%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU706^2 : 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 : n031.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 09:36:33 AM UTC 2026
% Result : Theorem 1.51s 1.29s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 424 ( 139 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 348 ( 41 ~; 25 |; 46 &; 194 @)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 15 con; 0-2 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 10 ^; 37 !; 19 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(f115,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f114,f110]) ).
thf(f110,plain,
sK16 != sK10,
inference(superposition,[status(thm)],[f72,f109]) ).
thf(f109,plain,
( sK16
= ( setunion @ sK9 ) ),
inference(superposition,[status(thm)],[f107,f106]) ).
thf(f106,plain,
( sK9
= ( setadjoin @ sK16 @ emptyset ) ),
inference(equality_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( $true
= ( ( setadjoin @ sK16 @ emptyset )
= sK9 ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $true
= ( ( in @ sK16 @ sK9 )
& ( ( setadjoin @ sK16 @ emptyset )
= sK9 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK9 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK9 ) )
@ sK16 ) ),
inference(sigma_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK9 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK9 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sK9 ) ),
inference(definition_unfolding,[status(thm)],[f70,f61]) ).
thf(f61,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( singleton
= ( ^ [X2: $i] :
? [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= X2 )
& ( in @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',singleton) ).
thf(f70,plain,
( $true
= ( singleton @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ( sK10
!= ( setunion @ sK9 ) )
& ( $true
= ( in @ sK10 @ sK9 ) )
& ( $true
= ( singleton @ sK9 ) )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( setunion__Cong = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f24,f47,f46]) ).
thf(f46,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( $true
= ( singleton @ X0 ) ) )
=> ( ? [X1: $i] :
( ( ( setunion @ sK9 )
!= X1 )
& ( $true
= ( in @ X1 @ sK9 ) ) )
& ( $true
= ( singleton @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ? [X1: $i] :
( ( ( setunion @ sK9 )
!= X1 )
& ( $true
= ( in @ X1 @ sK9 ) ) )
=> ( ( sK10
!= ( setunion @ sK9 ) )
& ( $true
= ( in @ sK10 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ? [X0: $i] :
( ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( $true
= ( singleton @ X0 ) ) )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( setunion__Cong = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( $true
= ( singleton @ X0 ) ) )
& ( setunionsingleton = $true )
& ( setunion__Cong = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( uniqinunit = $true )
=> ( ( in__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( setunionsingleton = $true )
=> ! [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
=> ! [X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X6: $i] :
( ( singleton @ X6 )
=> ! [X0: $i] :
( ( in @ X0 @ X6 )
=> ( ( setunion @ X6 )
= X0 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X6: $i] :
( ( singleton @ X6 )
=> ! [X0: $i] :
( ( in @ X0 @ X6 )
=> ( ( setunion @ X6 )
= X0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',theeq) ).
thf(f107,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(definition_unfolding,[status(thm)],[f66,f73]) ).
thf(f73,plain,
setunionsingleton = $true,
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f66,plain,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ( sK8
!= ( setunion @ ( setadjoin @ sK8 @ emptyset ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f43,f44]) ).
thf(f44,plain,
( ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 )
=> ( sK8
!= ( setunion @ ( setadjoin @ sK8 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
<=> ( setunionsingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
= setunionsingleton ),
file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',setunionsingleton) ).
thf(f72,plain,
( sK10
!= ( setunion @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f114,plain,
sK16 = sK10,
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( sK16 = sK10 ) ),
inference(superposition,[status(thm)],[f111,f71]) ).
thf(f71,plain,
( $true
= ( in @ sK10 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f111,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK9 ) )
| ( sK16 = X0 ) ),
inference(superposition,[status(thm)],[f108,f106]) ).
thf(f108,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f64,f74]) ).
thf(f74,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f64,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( $true
= ( in @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) )
& ( sK7 != sK6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f39,f40]) ).
thf(f40,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
& ( X2 != X3 ) )
=> ( ( $true
= ( in @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) )
& ( sK7 != sK6 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( uniqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',uniqinunit) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU706^2 : 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 : n031.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 12:32:33 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
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU706^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Conditionals
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! X:i.singleton X -> (! x:i.in x X -> setunion X = x))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC208l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 17 ( 6 unt; 10 typ; 6 def)
% 0.28/0.47 % Number of atoms : 34 ( 17 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 8 ( 4 avg)
% 0.28/0.47 % Number of connectives : 40 ( 0 ~; 0 |; 1 &; 25 @)
% 0.28/0.47 % ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 12 ( 3 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 11 ( 10 usr; 6 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 17 ( 1 ^; 15 !; 1 ?; 17 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=262
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong_type,type,
% 0.28/0.47 setadjoin__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong,definition,
% 0.28/0.47 ( setadjoin__Cong
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ! [Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( Xz = Xu )
% 0.28/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong_type,type,
% 0.28/0.47 setunion__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong,definition,
% 0.28/0.47 ( setunion__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( setunion @ A )
% 0.28/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton_type,type,
% 0.28/0.47 setunionsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton,definition,
% 0.28/0.47 ( setunionsingleton
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singleton,definition,
% 0.28/0.47 ( singleton
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theeq,conjecture,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( setunionsingleton
% 0.28/0.47 => ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ X )
% 0.28/0.47 => ( ( setunion @ X )
% 0.28/0.47 = Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.51/1.25 ---- Embedded in THF ---
% 1.51/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.25 %%% Generated on Tue Feb 24 12:32:34 EST 2026
% 1.51/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.25 %%% Logic specification used:
% 1.51/1.25 %%% thf(spec, logic, $$dhol).
% 1.51/1.25
% 1.51/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2DTF26023.p
% See solution above
% 1.51/1.25 ------------------------
% 1.51/1.26 ---- Cleaned THF ---
% 1.51/1.27 thf(in_type,type,
% 1.51/1.27 in: $i > $i > $o ).
% 1.51/1.27
% 1.51/1.27 thf(emptyset_type,type,
% 1.51/1.27 emptyset: $i ).
% 1.51/1.27
% 1.51/1.27 thf(setadjoin_type,type,
% 1.51/1.27 setadjoin: $i > $i > $i ).
% 1.51/1.27
% 1.51/1.27 thf(setunion_type,type,
% 1.51/1.27 setunion: $i > $i ).
% 1.51/1.27
% 1.51/1.27 thf(uniqinunit_type,type,
% 1.51/1.27 uniqinunit: $o ).
% 1.51/1.27
% 1.51/1.27 thf(uniqinunit,definition,
% 1.51/1.27 ( uniqinunit
% 1.51/1.27 = ( ! [Xx: $i,Xy: $i] :
% 1.51/1.27 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.51/1.27 => ( Xx = Xy ) ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(in__Cong_type,type,
% 1.51/1.27 in__Cong: $o ).
% 1.51/1.27
% 1.51/1.27 thf(in__Cong,definition,
% 1.51/1.27 ( in__Cong
% 1.51/1.27 = ( ! [A: $i,B: $i] :
% 1.51/1.27 ( ( A = B )
% 1.51/1.27 => ! [Xx: $i,Xy: $i] :
% 1.51/1.27 ( ( Xx = Xy )
% 1.51/1.27 => ( ( in @ Xx @ A )
% 1.51/1.27 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(setadjoin__Cong_type,type,
% 1.51/1.27 setadjoin__Cong: $o ).
% 1.51/1.27
% 1.51/1.27 thf(setadjoin__Cong,definition,
% 1.51/1.27 ( setadjoin__Cong
% 1.51/1.27 = ( ! [Xx: $i,Xy: $i] :
% 1.51/1.27 ( ( Xx = Xy )
% 1.51/1.27 => ! [Xz: $i,Xu: $i] :
% 1.51/1.27 ( ( Xz = Xu )
% 1.51/1.27 => ( ( setadjoin @ Xx @ Xz )
% 1.51/1.27 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(setunion__Cong_type,type,
% 1.51/1.27 setunion__Cong: $o ).
% 1.51/1.27
% 1.51/1.27 thf(setunion__Cong,definition,
% 1.51/1.27 ( setunion__Cong
% 1.51/1.27 = ( ! [A: $i,B: $i] :
% 1.51/1.27 ( ( A = B )
% 1.51/1.27 => ( ( setunion @ A )
% 1.51/1.27 = ( setunion @ B ) ) ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(setunionsingleton_type,type,
% 1.51/1.27 setunionsingleton: $o ).
% 1.51/1.27
% 1.51/1.27 thf(setunionsingleton,definition,
% 1.51/1.27 ( setunionsingleton
% 1.51/1.27 = ( ! [Xx: $i] :
% 1.51/1.27 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 1.51/1.27 = Xx ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(singleton_type,type,
% 1.51/1.27 singleton: $i > $o ).
% 1.51/1.27
% 1.51/1.27 thf(singleton,definition,
% 1.51/1.27 ( singleton
% 1.51/1.27 = ( ^ [A: $i] :
% 1.51/1.27 ? [Xx: $i] :
% 1.51/1.27 ( ( in @ Xx @ A )
% 1.51/1.27 & ( A
% 1.51/1.27 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.51/1.27
% 1.51/1.27 thf(theeq,conjecture,
% 1.51/1.27 ( uniqinunit
% 1.51/1.27 => ( in__Cong
% 1.51/1.27 => ( setadjoin__Cong
% 1.51/1.27 => ( setunion__Cong
% 1.51/1.27 => ( setunionsingleton
% 1.51/1.27 => ! [X: $i] :
% 1.51/1.27 ( ( singleton @ X )
% 1.51/1.27 => ! [Xx: $i] :
% 1.51/1.27 ( ( in @ Xx @ X )
% 1.51/1.27 => ( ( setunion @ X )
% 1.51/1.27 = Xx ) ) ) ) ) ) ) ) ).
% 1.51/1.27 ------------------------
% 1.51/1.28 % (26292)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_26023 for (2999ds/275Mi)
% 1.51/1.28 % (26290)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26023 for (2999ds/2Mi)
% 1.51/1.28 % (26290)Instruction limit reached!
% 1.51/1.28 % (26290)------------------------------
% 1.51/1.28 % (26290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (26290)Termination reason: Unknown
% 1.51/1.28 % (26290)Termination phase: Preprocessing 3
% 1.51/1.28
% 1.51/1.28 % (26290)Memory used [KB]: 1023
% 1.51/1.28 % (26290)Time elapsed: 0.002 s
% 1.51/1.28 % (26290)Instructions burned: 2 (million)
% 1.51/1.28 % (26290)------------------------------
% 1.51/1.28 % (26290)------------------------------
% 1.51/1.28 % (26292)Refutation not found, incomplete strategy
% 1.51/1.28 % (26292)------------------------------
% 1.51/1.28 % (26292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (26292)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.28
% 1.51/1.28
% 1.51/1.28 % (26292)Memory used [KB]: 5500
% 1.51/1.28 % (26292)Time elapsed: 0.003 s
% 1.51/1.28 % (26292)Instructions burned: 3 (million)
% 1.51/1.28 % (26292)------------------------------
% 1.51/1.28 % (26292)------------------------------
% 1.51/1.29 % (26288)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_26023 for (2999ds/4Mi)
% 1.51/1.29 % (26287)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26023 for (2999ds/183Mi)
% 1.51/1.29 % (26289)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_26023 for (2999ds/27Mi)
% 1.51/1.29 % (26291)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_26023 for (2999ds/2Mi)
% 1.51/1.29 % (26293)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26023 for (2999ds/18Mi)
% 1.51/1.29 % (26291)Instruction limit reached!
% 1.51/1.29 % (26291)------------------------------
% 1.51/1.29 % (26291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26291)Termination reason: Unknown
% 1.51/1.29 % (26291)Termination phase: shuffling
% 1.51/1.29
% 1.51/1.29 % (26291)Memory used [KB]: 1023
% 1.51/1.29 % (26291)Time elapsed: 0.003 s
% 1.51/1.29 % (26291)Instructions burned: 2 (million)
% 1.51/1.29 % (26291)------------------------------
% 1.51/1.29 % (26291)------------------------------
% 1.51/1.29 % (26288)Instruction limit reached!
% 1.51/1.29 % (26288)------------------------------
% 1.51/1.29 % (26288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26288)Termination reason: Unknown
% 1.51/1.29 % (26288)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (26288)Memory used [KB]: 5500
% 1.51/1.29 % (26288)Time elapsed: 0.005 s
% 1.51/1.29 % (26288)Instructions burned: 5 (million)
% 1.51/1.29 % (26288)------------------------------
% 1.51/1.29 % (26288)------------------------------
% 1.51/1.29 % (26294)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26023 for (2999ds/3Mi)
% 1.51/1.29 % (26293)First to succeed.
% 1.51/1.29 % (26295)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_26023 for (2999ds/37Mi)
% 1.51/1.29 % (26294)Instruction limit reached!
% 1.51/1.29 % (26294)------------------------------
% 1.51/1.29 % (26294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26294)Termination reason: Unknown
% 1.51/1.29 % (26294)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (26294)Memory used [KB]: 5500
% 1.51/1.29 % (26294)Time elapsed: 0.003 s
% 1.51/1.29 % (26294)Instructions burned: 4 (million)
% 1.51/1.29 % (26294)------------------------------
% 1.51/1.29 % (26294)------------------------------
% 1.51/1.29 % (26293)Refutation found. Thanks to Tanya!
% 1.51/1.29 % SZS status Theorem for DTF2THF_26023
% 1.51/1.29 % SZS output start Proof for DTF2THF_26023
% 1.51/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.51/1.29 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.51/1.29 thf(func_def_3, type, setunion: $i > $i).
% 1.51/1.29 thf(func_def_10, type, singleton: $i > $o).
% 1.51/1.29 thf(f115,plain,(
% 1.51/1.29 $false),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f114,f110])).
% 1.51/1.29 thf(f110,plain,(
% 1.51/1.29 (sK16 != sK10)),
% 1.51/1.29 inference(superposition,[status(thm)],[f72,f109])).
% 1.51/1.29 thf(f109,plain,(
% 1.51/1.29 (sK16 = (setunion @ sK9))),
% 1.51/1.29 inference(superposition,[status(thm)],[f107,f106])).
% 1.51/1.29 thf(f106,plain,(
% 1.51/1.29 (sK9 = (setadjoin @ sK16 @ emptyset))),
% 1.51/1.29 inference(equality_proxy_clausification,[status(thm)],[f104])).
% 1.51/1.29 thf(f104,plain,(
% 1.51/1.29 ($true = ((setadjoin @ sK16 @ emptyset) = sK9))),
% 1.51/1.29 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.51/1.29 thf(f103,plain,(
% 1.51/1.29 ($true = ((in @ sK16 @ sK9) & ((setadjoin @ sK16 @ emptyset) = sK9)))),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.51/1.29 thf(f102,plain,(
% 1.51/1.29 ($true = ((^[Y0 : $i]: ((in @ Y0 @ sK9) & ((setadjoin @ Y0 @ emptyset) = sK9))) @ sK16))),
% 1.51/1.29 inference(sigma_clausification,[status(thm)],[f101])).
% 1.51/1.29 thf(f101,plain,(
% 1.51/1.29 ($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK9) & ((setadjoin @ Y0 @ emptyset) = sK9)))))),
% 1.51/1.29 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.51/1.29 thf(f91,plain,(
% 1.51/1.29 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))) @ sK9))),
% 1.51/1.29 inference(definition_unfolding,[status(thm)],[f70,f61])).
% 1.51/1.29 thf(f61,plain,(
% 1.51/1.29 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.51/1.29 thf(f15,plain,(
% 1.51/1.29 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f14])).
% 1.51/1.29 thf(f14,plain,(
% 1.51/1.29 (singleton = (^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 1.51/1.29 inference(rectify,[status(thm)],[f6])).
% 1.51/1.29 thf(f6,axiom,(
% 1.51/1.29 (singleton = (^[X2 : $i] : (? [X0 : $i] : (((setadjoin @ X0 @ emptyset) = X2) & (in @ X0 @ X2)))))),
% 1.51/1.29 file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',singleton)).
% 1.51/1.29 thf(f70,plain,(
% 1.51/1.29 ($true = (singleton @ sK9))),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f48])).
% 1.51/1.29 thf(f48,plain,(
% 1.51/1.29 (uniqinunit = $true) & (setunionsingleton = $true) & (((sK10 != (setunion @ sK9)) & ($true = (in @ sK10 @ sK9))) & ($true = (singleton @ sK9))) & (setadjoin__Cong = $true) & (in__Cong = $true) & (setunion__Cong = $true)),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f24,f47,f46])).
% 1.51/1.29 thf(f46,plain,(
% 1.51/1.29 ? [X0 : $i] : (? [X1 : $i] : (((setunion @ X0) != X1) & ($true = (in @ X1 @ X0))) & ($true = (singleton @ X0))) => (? [X1 : $i] : (((setunion @ sK9) != X1) & ($true = (in @ X1 @ sK9))) & ($true = (singleton @ sK9)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f47,plain,(
% 1.51/1.29 ? [X1 : $i] : (((setunion @ sK9) != X1) & ($true = (in @ X1 @ sK9))) => ((sK10 != (setunion @ sK9)) & ($true = (in @ sK10 @ sK9)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f24,plain,(
% 1.51/1.29 (uniqinunit = $true) & (setunionsingleton = $true) & ? [X0 : $i] : (? [X1 : $i] : (((setunion @ X0) != X1) & ($true = (in @ X1 @ X0))) & ($true = (singleton @ X0))) & (setadjoin__Cong = $true) & (in__Cong = $true) & (setunion__Cong = $true)),
% 1.51/1.29 inference(flattening,[status(thm)],[f23])).
% 1.51/1.29 thf(f23,plain,(
% 1.51/1.29 ((((? [X0 : $i] : (? [X1 : $i] : (((setunion @ X0) != X1) & ($true = (in @ X1 @ X0))) & ($true = (singleton @ X0))) & (setunionsingleton = $true)) & (setunion__Cong = $true)) & (setadjoin__Cong = $true)) & (in__Cong = $true)) & (uniqinunit = $true)),
% 1.51/1.29 inference(ennf_transformation,[status(thm)],[f18])).
% 1.51/1.29 thf(f18,plain,(
% 1.51/1.29 ~((uniqinunit = $true) => ((in__Cong = $true) => ((setadjoin__Cong = $true) => ((setunion__Cong = $true) => ((setunionsingleton = $true) => ! [X0 : $i] : (($true = (singleton @ X0)) => ! [X1 : $i] : (($true = (in @ X1 @ X0)) => ((setunion @ X0) = X1))))))))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f17])).
% 1.51/1.29 thf(f17,plain,(
% 1.51/1.29 ~(uniqinunit => (in__Cong => (setadjoin__Cong => (setunion__Cong => (setunionsingleton => ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ((setunion @ X0) = X1))))))))),
% 1.51/1.29 inference(rectify,[status(thm)],[f8])).
% 1.51/1.29 thf(f8,negated_conjecture,(
% 1.51/1.29 ~(uniqinunit => (in__Cong => (setadjoin__Cong => (setunion__Cong => (setunionsingleton => ! [X6 : $i] : ((singleton @ X6) => ! [X0 : $i] : ((in @ X0 @ X6) => ((setunion @ X6) = X0))))))))),
% 1.51/1.29 inference(negated_conjecture,[status(cth)],[f7])).
% 1.51/1.29 thf(f7,conjecture,(
% 1.51/1.29 uniqinunit => (in__Cong => (setadjoin__Cong => (setunion__Cong => (setunionsingleton => ! [X6 : $i] : ((singleton @ X6) => ! [X0 : $i] : ((in @ X0 @ X6) => ((setunion @ X6) = X0)))))))),
% 1.51/1.29 file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',theeq)).
% 1.51/1.29 thf(f107,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.51/1.29 thf(f89,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (($true != $true) | ((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.51/1.29 inference(definition_unfolding,[status(thm)],[f66,f73])).
% 1.51/1.29 thf(f73,plain,(
% 1.51/1.29 (setunionsingleton = $true)),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f48])).
% 1.51/1.29 thf(f66,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f45])).
% 1.51/1.29 thf(f45,plain,(
% 1.51/1.29 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | (sK8 != (setunion @ (setadjoin @ sK8 @ emptyset))))),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f43,f44])).
% 1.51/1.29 thf(f44,plain,(
% 1.51/1.29 ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1) => (sK8 != (setunion @ (setadjoin @ sK8 @ emptyset)))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f43,plain,(
% 1.51/1.29 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1))),
% 1.51/1.29 inference(rectify,[status(thm)],[f42])).
% 1.51/1.29 thf(f42,plain,(
% 1.51/1.29 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0))),
% 1.51/1.29 inference(nnf_transformation,[status(thm)],[f16])).
% 1.51/1.29 thf(f16,plain,(
% 1.51/1.29 ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) <=> (setunionsingleton = $true)),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.51/1.29 thf(f5,axiom,(
% 1.51/1.29 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) = setunionsingleton)),
% 1.51/1.29 file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',setunionsingleton)).
% 1.51/1.29 thf(f72,plain,(
% 1.51/1.29 (sK10 != (setunion @ sK9))),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f48])).
% 1.51/1.29 thf(f114,plain,(
% 1.51/1.29 (sK16 = sK10)),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.51/1.29 thf(f112,plain,(
% 1.51/1.29 ($true != $true) | (sK16 = sK10)),
% 1.51/1.29 inference(superposition,[status(thm)],[f111,f71])).
% 1.51/1.29 thf(f71,plain,(
% 1.51/1.29 ($true = (in @ sK10 @ sK9))),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f48])).
% 1.51/1.29 thf(f111,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (($true != (in @ X0 @ sK9)) | (sK16 = X0)) )),
% 1.51/1.29 inference(superposition,[status(thm)],[f108,f106])).
% 1.51/1.29 thf(f108,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) )),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.51/1.29 thf(f86,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1) | ($true != $true)) )),
% 1.51/1.29 inference(definition_unfolding,[status(thm)],[f64,f74])).
% 1.51/1.29 thf(f74,plain,(
% 1.51/1.29 (uniqinunit = $true)),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f48])).
% 1.51/1.29 thf(f64,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1) | (uniqinunit != $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f41])).
% 1.51/1.29 thf(f41,plain,(
% 1.51/1.29 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | (($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset))) & (sK7 != sK6)))),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f39,f40])).
% 1.51/1.29 thf(f40,plain,(
% 1.51/1.29 ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ (setadjoin @ X3 @ emptyset))) & (X2 != X3)) => (($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset))) & (sK7 != sK6))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f39,plain,(
% 1.51/1.29 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X2 @ (setadjoin @ X3 @ emptyset))) & (X2 != X3)))),
% 1.51/1.29 inference(rectify,[status(thm)],[f38])).
% 1.51/1.29 thf(f38,plain,(
% 1.51/1.29 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1)))),
% 1.51/1.29 inference(nnf_transformation,[status(thm)],[f26])).
% 1.51/1.29 thf(f26,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) <=> (uniqinunit = $true)),
% 1.51/1.29 inference(ennf_transformation,[status(thm)],[f20])).
% 1.51/1.29 thf(f20,plain,(
% 1.51/1.29 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f19])).
% 1.51/1.29 thf(f19,plain,(
% 1.51/1.29 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.51/1.29 inference(rectify,[status(thm)],[f1])).
% 1.51/1.29 thf(f1,axiom,(
% 1.51/1.29 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 1.51/1.29 file('/export/starexec/sandbox2/tmp/tmp.X3mwlUDXaZ/DTF2THF_26023.p',uniqinunit)).
% 1.51/1.29 % SZS output end Proof for DTF2THF_26023
% 1.51/1.29 % (26293)------------------------------
% 1.51/1.29 % (26293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (26293)Termination reason: Refutation
% 1.51/1.29
% 1.51/1.29 % (26293)Memory used [KB]: 5500
% 1.51/1.29 % (26293)Time elapsed: 0.007 s
% 1.51/1.29 % (26293)Instructions burned: 5 (million)
% 1.51/1.29 % (26293)------------------------------
% 1.51/1.30 % (26293)------------------------------
% 1.51/1.30 % (26286)Success in time 0.022 s
%------------------------------------------------------------------------------