%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU633^2 : 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 : n010.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 09:35:47 AM UTC 2026
% Result : Theorem 1.64s 1.31s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 455 ( 145 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 465 ( 73 ~; 64 |; 39 &; 262 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 102 ( 0 ^; 78 !; 24 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_6,type,
sK0: $o > $i > $i > $i ).
thf(f51,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f49,f43]) ).
thf(f43,plain,
! [X0: $o] : ( $true = X0 ),
inference(subsumption_resolution,[status(thm)],[f42,f27]) ).
thf(f27,plain,
( ( in @ sK4 @ ( setunion @ sK5 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK5 ) )
| ( ( in @ sK4 @ X2 )
!= $true ) )
& ( ( in @ sK4 @ ( setunion @ sK5 ) )
= $true )
& ( setunionE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f11,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
& ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) )
=> ( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK5 ) )
| ( ( in @ sK4 @ X2 )
!= $true ) )
& ( ( in @ sK4 @ ( setunion @ sK5 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
& ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) )
& ( setunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setunionE = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
=> ? [X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X2 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ X1 ) )
=> ? [X2: $i] :
( ( in @ X0 @ X2 )
& ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setunionE
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X4: $i] :
( ( in @ X1 @ X4 )
& ( in @ X4 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setunionE
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X4: $i] :
( ( in @ X1 @ X4 )
& ( in @ X4 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TCdBs6ZUcb/DTF2THF_4610.p',setunionE2) ).
thf(f42,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ sK4 @ ( setunion @ sK5 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( ( in @ sK4 @ ( setunion @ sK5 ) )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( in @ sK4 @ ( setunion @ sK5 ) )
!= $true )
| ( $true != $true )
| ( $true = X0 )
| ( ( in @ sK4 @ ( setunion @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f39,f37]) ).
thf(f37,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( sK0 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( ( in @ X0 @ ( sK0 @ X2 @ X1 @ X0 ) )
= $true )
| ( $true = X2 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f25,f26]) ).
thf(f26,plain,
setunionE = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f25,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true = X2 )
| ( ( in @ X0 @ ( sK0 @ X2 @ X1 @ X0 ) )
= $true )
| ( setunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ! [X2: $o] :
( ( $true = X2 )
| ( ( ( in @ X0 @ ( sK0 @ X2 @ X1 @ X0 ) )
= $true )
& ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true != X2 ) ) ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ( ( $true
= ( in @ sK1 @ ( setunion @ sK2 ) ) )
& ( $true != sK3 )
& ! [X7: $i] :
( ( ( in @ sK1 @ X7 )
!= $true )
| ( ( in @ X7 @ sK2 )
!= $true )
| ( $true = sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f16,f15,f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X2 ) )
=> ( ( ( in @ X0 @ ( sK0 @ X2 @ X1 @ X0 ) )
= $true )
& ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
& ( $true != X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
& ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( ( in @ X4 @ X7 )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true = X6 ) ) ) )
=> ( ( $true
= ( in @ sK1 @ ( setunion @ sK2 ) ) )
& ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( ( in @ sK1 @ X7 )
!= $true )
| ( ( in @ X7 @ sK2 )
!= $true )
| ( $true = X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( ( in @ sK1 @ X7 )
!= $true )
| ( ( in @ X7 @ sK2 )
!= $true )
| ( $true = X6 ) ) )
=> ( ( $true != sK3 )
& ! [X7: $i] :
( ( ( in @ sK1 @ X7 )
!= $true )
| ( ( in @ X7 @ sK2 )
!= $true )
| ( $true = sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X2 ) ) ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
& ? [X6: $o] :
( ( $true != X6 )
& ! [X7: $i] :
( ( ( in @ X4 @ X7 )
!= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true = X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X2 ) ) ) )
| ( setunionE != $true ) )
& ( ( setunionE = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
& ? [X2: $o] :
( ( $true != X2 )
& ! [X3: $i] :
( ( ( in @ X0 @ X3 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( $true = X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( $true != X2 ) ) ) )
<=> ( setunionE = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( setunionE = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $o] :
( ( $true = X2 )
| ? [X3: $i] :
( ( $true != X2 )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X0 @ X3 )
= $true ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( setunionE = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
= $true )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
=> ( ( ( in @ X3 @ X1 )
= $true )
=> ( $true = X2 ) ) )
=> ( $true = X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setunionE
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ X1 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X0 @ X3 )
=> ( ( in @ X3 @ X1 )
=> X2 ) )
=> X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setunionE
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TCdBs6ZUcb/DTF2THF_4610.p',setunionE) ).
thf(f39,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( in @ sK4 @ ( sK0 @ X0 @ sK5 @ X1 ) ) )
| ( ( in @ X1 @ ( setunion @ sK5 ) )
!= $true )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( setunion @ sK5 ) )
!= $true )
| ( $true
!= ( in @ sK4 @ ( sK0 @ X0 @ sK5 @ X1 ) ) )
| ( $true != $true )
| ( $true = X0 ) ),
inference(superposition,[status(thm)],[f28,f36]) ).
thf(f36,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true = X2 )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( $true = X2 ) ),
inference(definition_unfolding,[status(thm)],[f24,f26]) ).
thf(f24,plain,
! [X2: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
| ( $true = X2 )
| ( $true
= ( in @ ( sK0 @ X2 @ X1 @ X0 ) @ X1 ) )
| ( setunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f28,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK5 ) )
| ( ( in @ sK4 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f49,plain,
! [X0: $i] :
( $true
!= ( in @ sK4 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK4 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU633^2 : 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 : n010.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 12:29:18 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
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU633^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : Ordered Pairs - Singletons
% 0.19/0.46 % Version : Especial > Reduced > Especial.
% 0.19/0.46 % English : (! A:i.! x:i.in x (setunion A) -> (? X:i.in X A & in x X))
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.46 % Source : [Bro08]
% 0.19/0.46 % Names : ZFC135l [Bro08]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % 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 v4.1.0, 0.00 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.19/0.46 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.46 % Number of connectives : 21 ( 0 ~; 0 |; 1 &; 14 @)
% 0.19/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : http://mathgate.info/detsetitem.php?id=190
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(in_type,type,
% 0.19/0.46 in: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(setunion_type,type,
% 0.19/0.46 setunion: $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(setunionE_type,type,
% 0.19/0.46 setunionE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setunionE,definition,
% 0.19/0.46 ( setunionE
% 0.19/0.46 = ( ! [A: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.46 => ! [Xphi: $o] :
% 0.19/0.46 ( ! [B: $i] :
% 0.19/0.46 ( ( in @ Xx @ B )
% 0.19/0.46 => ( ( in @ B @ A )
% 0.19/0.46 => Xphi ) )
% 0.19/0.46 => Xphi ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setunionE2,conjecture,
% 0.19/0.46 ( setunionE
% 0.19/0.46 => ! [A: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.46 => ? [X: $i] :
% 0.19/0.46 ( ( in @ X @ A )
% 0.19/0.46 & ( in @ Xx @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 12:29:19 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TCdBs6ZUcb/DTF2DTF4610.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.30 thf(in_type,type,
% 1.49/1.30 in: $i > $i > $o ).
% 1.49/1.30
% 1.49/1.30 thf(setunion_type,type,
% 1.49/1.30 setunion: $i > $i ).
% 1.49/1.30
% 1.49/1.30 thf(setunionE_type,type,
% 1.49/1.30 setunionE: $o ).
% 1.49/1.30
% 1.49/1.30 thf(setunionE,definition,
% 1.49/1.30 ( setunionE
% 1.49/1.30 = ( ! [A: $i,Xx: $i] :
% 1.49/1.30 ( ( in @ Xx @ ( setunion @ A ) )
% 1.49/1.30 => ! [Xphi: $o] :
% 1.49/1.30 ( ! [B: $i] :
% 1.49/1.30 ( ( in @ Xx @ B )
% 1.49/1.30 => ( ( in @ B @ A )
% 1.49/1.30 => Xphi ) )
% 1.49/1.30 => Xphi ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(setunionE2,conjecture,
% 1.49/1.30 ( setunionE
% 1.49/1.30 => ! [A: $i,Xx: $i] :
% 1.49/1.30 ( ( in @ Xx @ ( setunion @ A ) )
% 1.49/1.30 => ? [X: $i] :
% 1.49/1.30 ( ( in @ X @ A )
% 1.49/1.30 & ( in @ Xx @ X ) ) ) ) ).
% 1.49/1.30 ------------------------
% 1.64/1.31 % (4802)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4610 for (2999ds/2Mi)
% 1.64/1.31 % (4802)Instruction limit reached!
% 1.64/1.31 % (4802)------------------------------
% 1.64/1.31 % (4802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (4802)Termination reason: Unknown
% 1.64/1.31 % (4802)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (4802)Memory used [KB]: 895
% 1.64/1.31 % (4802)Time elapsed: 0.002 s
% 1.64/1.31 % (4802)Instructions burned: 2 (million)
% 1.64/1.31 % (4802)------------------------------
% 1.64/1.31 % (4802)------------------------------
% 1.64/1.31 % (4804)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_4610 for (2999ds/275Mi)
% 1.64/1.31 % (4804)First to succeed.
% 1.64/1.31 % (4804)Refutation found. Thanks to Tanya!
% 1.64/1.31 % SZS status Theorem for DTF2THF_4610
% 1.64/1.31 % SZS output start Proof for DTF2THF_4610
% 1.64/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.31 thf(func_def_1, type, setunion: $i > $i).
% 1.64/1.31 thf(func_def_6, type, sK0: $o > $i > $i > $i).
% 1.64/1.31 thf(f51,plain,(
% 1.64/1.31 $false),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f49,f43])).
% 1.64/1.31 thf(f43,plain,(
% 1.64/1.31 ( ! [X0 : $o] : (($true = X0)) )),
% 1.64/1.31 inference(subsumption_resolution,[status(thm)],[f42,f27])).
% 1.64/1.31 thf(f27,plain,(
% 1.64/1.31 ((in @ sK4 @ (setunion @ sK5)) = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.64/1.31 thf(f19,plain,(
% 1.64/1.31 (! [X2 : $i] : (($true != (in @ X2 @ sK5)) | ((in @ sK4 @ X2) != $true)) & ((in @ sK4 @ (setunion @ sK5)) = $true)) & (setunionE = $true)),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f11,f18])).
% 1.64/1.31 thf(f18,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true != (in @ X0 @ X2))) & ((in @ X0 @ (setunion @ X1)) = $true)) => (! [X2 : $i] : (($true != (in @ X2 @ sK5)) | ((in @ sK4 @ X2) != $true)) & ((in @ sK4 @ (setunion @ sK5)) = $true))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f11,plain,(
% 1.64/1.31 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true != (in @ X0 @ X2))) & ((in @ X0 @ (setunion @ X1)) = $true)) & (setunionE = $true)),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f8])).
% 1.64/1.31 thf(f8,plain,(
% 1.64/1.31 ~((setunionE = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) => ? [X2 : $i] : (($true = (in @ X0 @ X2)) & ($true = (in @ X2 @ X1)))))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.31 thf(f7,plain,(
% 1.64/1.31 ~(setunionE => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f3])).
% 1.64/1.31 thf(f3,negated_conjecture,(
% 1.64/1.31 ~(setunionE => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X4 : $i] : ((in @ X1 @ X4) & (in @ X4 @ X0))))),
% 1.64/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.31 thf(f2,conjecture,(
% 1.64/1.31 setunionE => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X4 : $i] : ((in @ X1 @ X4) & (in @ X4 @ X0)))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.TCdBs6ZUcb/DTF2THF_4610.p',setunionE2)).
% 1.64/1.31 thf(f42,plain,(
% 1.64/1.31 ( ! [X0 : $o] : (($true = X0) | ((in @ sK4 @ (setunion @ sK5)) != $true)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.64/1.31 thf(f41,plain,(
% 1.64/1.31 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | ((in @ sK4 @ (setunion @ sK5)) != $true)) )),
% 1.64/1.31 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.64/1.31 thf(f40,plain,(
% 1.64/1.31 ( ! [X0 : $o] : (($true = X0) | ((in @ sK4 @ (setunion @ sK5)) != $true) | ($true != $true) | ($true = X0) | ((in @ sK4 @ (setunion @ sK5)) != $true)) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f39,f37])).
% 1.64/1.31 thf(f37,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (sK0 @ X2 @ X1 @ X0)) = $true) | ((in @ X0 @ (setunion @ X1)) != $true) | ($true = X2)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.64/1.31 thf(f29,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ((in @ X0 @ (sK0 @ X2 @ X1 @ X0)) = $true) | ($true = X2) | ($true != $true)) )),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f25,f26])).
% 1.64/1.31 thf(f26,plain,(
% 1.64/1.31 (setunionE = $true)),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.64/1.31 thf(f25,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ($true = X2) | ((in @ X0 @ (sK0 @ X2 @ X1 @ X0)) = $true) | (setunionE != $true)) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.64/1.31 thf(f17,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ! [X2 : $o] : (($true = X2) | (((in @ X0 @ (sK0 @ X2 @ X1 @ X0)) = $true) & ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) & ($true != X2)))) | (setunionE != $true)) & ((setunionE = $true) | (($true = (in @ sK1 @ (setunion @ sK2))) & (($true != sK3) & ! [X7 : $i] : (((in @ sK1 @ X7) != $true) | ((in @ X7 @ sK2) != $true) | ($true = sK3)))))),
% 1.64/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f13,f16,f15,f14])).
% 1.64/1.31 thf(f14,plain,(
% 1.64/1.31 ! [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : (((in @ X0 @ X3) = $true) & ((in @ X3 @ X1) = $true) & ($true != X2)) => (((in @ X0 @ (sK0 @ X2 @ X1 @ X0)) = $true) & ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) & ($true != X2)))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f15,plain,(
% 1.64/1.31 ? [X4 : $i,X5 : $i] : (((in @ X4 @ (setunion @ X5)) = $true) & ? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (((in @ X4 @ X7) != $true) | ($true != (in @ X7 @ X5)) | ($true = X6)))) => (($true = (in @ sK1 @ (setunion @ sK2))) & ? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (((in @ sK1 @ X7) != $true) | ((in @ X7 @ sK2) != $true) | ($true = X6))))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f16,plain,(
% 1.64/1.31 ? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (((in @ sK1 @ X7) != $true) | ((in @ X7 @ sK2) != $true) | ($true = X6))) => (($true != sK3) & ! [X7 : $i] : (((in @ sK1 @ X7) != $true) | ((in @ X7 @ sK2) != $true) | ($true = sK3)))),
% 1.64/1.31 introduced(definition,[],[choice_axiom])).
% 1.64/1.31 thf(f13,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (((in @ X0 @ X3) = $true) & ((in @ X3 @ X1) = $true) & ($true != X2)))) | (setunionE != $true)) & ((setunionE = $true) | ? [X4 : $i,X5 : $i] : (((in @ X4 @ (setunion @ X5)) = $true) & ? [X6 : $o] : (($true != X6) & ! [X7 : $i] : (((in @ X4 @ X7) != $true) | ($true != (in @ X7 @ X5)) | ($true = X6)))))),
% 1.64/1.31 inference(rectify,[status(thm)],[f12])).
% 1.64/1.31 thf(f12,plain,(
% 1.64/1.31 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (((in @ X0 @ X3) = $true) & ((in @ X3 @ X1) = $true) & ($true != X2)))) | (setunionE != $true)) & ((setunionE = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) & ? [X2 : $o] : (($true != X2) & ! [X3 : $i] : (((in @ X0 @ X3) != $true) | ((in @ X3 @ X1) != $true) | ($true = X2)))))),
% 1.64/1.31 inference(nnf_transformation,[status(thm)],[f10])).
% 1.64/1.31 thf(f10,plain,(
% 1.64/1.31 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ! [X2 : $o] : (($true = X2) | ? [X3 : $i] : (((in @ X0 @ X3) = $true) & ((in @ X3 @ X1) = $true) & ($true != X2)))) <=> (setunionE = $true)),
% 1.64/1.31 inference(flattening,[status(thm)],[f9])).
% 1.64/1.31 thf(f9,plain,(
% 1.64/1.31 (setunionE = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $o] : (($true = X2) | ? [X3 : $i] : ((($true != X2) & ((in @ X3 @ X1) = $true)) & ((in @ X0 @ X3) = $true))) | ((in @ X0 @ (setunion @ X1)) != $true))),
% 1.64/1.31 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.31 thf(f6,plain,(
% 1.64/1.31 (setunionE = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X0 @ (setunion @ X1)) = $true) => ! [X2 : $o] : (! [X3 : $i] : (((in @ X0 @ X3) = $true) => (((in @ X3 @ X1) = $true) => ($true = X2))) => ($true = X2)))),
% 1.64/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.31 thf(f5,plain,(
% 1.64/1.31 (setunionE = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X1) => X2)) => X2)))),
% 1.64/1.31 inference(rectify,[status(thm)],[f1])).
% 1.64/1.31 thf(f1,axiom,(
% 1.64/1.31 (setunionE = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 1.64/1.31 file('/export/starexec/sandbox/tmp/tmp.TCdBs6ZUcb/DTF2THF_4610.p',setunionE)).
% 1.64/1.31 thf(f39,plain,(
% 1.64/1.31 ( ! [X0 : $o,X1 : $i] : (($true != (in @ sK4 @ (sK0 @ X0 @ sK5 @ X1))) | ((in @ X1 @ (setunion @ sK5)) != $true) | ($true = X0)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.64/1.31 thf(f38,plain,(
% 1.64/1.31 ( ! [X0 : $o,X1 : $i] : (((in @ X1 @ (setunion @ sK5)) != $true) | ($true != (in @ sK4 @ (sK0 @ X0 @ sK5 @ X1))) | ($true != $true) | ($true = X0)) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f28,f36])).
% 1.64/1.31 thf(f36,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | ($true = X2) | ((in @ X0 @ (setunion @ X1)) != $true)) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.64/1.31 thf(f30,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ (setunion @ X1)) != $true) | ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | ($true = X2)) )),
% 1.64/1.31 inference(definition_unfolding,[status(thm)],[f24,f26])).
% 1.64/1.31 thf(f24,plain,(
% 1.64/1.31 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (setunion @ X1)) != $true) | ($true = X2) | ($true = (in @ (sK0 @ X2 @ X1 @ X0) @ X1)) | (setunionE != $true)) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 1.64/1.31 thf(f28,plain,(
% 1.64/1.31 ( ! [X2 : $i] : (($true != (in @ X2 @ sK5)) | ((in @ sK4 @ X2) != $true)) )),
% 1.64/1.31 inference(cnf_transformation,[status(thm)],[f19])).
% 1.64/1.31 thf(f49,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true != (in @ sK4 @ X0))) )),
% 1.64/1.31 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.64/1.31 thf(f46,plain,(
% 1.64/1.31 ( ! [X0 : $i] : (($true != (in @ sK4 @ X0)) | ($true != $true)) )),
% 1.64/1.31 inference(superposition,[status(thm)],[f28,f43])).
% 1.64/1.31 % SZS output end Proof for DTF2THF_4610
% 1.64/1.31 % (4804)------------------------------
% 1.64/1.31 % (4804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (4804)Termination reason: Refutation
% 1.64/1.31
% 1.64/1.31 % (4804)Memory used [KB]: 5500
% 1.64/1.31 % (4804)Time elapsed: 0.003 s
% 1.64/1.31 % (4804)Instructions burned: 2 (million)
% 1.64/1.31 % (4804)------------------------------
% 1.64/1.31 % (4804)------------------------------
% 1.64/1.31 % (4798)Success in time 0.006 s
%------------------------------------------------------------------------------