)Instructions burned: 3 (million)
% 1.49/1.26 % (9569)------------------------------
% 1.49/1.26 % (9569)------------------------------
% 1.49/1.26 % (9566)Success in time 0.014 s
%------------------------------------------------------------------------------