%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU522^2 : 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 : n016.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 09:35:04 AM UTC 2026
% Result : Theorem 0.32s 1.33s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 418 ( 117 equ; 0 cnn)
% Maximal formula atoms : 14 ( 13 avg)
% Number of connectives : 424 ( 49 ~; 42 |; 42 &; 271 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 45 !; 29 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_9,type,
sK3: $i > $i > $i ).
thf(f45,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44,f27]) ).
thf(f27,plain,
( ( in @ sK5 @ ( setunion @ sK4 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( setunionAx = $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK5 @ ( setunion @ sK4 ) )
!= $true )
& ( ( in @ sK5 @ sK6 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) )
=> ( ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK5 @ ( setunion @ sK4 ) )
!= $true )
& ( ( in @ sK5 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( setunionAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ( setunionAx = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true )
& ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( setunionAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setunionAx = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setunionAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X0 @ ( setunion @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setunionAx
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setunionAx
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZAWnoIhYfk/DTF2THF_2352.p',setunionI) ).
thf(f44,plain,
( ( in @ sK5 @ ( setunion @ sK4 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( ( in @ sK5 @ ( setunion @ sK4 ) )
= $true ) ),
inference(superposition,[status(thm)],[f42,f28]) ).
thf(f28,plain,
( ( in @ sK6 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f42,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
= ( in @ sK5 @ ( setunion @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true != $true )
| ( $true
= ( in @ sK5 @ ( setunion @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f38,f26]) ).
thf(f26,plain,
( ( in @ sK5 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f38,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ( ( in @ X6 @ X5 )
!= $true )
| ( ( in @ X4 @ ( setunion @ X5 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X6 ) )
| ( $true != $true )
| ( ( in @ X6 @ X5 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f22,f29]) ).
thf(f29,plain,
setunionAx = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f22,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
| ( $true
!= ( in @ X4 @ X6 ) )
| ( ( in @ X6 @ X5 )
!= $true )
| ( setunionAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( setunionAx = $true )
| ( ( ! [X2: $i] :
( ( ( in @ sK0 @ X2 )
!= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) )
| ( $true
!= ( in @ sK0 @ ( setunion @ sK1 ) ) ) )
& ( ( ( $true
= ( in @ sK0 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK1 ) ) )
| ( $true
= ( in @ sK0 @ ( setunion @ sK1 ) ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
| ! [X6: $i] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ( ( in @ X6 @ X5 )
!= $true ) ) )
& ( ( ( $true
= ( in @ X4 @ ( sK3 @ X5 @ X4 ) ) )
& ( $true
= ( in @ ( sK3 @ X5 @ X4 ) @ X5 ) ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
!= $true ) ) )
| ( setunionAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f12,f15,f14,f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
& ( ? [X3: $i] :
( ( $true
= ( in @ X0 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) ) )
=> ( ( ! [X2: $i] :
( ( ( in @ sK0 @ X2 )
!= $true )
| ( ( in @ X2 @ sK1 )
!= $true ) )
| ( $true
!= ( in @ sK0 @ ( setunion @ sK1 ) ) ) )
& ( ? [X3: $i] :
( ( $true
= ( in @ sK0 @ X3 ) )
& ( $true
= ( in @ X3 @ sK1 ) ) )
| ( $true
= ( in @ sK0 @ ( setunion @ sK1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X3: $i] :
( ( $true
= ( in @ sK0 @ X3 ) )
& ( $true
= ( in @ X3 @ sK1 ) ) )
=> ( ( $true
= ( in @ sK0 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X4: $i,X5: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X4 @ X7 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
=> ( ( $true
= ( in @ X4 @ ( sK3 @ X5 @ X4 ) ) )
& ( $true
= ( in @ ( sK3 @ X5 @ X4 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( ( setunionAx = $true )
| ? [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
!= $true ) )
& ( ? [X3: $i] :
( ( $true
= ( in @ X0 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( ( in @ X0 @ ( setunion @ X1 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( ( in @ X4 @ ( setunion @ X5 ) )
= $true )
| ! [X6: $i] :
( ( $true
!= ( in @ X4 @ X6 ) )
| ( ( in @ X6 @ X5 )
!= $true ) ) )
& ( ? [X7: $i] :
( ( $true
= ( in @ X4 @ X7 ) )
& ( $true
= ( in @ X7 @ X5 ) ) )
| ( ( in @ X4 @ ( setunion @ X5 ) )
!= $true ) ) )
| ( setunionAx != $true ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( setunionAx = $true )
| ? [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true ) )
& ( ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
| ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
& ( ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true ) ) )
| ( setunionAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( setunionAx = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
<=> ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( in @ X1 @ X2 )
& ( in @ X2 @ X0 ) )
<=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( in @ X1 @ X2 )
& ( in @ X2 @ X0 ) )
<=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZAWnoIhYfk/DTF2THF_2352.p',setunionAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU522^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n016.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 12:26:06 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : SEU522^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.48 % Domain : Set Theory
% 0.26/0.48 % Problem : Preliminary Notions - Power Sets and Unions
% 0.26/0.48 % Version : Especial > Reduced > Especial.
% 0.26/0.48 % English : (! A:i.! x:i.! B:i.in x B -> in B A -> in x (setunion A))
% 0.26/0.48
% 0.26/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.48 % Source : [Bro08]
% 0.26/0.48 % Names : ZFC024l [Bro08]
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % 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 v6.1.0, 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
% 0.26/0.48 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.26/0.48 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 4 ( 4 avg)
% 0.26/0.48 % Number of connectives : 19 ( 0 ~; 0 |; 1 &; 14 @)
% 0.26/0.48 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 9 ( 5 avg)
% 0.26/0.48 % Number of types : 2 ( 0 usr)
% 0.26/0.48 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.26/0.48 % Number of variables : 6 ( 0 ^; 5 !; 1 ?; 6 :)
% 0.26/0.48 % SPC : TH0_THM_EQU_NAR
% 0.26/0.48
% 0.26/0.48 % Comments : http://mathgate.info/detsetitem.php?id=87
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(in_type,type,
% 0.26/0.48 in: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(setunion_type,type,
% 0.26/0.48 setunion: $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(setunionAx_type,type,
% 0.26/0.48 setunionAx: $o ).
% 0.26/0.48
% 0.26/0.48 thf(setunionAx,definition,
% 0.26/0.48 ( setunionAx
% 0.26/0.48 = ( ! [A: $i,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.26/0.48 <=> ? [B: $i] :
% 0.26/0.48 ( ( in @ Xx @ B )
% 0.26/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setunionI,conjecture,
% 0.26/0.48 ( setunionAx
% 0.26/0.48 => ! [A: $i,Xx: $i,B: $i] :
% 0.26/0.48 ( ( in @ Xx @ B )
% 0.26/0.48 => ( ( in @ B @ A )
% 0.26/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 12:26:07 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZAWnoIhYfk/DTF2DTF2352.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.31 thf(in_type,type,
% 0.32/1.31 in: $i > $i > $o ).
% 0.32/1.31
% 0.32/1.31 thf(setunion_type,type,
% 0.32/1.31 setunion: $i > $i ).
% 0.32/1.31
% 0.32/1.31 thf(setunionAx_type,type,
% 0.32/1.31 setunionAx: $o ).
% 0.32/1.31
% 0.32/1.31 thf(setunionAx,definition,
% 0.32/1.31 ( setunionAx
% 0.32/1.31 = ( ! [A: $i,Xx: $i] :
% 0.32/1.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.31 <=> ? [B: $i] :
% 0.32/1.31 ( ( in @ Xx @ B )
% 0.32/1.31 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/1.31
% 0.32/1.31 thf(setunionI,conjecture,
% 0.32/1.31 ( setunionAx
% 0.32/1.31 => ! [A: $i,Xx: $i,B: $i] :
% 0.32/1.31 ( ( in @ Xx @ B )
% 0.32/1.31 => ( ( in @ B @ A )
% 0.32/1.31 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ).
% 0.32/1.31 ------------------------
% 0.32/1.32 % (2472)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2352 for (3000ds/18Mi)
% 0.32/1.32 % (2470)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_2352 for (3000ds/2Mi)
% 0.32/1.32 % (2470)Instruction limit reached!
% 0.32/1.32 % (2470)------------------------------
% 0.32/1.32 % (2470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.32 % (2470)Termination reason: Unknown
% 0.32/1.32 % (2470)Termination phase: Saturation
% 0.32/1.32
% 0.32/1.32 % (2470)Memory used [KB]: 5500
% 0.32/1.32 % (2470)Time elapsed: 0.002 s
% 0.32/1.32 % (2470)Instructions burned: 2 (million)
% 0.32/1.32 % (2470)------------------------------
% 0.32/1.32 % (2470)------------------------------
% 0.32/1.32 % (2472)First to succeed.
% 0.32/1.33 % (2472)Refutation found. Thanks to Tanya!
% 0.32/1.33 % SZS status Theorem for DTF2THF_2352
% 0.32/1.33 % SZS output start Proof for DTF2THF_2352
% 0.32/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.33 thf(func_def_1, type, setunion: $i > $i).
% 0.32/1.33 thf(func_def_9, type, sK3: $i > $i > $i).
% 0.32/1.33 thf(f45,plain,(
% 0.32/1.33 $false),
% 0.32/1.33 inference(subsumption_resolution,[status(thm)],[f44,f27])).
% 0.32/1.33 thf(f27,plain,(
% 0.32/1.33 ((in @ sK5 @ (setunion @ sK4)) != $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f19])).
% 0.32/1.33 thf(f19,plain,(
% 0.32/1.33 (setunionAx = $true) & (((in @ sK6 @ sK4) = $true) & ((in @ sK5 @ (setunion @ sK4)) != $true) & ((in @ sK5 @ sK6) = $true))),
% 0.32/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f17,f18])).
% 0.32/1.33 thf(f18,plain,(
% 0.32/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X1 @ (setunion @ X0)) != $true) & ((in @ X1 @ X2) = $true)) => (((in @ sK6 @ sK4) = $true) & ((in @ sK5 @ (setunion @ sK4)) != $true) & ((in @ sK5 @ sK6) = $true))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f17,plain,(
% 0.32/1.33 (setunionAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X1 @ (setunion @ X0)) != $true) & ((in @ X1 @ X2) = $true))),
% 0.32/1.33 inference(rectify,[status(thm)],[f10])).
% 0.32/1.33 thf(f10,plain,(
% 0.32/1.33 (setunionAx = $true) & ? [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ((in @ X0 @ (setunion @ X1)) != $true) & ($true = (in @ X0 @ X2)))),
% 0.32/1.33 inference(flattening,[status(thm)],[f9])).
% 0.32/1.33 thf(f9,plain,(
% 0.32/1.33 ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setunion @ X1)) != $true) & ($true = (in @ X2 @ X1))) & ($true = (in @ X0 @ X2))) & (setunionAx = $true)),
% 0.32/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 0.32/1.33 thf(f8,plain,(
% 0.32/1.33 ~((setunionAx = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) => (($true = (in @ X2 @ X1)) => ((in @ X0 @ (setunion @ X1)) = $true))))),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 0.32/1.33 thf(f7,plain,(
% 0.32/1.33 ~(setunionAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X2 @ X1) => (in @ X0 @ (setunion @ X1)))))),
% 0.32/1.33 inference(rectify,[status(thm)],[f3])).
% 0.32/1.33 thf(f3,negated_conjecture,(
% 0.32/1.33 ~(setunionAx => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 0.32/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 0.32/1.33 thf(f2,conjecture,(
% 0.32/1.33 setunionAx => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0))))),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.ZAWnoIhYfk/DTF2THF_2352.p',setunionI)).
% 0.32/1.33 thf(f44,plain,(
% 0.32/1.33 ((in @ sK5 @ (setunion @ sK4)) = $true)),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 0.32/1.33 thf(f43,plain,(
% 0.32/1.33 ($true != $true) | ((in @ sK5 @ (setunion @ sK4)) = $true)),
% 0.32/1.33 inference(superposition,[status(thm)],[f42,f28])).
% 0.32/1.33 thf(f28,plain,(
% 0.32/1.33 ((in @ sK6 @ sK4) = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f19])).
% 0.32/1.33 thf(f42,plain,(
% 0.32/1.33 ( ! [X0 : $i] : (($true != (in @ sK6 @ X0)) | ($true = (in @ sK5 @ (setunion @ X0)))) )),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 0.32/1.33 thf(f39,plain,(
% 0.32/1.33 ( ! [X0 : $i] : (($true != (in @ sK6 @ X0)) | ($true != $true) | ($true = (in @ sK5 @ (setunion @ X0)))) )),
% 0.32/1.33 inference(superposition,[status(thm)],[f38,f26])).
% 0.32/1.33 thf(f26,plain,(
% 0.32/1.33 ((in @ sK5 @ sK6) = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f19])).
% 0.32/1.33 thf(f38,plain,(
% 0.32/1.33 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X6)) | ((in @ X6 @ X5) != $true) | ((in @ X4 @ (setunion @ X5)) = $true)) )),
% 0.32/1.33 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 0.32/1.33 thf(f33,plain,(
% 0.32/1.33 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setunion @ X5)) = $true) | ($true != (in @ X4 @ X6)) | ($true != $true) | ((in @ X6 @ X5) != $true)) )),
% 0.32/1.33 inference(definition_unfolding,[status(thm)],[f22,f29])).
% 0.32/1.33 thf(f29,plain,(
% 0.32/1.33 (setunionAx = $true)),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f19])).
% 0.32/1.33 thf(f22,plain,(
% 0.32/1.33 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setunion @ X5)) = $true) | ($true != (in @ X4 @ X6)) | ((in @ X6 @ X5) != $true) | (setunionAx != $true)) )),
% 0.32/1.33 inference(cnf_transformation,[status(thm)],[f16])).
% 0.32/1.33 thf(f16,plain,(
% 0.32/1.33 ((setunionAx = $true) | ((! [X2 : $i] : (((in @ sK0 @ X2) != $true) | ((in @ X2 @ sK1) != $true)) | ($true != (in @ sK0 @ (setunion @ sK1)))) & ((($true = (in @ sK0 @ sK2)) & ($true = (in @ sK2 @ sK1))) | ($true = (in @ sK0 @ (setunion @ sK1)))))) & (! [X4 : $i,X5 : $i] : ((((in @ X4 @ (setunion @ X5)) = $true) | ! [X6 : $i] : (($true != (in @ X4 @ X6)) | ((in @ X6 @ X5) != $true))) & ((($true = (in @ X4 @ (sK3 @ X5 @ X4))) & ($true = (in @ (sK3 @ X5 @ X4) @ X5))) | ((in @ X4 @ (setunion @ X5)) != $true))) | (setunionAx != $true))),
% 0.32/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f12,f15,f14,f13])).
% 0.32/1.33 thf(f13,plain,(
% 0.32/1.33 ? [X0 : $i,X1 : $i] : ((! [X2 : $i] : (($true != (in @ X0 @ X2)) | ($true != (in @ X2 @ X1))) | ((in @ X0 @ (setunion @ X1)) != $true)) & (? [X3 : $i] : (($true = (in @ X0 @ X3)) & ((in @ X3 @ X1) = $true)) | ((in @ X0 @ (setunion @ X1)) = $true))) => ((! [X2 : $i] : (((in @ sK0 @ X2) != $true) | ((in @ X2 @ sK1) != $true)) | ($true != (in @ sK0 @ (setunion @ sK1)))) & (? [X3 : $i] : (($true = (in @ sK0 @ X3)) & ($true = (in @ X3 @ sK1))) | ($true = (in @ sK0 @ (setunion @ sK1)))))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f14,plain,(
% 0.32/1.33 ? [X3 : $i] : (($true = (in @ sK0 @ X3)) & ($true = (in @ X3 @ sK1))) => (($true = (in @ sK0 @ sK2)) & ($true = (in @ sK2 @ sK1)))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f15,plain,(
% 0.32/1.33 ! [X4 : $i,X5 : $i] : (? [X7 : $i] : (($true = (in @ X4 @ X7)) & ($true = (in @ X7 @ X5))) => (($true = (in @ X4 @ (sK3 @ X5 @ X4))) & ($true = (in @ (sK3 @ X5 @ X4) @ X5))))),
% 0.32/1.33 introduced(definition,[],[choice_axiom])).
% 0.32/1.33 thf(f12,plain,(
% 0.32/1.33 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : ((! [X2 : $i] : (($true != (in @ X0 @ X2)) | ($true != (in @ X2 @ X1))) | ((in @ X0 @ (setunion @ X1)) != $true)) & (? [X3 : $i] : (($true = (in @ X0 @ X3)) & ((in @ X3 @ X1) = $true)) | ((in @ X0 @ (setunion @ X1)) = $true)))) & (! [X4 : $i,X5 : $i] : ((((in @ X4 @ (setunion @ X5)) = $true) | ! [X6 : $i] : (($true != (in @ X4 @ X6)) | ((in @ X6 @ X5) != $true))) & (? [X7 : $i] : (($true = (in @ X4 @ X7)) & ($true = (in @ X7 @ X5))) | ((in @ X4 @ (setunion @ X5)) != $true))) | (setunionAx != $true))),
% 0.32/1.33 inference(rectify,[status(thm)],[f11])).
% 0.32/1.33 thf(f11,plain,(
% 0.32/1.33 ((setunionAx = $true) | ? [X1 : $i,X0 : $i] : ((! [X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (setunion @ X0)) != $true)) & (? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) | ((in @ X1 @ (setunion @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : ((((in @ X1 @ (setunion @ X0)) = $true) | ! [X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true))) & (? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) | ((in @ X1 @ (setunion @ X0)) != $true))) | (setunionAx != $true))),
% 0.32/1.33 inference(nnf_transformation,[status(thm)],[f6])).
% 0.32/1.33 thf(f6,plain,(
% 0.32/1.33 (setunionAx = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setunion @ X0)) = $true) <=> ? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)))),
% 0.32/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 0.32/1.33 thf(f5,plain,(
% 0.32/1.33 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0)) <=> (in @ X1 @ (setunion @ X0))))),
% 0.32/1.33 inference(rectify,[status(thm)],[f1])).
% 0.32/1.33 thf(f1,axiom,(
% 0.32/1.33 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0)) <=> (in @ X1 @ (setunion @ X0))))),
% 0.32/1.33 file('/export/starexec/sandbox2/tmp/tmp.ZAWnoIhYfk/DTF2THF_2352.p',setunionAx)).
% 0.32/1.33 % SZS output end Proof for DTF2THF_2352
% 0.32/1.33 % (2472)------------------------------
% 0.32/1.33 % (2472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (2472)Termination reason: Refutation
% 0.32/1.33
% 0.32/1.33 % (2472)Memory used [KB]: 5500
% 0.32/1.33 % (2472)Time elapsed: 0.004 s
% 0.32/1.33 % (2472)Instructions burned: 4 (million)
% 0.32/1.33 % (2472)------------------------------
% 0.32/1.33 % (2472)------------------------------
% 0.32/1.33 % (2465)Success in time 0.003 s
%------------------------------------------------------------------------------