%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU508^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:34:59 AM UTC 2026
% Result : Theorem 1.60s 1.30s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 30 unt; 0 typ; 4 def)
% Number of atoms : 387 ( 80 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 545 ( 30 ~; 34 |; 11 &; 377 @)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 11 con; 0-2 aty)
% ( 36 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 128 ( 62 ^; 57 !; 9 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f61,f69,f75,f119]) ).
thf(f119,plain,
( spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
| spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true = $false )
| spl3_3
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f19,f97]) ).
thf(f97,plain,
( ( $false
= ( in @ sK1 @ sK2 ) )
| spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f96,f55]) ).
thf(f55,plain,
( ( ( sK0 @ sK1 )
!= $false )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl3_3
<=> ( ( sK0 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f96,plain,
( ( $false
= ( in @ sK1 @ sK2 ) )
| ( ( sK0 @ sK1 )
= $false )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( ( sK0 @ sK1 )
= $false )
| ( $false
= ( in @ sK1 @ sK2 ) )
| ( $true = $false )
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f60,f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X3 @ X2 ) )
| ( $true
= ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f16]) ).
thf(f16,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',dsetconstrI) ).
thf(f20,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( dsetconstrI = $true )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
!= ( sK0 @ sK1 ) )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= ( X0 @ X1 ) ) )
=> ( ( $true
= ( in @ sK1 @ sK2 ) )
& ( ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
!= ( sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( dsetconstrI = $true )
& ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= ( X0 @ X1 ) ) )
& ( dsetconstrER = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= ( X0 @ X1 ) ) )
& ( dsetconstrER = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrI = $true )
=> ( ( dsetconstrER = $true )
=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= ( X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrI
=> ( dsetconstrER
=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
<=> ( X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrER
=> ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrI
=> ( dsetconstrER
=> ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',setbeta) ).
thf(f60,plain,
( ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl3_4
<=> ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f19,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f75,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f74]) ).
thf(f74,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f56,f47]) ).
thf(f47,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl3_1
<=> ( ( sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f56,plain,
( ( ( sK0 @ sK1 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f69,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f66,f49,f45]) ).
thf(f49,definition,
( spl3_2
<=> ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f66,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( $true = $false )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f43,f51]) ).
thf(f51,plain,
( ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f43,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f17]) ).
thf(f17,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f21,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',dsetconstrER) ).
thf(f61,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f35,f58,f54]) ).
thf(f35,plain,
( ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $false )
| ( ( sK0 @ sK1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
!= ( sK0 @ sK1 ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f52,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f49,f45]) ).
thf(f34,plain,
( ( ( in @ sK1 @ ( dsetconstr @ sK2 @ sK0 ) )
= $true )
| ( ( sK0 @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU508^2 : 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
% 0.18/0.34 % Computer : n020.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:24:57 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU508^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.30/0.47 % Version : Especial > Reduced > Especial.
% 0.30/0.47 % English : (! A:i.! phi:i>o.! x:i.in x A -> (in x (dsetconstr A
% 0.30/0.47 % (^ y:i.phi y)) <-> phi x))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC010l [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.30/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.30/0.47 % Number of atoms : 11 ( 2 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.30/0.47 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 22 @)
% 0.30/0.47 % ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 12 ( 5 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 12 ( 3 ^; 9 !; 0 ?; 12 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=459
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstr_type,type,
% 0.30/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI_type,type,
% 0.30/0.47 dsetconstrI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI,definition,
% 0.30/0.47 ( dsetconstrI
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER_type,type,
% 0.30/0.47 dsetconstrER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER,definition,
% 0.30/0.47 ( dsetconstrER
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setbeta,conjecture,
% 0.30/0.47 ( dsetconstrI
% 0.30/0.47 => ( dsetconstrER
% 0.30/0.47 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.44/1.26 ---- Embedded in THF ---
% 1.44/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.26 %%% Generated on Tue Feb 24 12:24:58 EST 2026
% 1.44/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.26 %%% Logic specification used:
% 1.44/1.26 %%% thf(spec, logic, $$dhol).
% 1.44/1.26
% 1.44/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2DTF12186.p
% See solution above
% 1.44/1.27 ------------------------
% 1.44/1.28 ---- Cleaned THF ---
% 1.44/1.28 thf(in_type,type,
% 1.44/1.28 in: $i > $i > $o ).
% 1.44/1.28
% 1.44/1.28 thf(dsetconstr_type,type,
% 1.44/1.28 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.44/1.28
% 1.44/1.28 thf(dsetconstrI_type,type,
% 1.44/1.28 dsetconstrI: $o ).
% 1.44/1.28
% 1.44/1.28 thf(dsetconstrI,definition,
% 1.44/1.28 ( dsetconstrI
% 1.44/1.28 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.44/1.28 ( ( in @ Xx @ A )
% 1.44/1.28 => ( ( Xphi @ Xx )
% 1.44/1.28 => ( in @ Xx
% 1.44/1.28 @ ( dsetconstr @ A
% 1.44/1.28 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.44/1.28
% 1.44/1.28 thf(dsetconstrER_type,type,
% 1.44/1.28 dsetconstrER: $o ).
% 1.44/1.28
% 1.44/1.28 thf(dsetconstrER,definition,
% 1.44/1.28 ( dsetconstrER
% 1.44/1.28 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.44/1.28 ( ( in @ Xx
% 1.44/1.28 @ ( dsetconstr @ A
% 1.44/1.28 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.44/1.28 => ( Xphi @ Xx ) ) ) ) ).
% 1.44/1.28
% 1.44/1.28 thf(setbeta,conjecture,
% 1.44/1.28 ( dsetconstrI
% 1.44/1.28 => ( dsetconstrER
% 1.44/1.28 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.44/1.28 ( ( in @ Xx @ A )
% 1.44/1.28 => ( ( in @ Xx
% 1.44/1.28 @ ( dsetconstr @ A
% 1.44/1.28 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.44/1.28 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.44/1.28 ------------------------
% 1.44/1.29 % (12300)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12186 for (2999ds/183Mi)
% 1.60/1.30 % (12300)First to succeed.
% 1.60/1.30 % (12300)Refutation found. Thanks to Tanya!
% 1.60/1.30 % SZS status Theorem for DTF2THF_12186
% 1.60/1.30 % SZS output start Proof for DTF2THF_12186
% 1.60/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.60/1.30 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.60/1.30 thf(func_def_14, type, sK0: $i > $o).
% 1.60/1.30 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.60/1.30 thf(f120,plain,(
% 1.60/1.30 $false),
% 1.60/1.30 inference(avatar_sat_refutation,[status(thm)],[f52,f61,f69,f75,f119])).
% 1.60/1.30 thf(f119,plain,(
% 1.60/1.30 spl3_3 | ~spl3_4),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.60/1.30 thf(f118,plain,(
% 1.60/1.30 $false | (spl3_3 | ~spl3_4)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.60/1.30 thf(f115,plain,(
% 1.60/1.30 ($true = $false) | (spl3_3 | ~spl3_4)),
% 1.60/1.30 inference(superposition,[status(thm)],[f19,f97])).
% 1.60/1.30 thf(f97,plain,(
% 1.60/1.30 ($false = (in @ sK1 @ sK2)) | (spl3_3 | ~spl3_4)),
% 1.60/1.30 inference(subsumption_resolution,[status(thm)],[f96,f55])).
% 1.60/1.30 thf(f55,plain,(
% 1.60/1.30 ((sK0 @ sK1) != $false) | spl3_3),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.60/1.30 thf(f54,definition,(
% 1.60/1.30 spl3_3 <=> ((sK0 @ sK1) = $false)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.60/1.30 thf(f96,plain,(
% 1.60/1.30 ($false = (in @ sK1 @ sK2)) | ((sK0 @ sK1) = $false) | ~spl3_4),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.60/1.30 thf(f88,plain,(
% 1.60/1.30 ((sK0 @ sK1) = $false) | ($false = (in @ sK1 @ sK2)) | ($true = $false) | ~spl3_4),
% 1.60/1.30 inference(superposition,[status(thm)],[f60,f32])).
% 1.60/1.30 thf(f32,plain,(
% 1.60/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (in @ X3 @ (dsetconstr @ X2 @ X1))) | ($false = (in @ X3 @ X2)) | ((X1 @ X3) = $false)) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.60/1.30 thf(f31,plain,(
% 1.60/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X3 @ X2)) | ($true = ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1))))) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.60/1.30 thf(f30,plain,(
% 1.60/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X3 @ X2) => ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.60/1.30 thf(f29,plain,(
% 1.60/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1))))) @ X3))) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f28])).
% 1.60/1.30 thf(f28,plain,(
% 1.60/1.30 ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1)))))))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.60/1.30 thf(f27,plain,(
% 1.60/1.30 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))) @ X2))) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f26])).
% 1.60/1.30 thf(f26,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))) = $true)) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.60/1.30 thf(f25,plain,(
% 1.60/1.30 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))) @ X1))) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f24])).
% 1.60/1.30 thf(f24,plain,(
% 1.60/1.30 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.60/1.30 thf(f22,plain,(
% 1.60/1.30 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 1.60/1.30 inference(definition_unfolding,[status(thm)],[f20,f16])).
% 1.60/1.30 thf(f16,plain,(
% 1.60/1.30 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.30 thf(f9,plain,(
% 1.60/1.30 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.60/1.30 thf(f8,plain,(
% 1.60/1.30 (dsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))),
% 1.60/1.30 inference(rectify,[status(thm)],[f1])).
% 1.60/1.30 thf(f1,axiom,(
% 1.60/1.30 (dsetconstrI = ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',dsetconstrI)).
% 1.60/1.30 thf(f20,plain,(
% 1.60/1.30 (dsetconstrI = $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.60/1.30 thf(f15,plain,(
% 1.60/1.30 (dsetconstrI = $true) & (($true = (in @ sK1 @ sK2)) & ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))) != (sK0 @ sK1))) & (dsetconstrER = $true)),
% 1.60/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.60/1.30 thf(f14,plain,(
% 1.60/1.30 ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != (X0 @ X1))) => (($true = (in @ sK1 @ sK2)) & ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))) != (sK0 @ sK1)))),
% 1.60/1.30 introduced(definition,[],[choice_axiom])).
% 1.60/1.30 thf(f13,plain,(
% 1.60/1.30 (dsetconstrI = $true) & ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != (X0 @ X1))) & (dsetconstrER = $true)),
% 1.60/1.30 inference(flattening,[status(thm)],[f12])).
% 1.60/1.30 thf(f12,plain,(
% 1.60/1.30 (? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != (X0 @ X1))) & (dsetconstrER = $true)) & (dsetconstrI = $true)),
% 1.60/1.30 inference(ennf_transformation,[status(thm)],[f7])).
% 1.60/1.30 thf(f7,plain,(
% 1.60/1.30 ~((dsetconstrI = $true) => ((dsetconstrER = $true) => ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = (X0 @ X1)))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.60/1.30 thf(f6,plain,(
% 1.60/1.30 ~(dsetconstrI => (dsetconstrER => ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) <=> (X0 @ X1)))))),
% 1.60/1.30 inference(rectify,[status(thm)],[f4])).
% 1.60/1.30 thf(f4,negated_conjecture,(
% 1.60/1.30 ~(dsetconstrI => (dsetconstrER => ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) <=> (X1 @ X2)))))),
% 1.60/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.60/1.30 thf(f3,conjecture,(
% 1.60/1.30 dsetconstrI => (dsetconstrER => ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) <=> (X1 @ X2))))),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',setbeta)).
% 1.60/1.30 thf(f60,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $false) | ~spl3_4),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.60/1.30 thf(f58,definition,(
% 1.60/1.30 spl3_4 <=> ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $false)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.60/1.30 thf(f19,plain,(
% 1.60/1.30 ($true = (in @ sK1 @ sK2))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.60/1.30 thf(f75,plain,(
% 1.60/1.30 ~spl3_1 | ~spl3_3),
% 1.60/1.30 inference(avatar_contradiction_clause,[status(thm)],[f74])).
% 1.60/1.30 thf(f74,plain,(
% 1.60/1.30 $false | (~spl3_1 | ~spl3_3)),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.60/1.30 thf(f71,plain,(
% 1.60/1.30 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 1.60/1.30 inference(superposition,[status(thm)],[f56,f47])).
% 1.60/1.30 thf(f47,plain,(
% 1.60/1.30 ((sK0 @ sK1) = $true) | ~spl3_1),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.60/1.30 thf(f45,definition,(
% 1.60/1.30 spl3_1 <=> ((sK0 @ sK1) = $true)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.60/1.30 thf(f56,plain,(
% 1.60/1.30 ((sK0 @ sK1) = $false) | ~spl3_3),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.60/1.30 thf(f69,plain,(
% 1.60/1.30 spl3_1 | ~spl3_2),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f66,f49,f45])).
% 1.60/1.30 thf(f49,definition,(
% 1.60/1.30 spl3_2 <=> ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $true)),
% 1.60/1.30 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.60/1.30 thf(f66,plain,(
% 1.60/1.30 ((sK0 @ sK1) = $true) | ~spl3_2),
% 1.60/1.30 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.60/1.30 thf(f62,plain,(
% 1.60/1.30 ((sK0 @ sK1) = $true) | ($true = $false) | ~spl3_2),
% 1.60/1.30 inference(superposition,[status(thm)],[f43,f51])).
% 1.60/1.30 thf(f51,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $true) | ~spl3_2),
% 1.60/1.30 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.60/1.30 thf(f43,plain,(
% 1.60/1.30 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ X3 @ X2))) | ((X2 @ X1) = $true)) )),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.60/1.30 thf(f42,plain,(
% 1.60/1.30 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X3 @ X2)) => (X2 @ X1)))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.60/1.30 thf(f41,plain,(
% 1.60/1.30 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1))) @ X3) = $true)) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f40])).
% 1.60/1.30 thf(f40,plain,(
% 1.60/1.30 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1)))))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.60/1.30 thf(f39,plain,(
% 1.60/1.30 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1))))) @ X2) = $true)) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f38])).
% 1.60/1.30 thf(f38,plain,(
% 1.60/1.30 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1)))))))) )),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.60/1.30 thf(f37,plain,(
% 1.60/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0))))))) @ X1))) )),
% 1.60/1.30 inference(pi_clausification,[status(thm)],[f36])).
% 1.60/1.30 thf(f36,plain,(
% 1.60/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))))),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.60/1.30 thf(f23,plain,(
% 1.60/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.60/1.30 inference(definition_unfolding,[status(thm)],[f21,f17])).
% 1.60/1.30 thf(f17,plain,(
% 1.60/1.30 (dsetconstrER = $true)),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.60/1.30 thf(f21,plain,(
% 1.60/1.30 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.60/1.30 thf(f11,plain,(
% 1.60/1.30 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 1.60/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.60/1.30 thf(f10,plain,(
% 1.60/1.30 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.60/1.30 inference(rectify,[status(thm)],[f2])).
% 1.60/1.30 thf(f2,axiom,(
% 1.60/1.30 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.60/1.30 file('/export/starexec/sandbox2/tmp/tmp.Zcbfgt1ocJ/DTF2THF_12186.p',dsetconstrER)).
% 1.60/1.30 thf(f61,plain,(
% 1.60/1.30 spl3_3 | spl3_4),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f35,f58,f54])).
% 1.60/1.30 thf(f35,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $false) | ((sK0 @ sK1) = $false)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.60/1.30 thf(f33,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) != (sK0 @ sK1))),
% 1.60/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.60/1.30 thf(f18,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))) != (sK0 @ sK1))),
% 1.60/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.60/1.30 thf(f52,plain,(
% 1.60/1.30 spl3_1 | spl3_2),
% 1.60/1.30 inference(avatar_split_clause,[status(thm)],[f34,f49,f45])).
% 1.60/1.30 thf(f34,plain,(
% 1.60/1.30 ((in @ sK1 @ (dsetconstr @ sK2 @ sK0)) = $true) | ((sK0 @ sK1) = $true)),
% 1.60/1.30 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.60/1.30 % SZS output end Proof for DTF2THF_12186
% 1.60/1.30 % (12300)------------------------------
% 1.60/1.30 % (12300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (12300)Termination reason: Refutation
% 1.60/1.30
% 1.60/1.30 % (12300)Memory used [KB]: 5628
% 1.60/1.30 % (12300)Time elapsed: 0.006 s
% 1.60/1.30 % (12300)Instructions burned: 8 (million)
% 1.60/1.30 % (12300)------------------------------
% 1.60/1.30 % (12300)------------------------------
% 1.60/1.30 % (12299)Success in time 0.016 s
%------------------------------------------------------------------------------