%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU533^2 : 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 : n024.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 09:35:08 AM UTC 2026
% Result : Theorem 1.03s 0.91s
% Output : Refutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 81 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 311 ( 39 ~; 24 |; 17 &; 214 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 77 ( 0 ^; 56 !; 21 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f42,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f26]) ).
thf(f26,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( $true
!= ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
=> ( $true
!= ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setadjoinIR = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( setadjoinIL
=> ( setadjoinIR
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinIR
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setadjoinIL
=> ( setadjoinIR
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',upairsetIR) ).
thf(f28,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK3 @ ( setadjoin @ sK3 @ sK2 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ sK3 @ ( setadjoin @ sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( setadjoinIL = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',setadjoinIL) ).
thf(f41,plain,
( $true
!= ( in @ sK0 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true
!= ( in @ sK0 @ ( setadjoin @ sK0 @ emptyset ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f39]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true != $true )
| ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f32,f27]) ).
thf(f27,plain,
setadjoinIR = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f32,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( setadjoinIR != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( setadjoinIR != $true ) )
& ( ( setadjoinIR = $true )
| ( ( $true
!= ( in @ sK6 @ ( setadjoin @ sK4 @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ sK5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( setadjoin @ X3 @ X4 ) ) )
& ( $true
= ( in @ X5 @ X4 ) ) )
=> ( ( $true
!= ( in @ sK6 @ ( setadjoin @ sK4 @ sK5 ) ) )
& ( $true
= ( in @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( setadjoinIR != $true ) )
& ( ( setadjoinIR = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( setadjoin @ X3 @ X4 ) ) )
& ( $true
= ( in @ X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
| ( setadjoinIR != $true ) )
& ( ( setadjoinIR = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
& ( $true
= ( in @ X2 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
<=> ( setadjoinIR = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
=> ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) )
<=> ( setadjoinIR = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
= setadjoinIR ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
= setadjoinIR ),
file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',setadjoinIR) ).
thf(f25,plain,
( $true
!= ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU533^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:25:55 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU533^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Preliminary Notions - Equality Laws - Kuratowski Pairs
% 0.07/0.32 % Version : Especial > Reduced > Especial.
% 0.07/0.32 % English : (! x:i.! y:i.in y (setadjoin x (setadjoin y emptyset)))
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC035l [Bro08]
% 0.07/0.32 % : ZFC085l [Bro08]
% 0.07/0.32 % : ZFC118l [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.07/0.32 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 3 ( 3 avg)
% 0.07/0.32 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 16 @)
% 0.07/0.32 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 9 ( 4 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=506
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL_type,type,
% 0.07/0.32 setadjoinIL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL,definition,
% 0.07/0.32 ( setadjoinIL
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR_type,type,
% 0.07/0.32 setadjoinIR: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR,definition,
% 0.07/0.32 ( setadjoinIR
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetIR,conjecture,
% 0.07/0.32 ( setadjoinIL
% 0.07/0.32 => ( setadjoinIR
% 0.07/0.32 => ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.85/0.89 ---- Embedded in THF ---
% 0.85/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.85/0.89 %%% Generated on Tue Feb 24 07:25:56 EST 2026
% 0.85/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.85/0.89 %%% Logic specification used:
% 0.85/0.89 %%% thf(spec, logic, $$dhol).
% 0.85/0.89
% 0.85/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2DTF14319.p
% See solution above
% 0.85/0.89 ------------------------
% 1.03/0.90 ---- Cleaned THF ---
% 1.03/0.90 thf(in_type,type,
% 1.03/0.90 in: $i > $i > $o ).
% 1.03/0.90
% 1.03/0.90 thf(emptyset_type,type,
% 1.03/0.90 emptyset: $i ).
% 1.03/0.90
% 1.03/0.90 thf(setadjoin_type,type,
% 1.03/0.90 setadjoin: $i > $i > $i ).
% 1.03/0.90
% 1.03/0.90 thf(setadjoinIL_type,type,
% 1.03/0.90 setadjoinIL: $o ).
% 1.03/0.90
% 1.03/0.90 thf(setadjoinIL,definition,
% 1.03/0.90 ( setadjoinIL
% 1.03/0.90 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.03/0.90
% 1.03/0.90 thf(setadjoinIR_type,type,
% 1.03/0.90 setadjoinIR: $o ).
% 1.03/0.90
% 1.03/0.90 thf(setadjoinIR,definition,
% 1.03/0.90 ( setadjoinIR
% 1.03/0.90 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.03/0.90 ( ( in @ Xy @ A )
% 1.03/0.90 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.03/0.90
% 1.03/0.90 thf(upairsetIR,conjecture,
% 1.03/0.90 ( setadjoinIL
% 1.03/0.90 => ( setadjoinIR
% 1.03/0.90 => ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.03/0.90 ------------------------
% 1.03/0.91 % (14512)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14319 for (3000ds/2Mi)
% 1.03/0.91 % (14509)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14319 for (3000ds/183Mi)
% 1.03/0.91 % (14513)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_14319 for (3000ds/2Mi)
% 1.03/0.91 % (14514)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_14319 for (3000ds/275Mi)
% 1.03/0.91 % (14510)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_14319 for (3000ds/4Mi)
% 1.03/0.91 % (14515)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14319 for (3000ds/18Mi)
% 1.03/0.91 % (14512)Instruction limit reached!
% 1.03/0.91 % (14512)------------------------------
% 1.03/0.91 % (14512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.03/0.91 % (14512)Termination reason: Unknown
% 1.03/0.91 % (14512)Termination phase: Saturation
% 1.03/0.91
% 1.03/0.91 % (14512)Memory used [KB]: 5500
% 1.03/0.91 % (14512)Time elapsed: 0.002 s
% 1.03/0.91 % (14512)Instructions burned: 2 (million)
% 1.03/0.91 % (14512)------------------------------
% 1.03/0.91 % (14512)------------------------------
% 1.03/0.91 % (14513)Instruction limit reached!
% 1.03/0.91 % (14513)------------------------------
% 1.03/0.91 % (14513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.03/0.91 % (14513)Termination reason: Unknown
% 1.03/0.91 % (14513)Termination phase: Saturation
% 1.03/0.91
% 1.03/0.91 % (14513)Memory used [KB]: 5500
% 1.03/0.91 % (14513)Time elapsed: 0.002 s
% 1.03/0.91 % (14511)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_14319 for (3000ds/27Mi)
% 1.03/0.91 % (14513)Instructions burned: 2 (million)
% 1.03/0.91 % (14513)------------------------------
% 1.03/0.91 % (14513)------------------------------
% 1.03/0.91 % (14514)First to succeed.
% 1.03/0.91 % (14510)Instruction limit reached!
% 1.03/0.91 % (14510)------------------------------
% 1.03/0.91 % (14510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.03/0.91 % (14510)Termination reason: Unknown
% 1.03/0.91 % (14510)Termination phase: Saturation
% 1.03/0.91
% 1.03/0.91 % (14510)Memory used [KB]: 5500
% 1.03/0.91 % (14510)Time elapsed: 0.003 s
% 1.03/0.91 % (14510)Instructions burned: 4 (million)
% 1.03/0.91 % (14510)------------------------------
% 1.03/0.91 % (14510)------------------------------
% 1.03/0.91 % (14509)Also succeeded, but the first one will report.
% 1.03/0.91 % (14515)Also succeeded, but the first one will report.
% 1.03/0.91 % (14514)Refutation found. Thanks to Tanya!
% 1.03/0.91 % SZS status Theorem for DTF2THF_14319
% 1.03/0.91 % SZS output start Proof for DTF2THF_14319
% 1.03/0.91 thf(func_def_0, type, in: $i > $i > $o).
% 1.03/0.91 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.03/0.91 thf(f42,plain,(
% 1.03/0.91 $false),
% 1.03/0.91 inference(subsumption_resolution,[status(thm)],[f41,f38])).
% 1.03/0.91 thf(f38,plain,(
% 1.03/0.91 ( ! [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X3 @ X2)))) )),
% 1.03/0.91 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.03/0.91 thf(f34,plain,(
% 1.03/0.91 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true = (in @ X3 @ (setadjoin @ X3 @ X2)))) )),
% 1.03/0.91 inference(definition_unfolding,[status(thm)],[f28,f26])).
% 1.03/0.91 thf(f26,plain,(
% 1.03/0.91 (setadjoinIL = $true)),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f16])).
% 1.03/0.91 thf(f16,plain,(
% 1.03/0.91 (setadjoinIR = $true) & (setadjoinIL = $true) & ($true != (in @ sK0 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))),
% 1.03/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15])).
% 1.03/0.91 thf(f15,plain,(
% 1.03/0.91 ? [X0 : $i,X1 : $i] : ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) => ($true != (in @ sK0 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))),
% 1.03/0.91 introduced(definition,[],[choice_axiom])).
% 1.03/0.91 thf(f14,plain,(
% 1.03/0.91 (setadjoinIR = $true) & (setadjoinIL = $true) & ? [X0 : $i,X1 : $i] : ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.03/0.91 inference(flattening,[status(thm)],[f13])).
% 1.03/0.91 thf(f13,plain,(
% 1.03/0.91 (? [X0 : $i,X1 : $i] : ($true != (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) & (setadjoinIR = $true)) & (setadjoinIL = $true)),
% 1.03/0.91 inference(ennf_transformation,[status(thm)],[f7])).
% 1.03/0.91 thf(f7,plain,(
% 1.03/0.91 ~((setadjoinIL = $true) => ((setadjoinIR = $true) => ! [X0 : $i,X1 : $i] : ($true = (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))))),
% 1.03/0.91 inference(fool_elimination,[status(thm)],[f6])).
% 1.03/0.91 thf(f6,plain,(
% 1.03/0.91 ~(setadjoinIL => (setadjoinIR => ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 1.03/0.91 inference(rectify,[status(thm)],[f4])).
% 1.03/0.91 thf(f4,negated_conjecture,(
% 1.03/0.91 ~(setadjoinIL => (setadjoinIR => ! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))),
% 1.03/0.91 inference(negated_conjecture,[status(cth)],[f3])).
% 1.03/0.91 thf(f3,conjecture,(
% 1.03/0.91 setadjoinIL => (setadjoinIR => ! [X1 : $i,X0 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.03/0.91 file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',upairsetIR)).
% 1.03/0.91 thf(f28,plain,(
% 1.03/0.91 ( ! [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true)) )),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f20])).
% 1.03/0.91 thf(f20,plain,(
% 1.03/0.91 ((setadjoinIL = $true) | ($true != (in @ sK3 @ (setadjoin @ sK3 @ sK2)))) & (! [X2 : $i,X3 : $i] : ($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true))),
% 1.03/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f18,f19])).
% 1.03/0.91 thf(f19,plain,(
% 1.03/0.91 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) => ($true != (in @ sK3 @ (setadjoin @ sK3 @ sK2)))),
% 1.03/0.91 introduced(definition,[],[choice_axiom])).
% 1.03/0.91 thf(f18,plain,(
% 1.03/0.91 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X2 : $i,X3 : $i] : ($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true))),
% 1.03/0.91 inference(rectify,[status(thm)],[f17])).
% 1.03/0.91 thf(f17,plain,(
% 1.03/0.91 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true))),
% 1.03/0.91 inference(nnf_transformation,[status(thm)],[f9])).
% 1.03/0.91 thf(f9,plain,(
% 1.03/0.91 (setadjoinIL = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.03/0.91 inference(fool_elimination,[status(thm)],[f8])).
% 1.03/0.91 thf(f8,plain,(
% 1.03/0.91 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.03/0.91 inference(rectify,[status(thm)],[f1])).
% 1.03/0.91 thf(f1,axiom,(
% 1.03/0.91 (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.03/0.91 file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',setadjoinIL)).
% 1.03/0.91 thf(f41,plain,(
% 1.03/0.91 ($true != (in @ sK0 @ (setadjoin @ sK0 @ emptyset)))),
% 1.03/0.91 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.03/0.91 thf(f40,plain,(
% 1.03/0.91 ($true != (in @ sK0 @ (setadjoin @ sK0 @ emptyset))) | ($true != $true)),
% 1.03/0.91 inference(superposition,[status(thm)],[f25,f39])).
% 1.03/0.91 thf(f39,plain,(
% 1.03/0.91 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1))) )),
% 1.03/0.91 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.03/0.91 thf(f35,plain,(
% 1.03/0.91 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true != $true) | ($true = (in @ X2 @ (setadjoin @ X0 @ X1)))) )),
% 1.03/0.91 inference(definition_unfolding,[status(thm)],[f32,f27])).
% 1.03/0.91 thf(f27,plain,(
% 1.03/0.91 (setadjoinIR = $true)),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f16])).
% 1.03/0.91 thf(f32,plain,(
% 1.03/0.91 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1)) | (setadjoinIR != $true)) )),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f24])).
% 1.03/0.91 thf(f24,plain,(
% 1.03/0.91 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1))) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | (($true != (in @ sK6 @ (setadjoin @ sK4 @ sK5))) & ($true = (in @ sK6 @ sK5))))),
% 1.03/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f23])).
% 1.03/0.91 thf(f23,plain,(
% 1.03/0.91 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (setadjoin @ X3 @ X4))) & ($true = (in @ X5 @ X4))) => (($true != (in @ sK6 @ (setadjoin @ sK4 @ sK5))) & ($true = (in @ sK6 @ sK5)))),
% 1.03/0.91 introduced(definition,[],[choice_axiom])).
% 1.03/0.91 thf(f22,plain,(
% 1.03/0.91 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X0 @ X1))) | ($true != (in @ X2 @ X1))) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (setadjoin @ X3 @ X4))) & ($true = (in @ X5 @ X4))))),
% 1.03/0.91 inference(rectify,[status(thm)],[f21])).
% 1.03/0.91 thf(f21,plain,(
% 1.03/0.91 (! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | ($true != (in @ X2 @ X0))) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true != (in @ X2 @ (setadjoin @ X1 @ X0))) & ($true = (in @ X2 @ X0))))),
% 1.03/0.91 inference(nnf_transformation,[status(thm)],[f12])).
% 1.03/0.91 thf(f12,plain,(
% 1.03/0.91 ! [X1 : $i,X0 : $i,X2 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | ($true != (in @ X2 @ X0))) <=> (setadjoinIR = $true)),
% 1.03/0.91 inference(ennf_transformation,[status(thm)],[f11])).
% 1.03/0.91 thf(f11,plain,(
% 1.03/0.91 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = (in @ X2 @ X0)) => ($true = (in @ X2 @ (setadjoin @ X1 @ X0)))) <=> (setadjoinIR = $true)),
% 1.03/0.91 inference(fool_elimination,[status(thm)],[f10])).
% 1.03/0.91 thf(f10,plain,(
% 1.03/0.91 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (setadjoin @ X1 @ X0))) = setadjoinIR)),
% 1.03/0.91 inference(rectify,[status(thm)],[f2])).
% 1.03/0.91 thf(f2,axiom,(
% 1.03/0.91 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (setadjoin @ X0 @ X2))) = setadjoinIR)),
% 1.03/0.91 file('/export/starexec/sandbox/tmp/tmp.xWVfFo09gu/DTF2THF_14319.p',setadjoinIR)).
% 1.03/0.91 thf(f25,plain,(
% 1.03/0.91 ($true != (in @ sK0 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f16])).
% 1.03/0.91 % SZS output end Proof for DTF2THF_14319
% 1.03/0.91 % (14514)------------------------------
% 1.03/0.91 % (14514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.03/0.91 % (14514)Termination reason: Refutation
% 1.03/0.91
% 1.03/0.91 % (14514)Memory used [KB]: 5500
% 1.03/0.91 % (14514)Time elapsed: 0.003 s
% 1.03/0.91 % (14514)Instructions burned: 2 (million)
% 1.03/0.91 % (14514)------------------------------
% 1.03/0.91 % (14514)------------------------------
% 1.03/0.91 % (14508)Success in time 0.004 s
%------------------------------------------------------------------------------