%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU747^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 1.40s 1.19s
% Output : Refutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 491 ( 130 equ; 0 cnn)
% Maximal formula atoms : 12 ( 15 avg)
% Number of connectives : 540 ( 63 ~; 30 |; 55 &; 352 @)
% ( 3 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 80 ( 0 ^; 53 !; 27 ?; 80 :)
% 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(f41,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f40,f26]) ).
thf(f26,plain,
( $true
!= ( in @ sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
!= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
!= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( binunionE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f16,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X3 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ sK1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( $true
!= ( in @ X3 @ sK1 ) ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ sK1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( $true
!= ( in @ X3 @ sK1 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ sK1 @ sK2 ) ) )
& ( ( in @ X3 @ sK2 )
!= $true )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( $true
!= ( in @ X3 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ sK1 @ sK2 ) ) )
& ( ( in @ X3 @ sK2 )
!= $true )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( $true
!= ( in @ X3 @ sK1 ) ) )
=> ( ( $true
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
!= ( in @ sK3 @ sK2 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
!= ( in @ sK3 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X3 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ X3 @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( binunionE = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
inference(flattening,[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: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( $true
!= ( in @ X3 @ X1 ) )
=> ( ( $true
!= ( in @ X3 @ X2 ) )
=> ( $true
!= ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ),
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: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionE
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RhTafZrfx8/DTF2THF_12082.p',binunionTEcontra) ).
thf(f40,plain,
( $true
= ( in @ sK3 @ sK2 ) ),
inference(subsumption_resolution,[status(thm)],[f39,f24]) ).
thf(f24,plain,
( $true
!= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f39,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( $true
= ( in @ sK3 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ( $true
= ( in @ sK3 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f37,f27]) ).
thf(f27,plain,
( $true
= ( in @ sK3 @ ( binunion @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f22]) ).
thf(f22,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( binunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( $true
!= ( in @ sK5 @ sK4 ) )
& ( $true
= ( in @ sK5 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
!= ( in @ sK5 @ sK6 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f19,f20]) ).
thf(f20,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ ( binunion @ X3 @ X5 ) ) )
& ( $true
!= ( in @ X4 @ X5 ) ) )
=> ( ( $true
!= ( in @ sK5 @ sK4 ) )
& ( $true
= ( in @ sK5 @ ( binunion @ sK4 @ sK6 ) ) )
& ( $true
!= ( in @ sK5 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X3 ) )
& ( $true
= ( in @ X4 @ ( binunion @ X3 @ X5 ) ) )
& ( $true
!= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true ) )
<=> ( binunionE = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RhTafZrfx8/DTF2THF_12082.p',binunionE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU747^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n020.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:32:57 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SEU747^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.40 % Domain : Set Theory
% 0.17/0.40 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.17/0.40 % Version : Especial > Reduced > Especial.
% 0.17/0.40 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.17/0.40 % (! x:i.in x A -> ~(in x X) -> ~(in x Y) ->
% 0.17/0.40 % ~(in x (binunion X Y)))))
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.40 % Source : [Bro08]
% 0.17/0.40 % Names : ZFC249l [Bro08]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % 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
% 0.17/0.40 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.17/0.40 % Number of atoms : 12 ( 1 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 7 ( 6 avg)
% 0.17/0.40 % Number of connectives : 35 ( 3 ~; 1 |; 0 &; 24 @)
% 0.17/0.40 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 15 ( 8 avg)
% 0.17/0.40 % Number of types : 2 ( 0 usr)
% 0.17/0.40 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : http://mathgate.info/detsetitem.php?id=309
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(in_type,type,
% 0.17/0.40 in: $i > $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(powerset_type,type,
% 0.17/0.40 powerset: $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(binunion_type,type,
% 0.17/0.40 binunion: $i > $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(binunionE_type,type,
% 0.17/0.40 binunionE: $o ).
% 0.17/0.40
% 0.17/0.40 thf(binunionE,definition,
% 0.17/0.40 ( binunionE
% 0.17/0.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.40 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.40 => ( ( in @ Xx @ A )
% 0.17/0.40 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 thf(binunionTEcontra,conjecture,
% 0.17/0.40 ( binunionE
% 0.17/0.40 => ! [A: $i,X: $i] :
% 0.17/0.40 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.40 => ! [Y: $i] :
% 0.17/0.40 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.40 => ! [Xx: $i] :
% 0.17/0.40 ( ( in @ Xx @ A )
% 0.17/0.40 => ( ~ ( in @ Xx @ X )
% 0.17/0.40 => ( ~ ( in @ Xx @ Y )
% 0.17/0.40 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.40/1.15 ---- Embedded in THF ---
% 1.40/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.15 %%% Generated on Tue Feb 24 12:32:58 EST 2026
% 1.40/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.15 %%% Logic specification used:
% 1.40/1.15 %%% thf(spec, logic, $$dhol).
% 1.40/1.15
% 1.40/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.RhTafZrfx8/DTF2DTF12082.p
% See solution above
% 1.40/1.15 ------------------------
% 1.40/1.16 ---- Cleaned THF ---
% 1.40/1.16 thf(in_type,type,
% 1.40/1.16 in: $i > $i > $o ).
% 1.40/1.16
% 1.40/1.16 thf(powerset_type,type,
% 1.40/1.16 powerset: $i > $i ).
% 1.40/1.16
% 1.40/1.16 thf(binunion_type,type,
% 1.40/1.16 binunion: $i > $i > $i ).
% 1.40/1.16
% 1.40/1.16 thf(binunionE_type,type,
% 1.40/1.16 binunionE: $o ).
% 1.40/1.16
% 1.40/1.16 thf(binunionE,definition,
% 1.40/1.16 ( binunionE
% 1.40/1.16 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.40/1.16 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.40/1.16 => ( ( in @ Xx @ A )
% 1.40/1.16 | ( in @ Xx @ B ) ) ) ) ) ).
% 1.40/1.16
% 1.40/1.16 thf(binunionTEcontra,conjecture,
% 1.40/1.16 ( binunionE
% 1.40/1.16 => ! [A: $i,X: $i] :
% 1.40/1.16 ( ( in @ X @ ( powerset @ A ) )
% 1.40/1.16 => ! [Y: $i] :
% 1.40/1.16 ( ( in @ Y @ ( powerset @ A ) )
% 1.40/1.16 => ! [Xx: $i] :
% 1.40/1.16 ( ( in @ Xx @ A )
% 1.40/1.16 => ( ~ ( in @ Xx @ X )
% 1.40/1.16 => ( ~ ( in @ Xx @ Y )
% 1.40/1.16 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.40/1.16 ------------------------
% 1.40/1.17 % (12318)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12082 for (3000ds/2Mi)
% 1.40/1.18 % (12318)Instruction limit reached!
% 1.40/1.18 % (12318)------------------------------
% 1.40/1.18 % (12318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.18 % (12318)Termination reason: Unknown
% 1.40/1.18 % (12318)Termination phase: Preprocessing 3
% 1.40/1.18
% 1.40/1.18 % (12318)Memory used [KB]: 895
% 1.40/1.18 % (12318)Time elapsed: 0.002 s
% 1.40/1.18 % (12318)Instructions burned: 2 (million)
% 1.40/1.18 % (12318)------------------------------
% 1.40/1.18 % (12318)------------------------------
% 1.40/1.18 % (12316)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_12082 for (3000ds/4Mi)
% 1.40/1.18 % (12315)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12082 for (3000ds/183Mi)
% 1.40/1.18 % (12317)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_12082 for (3000ds/27Mi)
% 1.40/1.18 % (12319)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_12082 for (3000ds/2Mi)
% 1.40/1.18 % (12320)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_12082 for (3000ds/275Mi)
% 1.40/1.18 % (12321)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12082 for (3000ds/18Mi)
% 1.40/1.18 % (12319)Instruction limit reached!
% 1.40/1.18 % (12319)------------------------------
% 1.40/1.18 % (12319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.18 % (12319)Termination reason: Unknown
% 1.40/1.18 % (12319)Termination phase: Property scanning
% 1.40/1.18
% 1.40/1.18 % (12319)Memory used [KB]: 895
% 1.40/1.18 % (12319)Time elapsed: 0.003 s
% 1.40/1.18 % (12319)Instructions burned: 2 (million)
% 1.40/1.18 % (12319)------------------------------
% 1.40/1.18 % (12319)------------------------------
% 1.40/1.19 % (12322)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12082 for (2999ds/3Mi)
% 1.40/1.19 % (12316)Instruction limit reached!
% 1.40/1.19 % (12316)------------------------------
% 1.40/1.19 % (12316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (12316)Termination reason: Unknown
% 1.40/1.19 % (12316)Termination phase: Saturation
% 1.40/1.19
% 1.40/1.19 % (12316)Memory used [KB]: 5500
% 1.40/1.19 % (12316)Time elapsed: 0.005 s
% 1.40/1.19 % (12316)Instructions burned: 4 (million)
% 1.40/1.19 % (12316)------------------------------
% 1.40/1.19 % (12316)------------------------------
% 1.40/1.19 % (12320)First to succeed.
% 1.40/1.19 % (12322)Refutation not found, incomplete strategy
% 1.40/1.19 % (12322)------------------------------
% 1.40/1.19 % (12322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (12322)Termination reason: Refutation not found, incomplete strategy
% 1.40/1.19
% 1.40/1.19
% 1.40/1.19 % (12322)Memory used [KB]: 5500
% 1.40/1.19 % (12322)Time elapsed: 0.002 s
% 1.40/1.19 % (12322)Instructions burned: 2 (million)
% 1.40/1.19 % (12322)------------------------------
% 1.40/1.19 % (12322)------------------------------
% 1.40/1.19 % (12315)Also succeeded, but the first one will report.
% 1.40/1.19 % (12317)Also succeeded, but the first one will report.
% 1.40/1.19 % (12320)Refutation found. Thanks to Tanya!
% 1.40/1.19 % SZS status Theorem for DTF2THF_12082
% 1.40/1.19 % SZS output start Proof for DTF2THF_12082
% 1.40/1.19 thf(func_def_0, type, in: $i > $i > $o).
% 1.40/1.19 thf(func_def_1, type, powerset: $i > $i).
% 1.40/1.19 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.40/1.19 thf(f41,plain,(
% 1.40/1.19 $false),
% 1.40/1.19 inference(subsumption_resolution,[status(thm)],[f40,f26])).
% 1.40/1.19 thf(f26,plain,(
% 1.40/1.19 ($true != (in @ sK3 @ sK2))),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.19 thf(f17,plain,(
% 1.40/1.19 ((($true = (in @ sK2 @ (powerset @ sK0))) & (($true = (in @ sK3 @ (binunion @ sK1 @ sK2))) & ($true != (in @ sK3 @ sK2)) & ($true = (in @ sK3 @ sK0)) & ($true != (in @ sK3 @ sK1)))) & ($true = (in @ sK1 @ (powerset @ sK0)))) & (binunionE = $true)),
% 1.40/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f16,f15,f14])).
% 1.40/1.19 thf(f14,plain,(
% 1.40/1.19 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ X1 @ X2))) & ($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ X0)) & ($true != (in @ X3 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ sK1 @ X2))) & ($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ sK0)) & ($true != (in @ X3 @ sK1)))) & ($true = (in @ sK1 @ (powerset @ sK0))))),
% 1.40/1.19 introduced(definition,[],[choice_axiom])).
% 1.40/1.19 thf(f15,plain,(
% 1.40/1.19 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ sK1 @ X2))) & ($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ sK0)) & ($true != (in @ X3 @ sK1)))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ sK1 @ sK2))) & ((in @ X3 @ sK2) != $true) & ($true = (in @ X3 @ sK0)) & ($true != (in @ X3 @ sK1))))),
% 1.40/1.19 introduced(definition,[],[choice_axiom])).
% 1.40/1.19 thf(f16,plain,(
% 1.40/1.19 ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ sK1 @ sK2))) & ((in @ X3 @ sK2) != $true) & ($true = (in @ X3 @ sK0)) & ($true != (in @ X3 @ sK1))) => (($true = (in @ sK3 @ (binunion @ sK1 @ sK2))) & ($true != (in @ sK3 @ sK2)) & ($true = (in @ sK3 @ sK0)) & ($true != (in @ sK3 @ sK1)))),
% 1.40/1.19 introduced(definition,[],[choice_axiom])).
% 1.40/1.19 thf(f11,plain,(
% 1.40/1.19 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) & ? [X3 : $i] : (($true = (in @ X3 @ (binunion @ X1 @ X2))) & ($true != (in @ X3 @ X2)) & ($true = (in @ X3 @ X0)) & ($true != (in @ X3 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionE = $true)),
% 1.40/1.19 inference(flattening,[status(thm)],[f10])).
% 1.40/1.19 thf(f10,plain,(
% 1.40/1.19 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((($true = (in @ X3 @ (binunion @ X1 @ X2))) & ($true != (in @ X3 @ X2))) & ($true != (in @ X3 @ X1))) & ($true = (in @ X3 @ X0))) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionE = $true)),
% 1.40/1.19 inference(ennf_transformation,[status(thm)],[f9])).
% 1.40/1.19 thf(f9,plain,(
% 1.40/1.19 ~((binunionE = $true) => ! [X1 : $i,X0 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (($true != (in @ X3 @ X1)) => (($true != (in @ X3 @ X2)) => ($true != (in @ X3 @ (binunion @ X1 @ X2)))))))))),
% 1.40/1.19 inference(flattening,[status(thm)],[f6])).
% 1.40/1.19 thf(f6,plain,(
% 1.40/1.19 ~((binunionE = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => (~($true = (in @ X3 @ X1)) => (~($true = (in @ X3 @ X2)) => ~($true = (in @ X3 @ (binunion @ X1 @ X2)))))))))),
% 1.40/1.19 inference(fool_elimination,[status(thm)],[f5])).
% 1.40/1.19 thf(f5,plain,(
% 1.40/1.19 ~(binunionE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binunion @ X1 @ X2))))))))),
% 1.40/1.19 inference(rectify,[status(thm)],[f3])).
% 1.40/1.19 thf(f3,negated_conjecture,(
% 1.40/1.19 ~(binunionE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binunion @ X3 @ X4))))))))),
% 1.40/1.19 inference(negated_conjecture,[status(cth)],[f2])).
% 1.40/1.19 thf(f2,conjecture,(
% 1.40/1.19 binunionE => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binunion @ X3 @ X4)))))))),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.RhTafZrfx8/DTF2THF_12082.p',binunionTEcontra)).
% 1.40/1.19 thf(f40,plain,(
% 1.40/1.19 ($true = (in @ sK3 @ sK2))),
% 1.40/1.19 inference(subsumption_resolution,[status(thm)],[f39,f24])).
% 1.40/1.19 thf(f24,plain,(
% 1.40/1.19 ($true != (in @ sK3 @ sK1))),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.19 thf(f39,plain,(
% 1.40/1.19 ($true = (in @ sK3 @ sK1)) | ($true = (in @ sK3 @ sK2))),
% 1.40/1.19 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.40/1.19 thf(f38,plain,(
% 1.40/1.19 ($true = (in @ sK3 @ sK1)) | ($true = (in @ sK3 @ sK2)) | ($true != $true)),
% 1.40/1.19 inference(superposition,[status(thm)],[f37,f27])).
% 1.40/1.19 thf(f27,plain,(
% 1.40/1.19 ($true = (in @ sK3 @ (binunion @ sK1 @ sK2)))),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.19 thf(f37,plain,(
% 1.40/1.19 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (binunion @ X0 @ X2))) | ($true = (in @ X1 @ X0)) | ($true = (in @ X1 @ X2))) )),
% 1.40/1.19 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.40/1.19 thf(f33,plain,(
% 1.40/1.19 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ X0)) | ($true != $true) | ($true != (in @ X1 @ (binunion @ X0 @ X2)))) )),
% 1.40/1.19 inference(definition_unfolding,[status(thm)],[f32,f22])).
% 1.40/1.19 thf(f22,plain,(
% 1.40/1.19 (binunionE = $true)),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.19 thf(f32,plain,(
% 1.40/1.19 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (binunion @ X0 @ X2))) | ($true = (in @ X1 @ X2)) | (binunionE != $true)) )),
% 1.40/1.19 inference(cnf_transformation,[status(thm)],[f21])).
% 1.40/1.19 thf(f21,plain,(
% 1.40/1.19 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (binunion @ X0 @ X2))) | ($true = (in @ X1 @ X2))) | (binunionE != $true)) & ((binunionE = $true) | (($true != (in @ sK5 @ sK4)) & ($true = (in @ sK5 @ (binunion @ sK4 @ sK6))) & ($true != (in @ sK5 @ sK6))))),
% 1.40/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f19,f20])).
% 1.40/1.19 thf(f20,plain,(
% 1.40/1.19 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ (binunion @ X3 @ X5))) & ($true != (in @ X4 @ X5))) => (($true != (in @ sK5 @ sK4)) & ($true = (in @ sK5 @ (binunion @ sK4 @ sK6))) & ($true != (in @ sK5 @ sK6)))),
% 1.40/1.19 introduced(definition,[],[choice_axiom])).
% 1.40/1.19 thf(f19,plain,(
% 1.40/1.19 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (binunion @ X0 @ X2))) | ($true = (in @ X1 @ X2))) | (binunionE != $true)) & ((binunionE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X3)) & ($true = (in @ X4 @ (binunion @ X3 @ X5))) & ($true != (in @ X4 @ X5))))),
% 1.40/1.19 inference(rectify,[status(thm)],[f18])).
% 1.40/1.19 thf(f18,plain,(
% 1.40/1.19 (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ (binunion @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) | (binunionE != $true)) & ((binunionE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0))) & ((in @ X2 @ X0) != $true)))),
% 1.40/1.19 inference(nnf_transformation,[status(thm)],[f13])).
% 1.40/1.19 thf(f13,plain,(
% 1.40/1.19 ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ (binunion @ X1 @ X0))) | ((in @ X2 @ X0) = $true)) <=> (binunionE = $true)),
% 1.40/1.19 inference(flattening,[status(thm)],[f12])).
% 1.40/1.19 thf(f12,plain,(
% 1.40/1.19 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)) | ($true != (in @ X2 @ (binunion @ X1 @ X0))))),
% 1.40/1.19 inference(ennf_transformation,[status(thm)],[f8])).
% 1.40/1.19 thf(f8,plain,(
% 1.40/1.19 (binunionE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X2 @ (binunion @ X1 @ X0))) => (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)))),
% 1.40/1.19 inference(fool_elimination,[status(thm)],[f7])).
% 1.40/1.19 thf(f7,plain,(
% 1.40/1.19 (binunionE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X1 @ X0)) => ((in @ X2 @ X0) | (in @ X2 @ X1))))),
% 1.40/1.19 inference(rectify,[status(thm)],[f1])).
% 1.40/1.19 thf(f1,axiom,(
% 1.40/1.19 (binunionE = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 1.40/1.19 file('/export/starexec/sandbox2/tmp/tmp.RhTafZrfx8/DTF2THF_12082.p',binunionE)).
% 1.40/1.19 % SZS output end Proof for DTF2THF_12082
% 1.40/1.19 % (12320)------------------------------
% 1.40/1.19 % (12320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.19 % (12320)Termination reason: Refutation
% 1.40/1.19
% 1.40/1.19 % (12320)Memory used [KB]: 5500
% 1.40/1.19 % (12320)Time elapsed: 0.006 s
% 1.40/1.19 % (12320)Instructions burned: 4 (million)
% 1.40/1.19 % (12320)------------------------------
% 1.40/1.19 % (12320)------------------------------
% 1.40/1.19 % (12314)Success in time 0.02 s
%------------------------------------------------------------------------------