%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU679^2 : 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 : n028.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 09:36:17 AM UTC 2026
% Result : Theorem 1.54s 1.29s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 394 ( 127 equ; 3 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 570 ( 49 ~; 35 |; 20 &; 443 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 8 con; 0-3 aty)
% Number of variables : 170 ( 74 ^; 77 !; 19 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_12,type,
func: $i > $i > $i > $o ).
thf(func_def_14,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_28,type,
sK1: $i > $i ).
thf(func_def_30,type,
sK3: $i > $i ).
thf(func_def_33,type,
sK6: $i > $i > ( $i > $i ) > $i ).
thf(func_def_35,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f57,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f56,f52]) ).
thf(f52,plain,
( ( in @ ( sK6 @ sK2 @ sK0 @ sK1 ) @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( in @ ( sK6 @ sK2 @ sK0 @ sK1 ) @ sK2 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f46,f50]) ).
thf(f50,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i] : ( (=) @ ( X4 @ Y0 ) ) ) )
= $true )
| ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true )
| ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true )
| ( $true != $true )
| ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f37,f33]) ).
thf(f33,plain,
lamProp = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( func @ sK2 @ sK0
@ ( lam @ sK2 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK2 )
!= $true )
| ( ( in @ ( sK1 @ X3 ) @ sK0 )
= $true ) )
& ( lamProp = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ ( X1 @ X3 ) @ X0 )
= $true ) ) )
=> ( ( ( func @ sK2 @ sK0
@ ( lam @ sK2 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK2 )
!= $true )
| ( ( in @ ( sK1 @ X3 ) @ sK0 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ ( X1 @ X3 ) @ X0 )
= $true ) ) )
& ( lamProp = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( lamProp = $true )
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ ( X1 @ X3 ) @ X0 )
= $true ) )
=> ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( lamProp
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X1 @ X3 ) @ X0 ) )
=> ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( lamProp
=> ! [X3: $i,X7: $i > $i,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( func @ X0 @ X3
@ ( lam @ X0 @ X3
@ ^ [X1: $i] : ( X7 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( lamProp
=> ! [X3: $i,X7: $i > $i,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( func @ X0 @ X3
@ ( lam @ X0 @ X3
@ ^ [X1: $i] : ( X7 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lamp) ).
thf(f37,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true )
| ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true )
| ( lamProp != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( lamProp = $true )
| ( ( ( func @ sK5 @ sK4
@ ( dpsetconstr @ sK5 @ sK4
@ ^ [Y0: $i,Y1: $i] :
( ( sK3 @ Y0 )
= Y1 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ ( sK3 @ X3 ) @ sK4 )
= $true )
| ( ( in @ X3 @ sK5 )
!= $true ) ) ) )
& ( ! [X4: $i > $i,X5: $i,X6: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true )
| ( ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true )
& ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true ) ) )
| ( lamProp != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f29,f31,f30]) ).
thf(f30,plain,
( ? [X0: $i > $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
=> ( ( ( func @ sK5 @ sK4
@ ( dpsetconstr @ sK5 @ sK4
@ ^ [Y0: $i,Y1: $i] :
( ( sK3 @ Y0 )
= Y1 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ ( sK3 @ X3 ) @ sK4 )
= $true )
| ( ( in @ X3 @ sK5 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
! [X4: $i > $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( ( in @ ( X4 @ X7 ) @ X5 )
!= $true )
& ( ( in @ X7 @ X6 )
= $true ) )
=> ( ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true )
& ( ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ( lamProp = $true )
| ? [X0: $i > $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) ) )
& ( ! [X4: $i > $i,X5: $i,X6: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true )
| ? [X7: $i] :
( ( ( in @ ( X4 @ X7 ) @ X5 )
!= $true )
& ( ( in @ X7 @ X6 )
= $true ) ) )
| ( lamProp != $true ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( lamProp = $true )
| ? [X0: $i > $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) ) )
& ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
= $true )
| ? [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
| ( lamProp != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( lamProp = $true )
<=> ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
= $true )
| ? [X3: $i] :
( ( ( in @ ( X0 @ X3 ) @ X1 )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( lamProp = $true )
<=> ! [X0: $i > $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ ( X0 @ X3 ) @ X1 )
= $true ) )
=> ( ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 )
= Y1 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X0 @ X3 ) @ X1 ) )
=> ( func @ X2 @ X1
@ ( dpsetconstr @ X2 @ X1
@ ^ [X4: $i,X5: $i] :
( ( X0 @ X4 )
= X5 ) ) ) )
= lamProp ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X7: $i > $i,X3: $i,X0: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( func @ X0 @ X3
@ ( dpsetconstr @ X0 @ X3
@ ^ [X1: $i,X6: $i] :
( ( X7 @ X1 )
= X6 ) ) ) )
= lamProp ),
file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lamProp) ).
thf(f46,plain,
( ( func @ sK2 @ sK0
@ ( dpsetconstr @ sK2 @ sK0
@ ^ [Y0: $i] : ( (=) @ ( sK1 @ Y0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( func @ sK2 @ sK0
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ sK2
@ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f35,f36]) ).
thf(f36,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( lam
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i] :
( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [X0: $i,X1: $i,X2: $i > $i] :
( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] :
( ( X2 @ X3 )
= X4 ) ) )
= lam ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: $i,X3: $i,X7: $i > $i] :
( dpsetconstr @ X0 @ X3
@ ^ [X1: $i,X6: $i] :
( ( X7 @ X1 )
= X6 ) ) )
= lam ),
file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lam) ).
thf(f35,plain,
( ( func @ sK2 @ sK0
@ ( lam @ sK2 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f56,plain,
( ( in @ ( sK6 @ sK2 @ sK0 @ sK1 ) @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( in @ ( sK6 @ sK2 @ sK0 @ sK1 ) @ sK2 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f54,f34]) ).
thf(f34,plain,
! [X3: $i] :
( ( ( in @ ( sK1 @ X3 ) @ sK0 )
= $true )
| ( ( in @ X3 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f54,plain,
( ( in @ ( sK1 @ ( sK6 @ sK2 @ sK0 @ sK1 ) ) @ sK0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ( ( in @ ( sK1 @ ( sK6 @ sK2 @ sK0 @ sK1 ) ) @ sK0 )
!= $true ) ),
inference(superposition,[status(thm)],[f46,f48]) ).
thf(f48,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i] : ( (=) @ ( X4 @ Y0 ) ) ) )
= $true )
| ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true )
| ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( $true != $true )
| ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true )
| ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f33]) ).
thf(f38,plain,
! [X6: $i,X4: $i > $i,X5: $i] :
( ( ( func @ X6 @ X5
@ ( dpsetconstr @ X6 @ X5
@ ^ [Y0: $i,Y1: $i] :
( ( X4 @ Y0 )
= Y1 ) ) )
= $true )
| ( ( in @ ( X4 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X5 )
!= $true )
| ( lamProp != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU679^2 : 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
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:30:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU679^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Functions - Lambda Abstraction
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.31/0.46 % func A B (lam A B (^ x:i.f x)))
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC181l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 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 v4.0.0, 0.67 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 21 ( 6 unt; 14 typ; 6 def)
% 0.31/0.46 % Number of atoms : 28 ( 9 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 59 ( 0 ~; 0 |; 2 &; 51 @)
% 0.31/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 11 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 15 ( 14 usr; 2 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 29 ( 19 ^; 9 !; 1 ?; 29 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=237
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(in_type,type,
% 0.31/0.46 in: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptyset_type,type,
% 0.31/0.46 emptyset: $i ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoin_type,type,
% 0.31/0.46 setadjoin: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstr_type,type,
% 0.31/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(subset_type,type,
% 0.31/0.46 subset: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(kpair_type,type,
% 0.31/0.46 kpair: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(cartprod_type,type,
% 0.31/0.46 cartprod: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_type,type,
% 0.31/0.46 singleton: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(singleton,definition,
% 0.31/0.46 ( singleton
% 0.31/0.46 = ( ^ [A: $i] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 & ( A
% 0.31/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(ex1_type,type,
% 0.31/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(ex1,definition,
% 0.31/0.46 ( ex1
% 0.31/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.31/0.46 ( singleton
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(breln_type,type,
% 0.31/0.46 breln: $i > $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(breln,definition,
% 0.31/0.46 ( breln
% 0.31/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(dpsetconstr_type,type,
% 0.31/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(func_type,type,
% 0.31/0.46 func: $i > $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(func,definition,
% 0.31/0.46 ( func
% 0.31/0.46 = ( ^ [A: $i,B: $i,R: $i] :
% 0.31/0.46 ( ( breln @ A @ B @ R )
% 0.31/0.46 & ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( ex1 @ B
% 0.31/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lamProp_type,type,
% 0.31/0.46 lamProp: $o ).
% 0.31/0.46
% 0.31/0.46 thf(lamProp,definition,
% 0.31/0.46 ( lamProp
% 0.31/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.46 => ( func @ A @ B
% 0.31/0.46 @ ( dpsetconstr @ A @ B
% 0.31/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.46 ( ( Xf @ Xx )
% 0.31/0.46 = Xy ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lam_type,type,
% 0.31/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(lam,definition,
% 0.31/0.46 ( lam
% 0.31/0.46 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( dpsetconstr @ A @ B
% 0.31/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.46 ( ( Xf @ Xx )
% 0.31/0.46 = Xy ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lamp,conjecture,
% 0.31/0.46 ( lamProp
% 0.31/0.46 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.46 => ( func @ A @ B
% 0.31/0.46 @ ( lam @ A @ B
% 0.31/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.54/1.26 ---- Embedded in THF ---
% 1.54/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.26 %%% Generated on Tue Feb 24 12:30:57 EST 2026
% 1.54/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.26 %%% Logic specification used:
% 1.54/1.26 %%% thf(spec, logic, $$dhol).
% 1.54/1.26
% 1.54/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2DTF20676.p
% See solution above
% 1.54/1.26 ------------------------
% 1.54/1.27 ---- Cleaned THF ---
% 1.54/1.27 thf(in_type,type,
% 1.54/1.27 in: $i > $i > $o ).
% 1.54/1.27
% 1.54/1.27 thf(emptyset_type,type,
% 1.54/1.27 emptyset: $i ).
% 1.54/1.27
% 1.54/1.27 thf(setadjoin_type,type,
% 1.54/1.27 setadjoin: $i > $i > $i ).
% 1.54/1.27
% 1.54/1.27 thf(dsetconstr_type,type,
% 1.54/1.27 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.54/1.27
% 1.54/1.27 thf(subset_type,type,
% 1.54/1.27 subset: $i > $i > $o ).
% 1.54/1.27
% 1.54/1.27 thf(kpair_type,type,
% 1.54/1.27 kpair: $i > $i > $i ).
% 1.54/1.27
% 1.54/1.27 thf(cartprod_type,type,
% 1.54/1.27 cartprod: $i > $i > $i ).
% 1.54/1.27
% 1.54/1.27 thf(singleton_type,type,
% 1.54/1.27 singleton: $i > $o ).
% 1.54/1.27
% 1.54/1.27 thf(singleton,definition,
% 1.54/1.27 ( singleton
% 1.54/1.27 = ( ^ [A: $i] :
% 1.54/1.27 ? [Xx: $i] :
% 1.54/1.27 ( ( in @ Xx @ A )
% 1.54/1.27 & ( A
% 1.54/1.27 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(ex1_type,type,
% 1.54/1.27 ex1: $i > ( $i > $o ) > $o ).
% 1.54/1.27
% 1.54/1.27 thf(ex1,definition,
% 1.54/1.27 ( ex1
% 1.54/1.27 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.54/1.27 ( singleton
% 1.54/1.27 @ ( dsetconstr @ A
% 1.54/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(breln_type,type,
% 1.54/1.27 breln: $i > $i > $i > $o ).
% 1.54/1.27
% 1.54/1.27 thf(breln,definition,
% 1.54/1.27 ( breln
% 1.54/1.27 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(dpsetconstr_type,type,
% 1.54/1.27 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.54/1.27
% 1.54/1.27 thf(func_type,type,
% 1.54/1.27 func: $i > $i > $i > $o ).
% 1.54/1.27
% 1.54/1.27 thf(func,definition,
% 1.54/1.27 ( func
% 1.54/1.27 = ( ^ [A: $i,B: $i,R: $i] :
% 1.54/1.27 ( ( breln @ A @ B @ R )
% 1.54/1.27 & ! [Xx: $i] :
% 1.54/1.27 ( ( in @ Xx @ A )
% 1.54/1.27 => ( ex1 @ B
% 1.54/1.27 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(lamProp_type,type,
% 1.54/1.27 lamProp: $o ).
% 1.54/1.27
% 1.54/1.27 thf(lamProp,definition,
% 1.54/1.27 ( lamProp
% 1.54/1.27 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 1.54/1.27 ( ! [Xx: $i] :
% 1.54/1.27 ( ( in @ Xx @ A )
% 1.54/1.27 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.54/1.27 => ( func @ A @ B
% 1.54/1.27 @ ( dpsetconstr @ A @ B
% 1.54/1.27 @ ^ [Xx: $i,Xy: $i] :
% 1.54/1.27 ( ( Xf @ Xx )
% 1.54/1.27 = Xy ) ) ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(lam_type,type,
% 1.54/1.27 lam: $i > $i > ( $i > $i ) > $i ).
% 1.54/1.27
% 1.54/1.27 thf(lam,definition,
% 1.54/1.27 ( lam
% 1.54/1.27 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 1.54/1.27 ( dpsetconstr @ A @ B
% 1.54/1.27 @ ^ [Xx: $i,Xy: $i] :
% 1.54/1.27 ( ( Xf @ Xx )
% 1.54/1.27 = Xy ) ) ) ) ).
% 1.54/1.27
% 1.54/1.27 thf(lamp,conjecture,
% 1.54/1.27 ( lamProp
% 1.54/1.27 => ! [A: $i,B: $i,Xf: $i > $i] :
% 1.54/1.27 ( ! [Xx: $i] :
% 1.54/1.27 ( ( in @ Xx @ A )
% 1.54/1.27 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.54/1.27 => ( func @ A @ B
% 1.54/1.27 @ ( lam @ A @ B
% 1.54/1.27 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ).
% 1.54/1.27 ------------------------
% 1.54/1.29 % (20890)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_20676 for (2999ds/275Mi)
% 1.54/1.29 % (20887)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_20676 for (2999ds/27Mi)
% 1.54/1.29 % (20890)First to succeed.
% 1.54/1.29 % (20890)Refutation found. Thanks to Tanya!
% 1.54/1.29 % SZS status Theorem for DTF2THF_20676
% 1.54/1.29 % SZS output start Proof for DTF2THF_20676
% 1.54/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.54/1.29 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.54/1.29 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.54/1.29 thf(func_def_4, type, subset: $i > $i > $o).
% 1.54/1.29 thf(func_def_5, type, kpair: $i > $i > $i).
% 1.54/1.29 thf(func_def_6, type, cartprod: $i > $i > $i).
% 1.54/1.29 thf(func_def_7, type, singleton: $i > $o).
% 1.54/1.29 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 1.54/1.29 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 1.54/1.29 thf(func_def_11, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.54/1.29 thf(func_def_12, type, func: $i > $i > $i > $o).
% 1.54/1.29 thf(func_def_14, type, lam: $i > $i > ($i > $i) > $i).
% 1.54/1.29 thf(func_def_28, type, sK1: $i > $i).
% 1.54/1.29 thf(func_def_30, type, sK3: $i > $i).
% 1.54/1.29 thf(func_def_33, type, sK6: $i > $i > ($i > $i) > $i).
% 1.54/1.29 thf(func_def_35, type, ph8: !>[X0: $tType]:(X0)).
% 1.54/1.29 thf(f57,plain,(
% 1.54/1.29 $false),
% 1.54/1.29 inference(subsumption_resolution,[status(thm)],[f56,f52])).
% 1.54/1.29 thf(f52,plain,(
% 1.54/1.29 ((in @ (sK6 @ sK2 @ sK0 @ sK1) @ sK2) = $true)),
% 1.54/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.54/1.29 thf(f51,plain,(
% 1.54/1.29 ((in @ (sK6 @ sK2 @ sK0 @ sK1) @ sK2) = $true) | ($true != $true)),
% 1.54/1.29 inference(superposition,[status(thm)],[f46,f50])).
% 1.54/1.29 thf(f50,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: (= @ (X4 @ Y0))))) = $true) | ((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true)) )),
% 1.54/1.29 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.54/1.29 thf(f49,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true) | ((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true)) )),
% 1.54/1.29 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.54/1.29 thf(f45,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true) | ($true != $true) | ((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true)) )),
% 1.54/1.29 inference(definition_unfolding,[status(thm)],[f37,f33])).
% 1.54/1.29 thf(f33,plain,(
% 1.54/1.29 (lamProp = $true)),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f27])).
% 1.54/1.29 thf(f27,plain,(
% 1.54/1.29 (((func @ sK2 @ sK0 @ (lam @ sK2 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) != $true) & ! [X3 : $i] : (((in @ X3 @ sK2) != $true) | ((in @ (sK1 @ X3) @ sK0) = $true))) & (lamProp = $true)),
% 1.54/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f26])).
% 1.54/1.29 thf(f26,plain,(
% 1.54/1.29 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ((in @ (X1 @ X3) @ X0) = $true))) => (((func @ sK2 @ sK0 @ (lam @ sK2 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) != $true) & ! [X3 : $i] : (((in @ X3 @ sK2) != $true) | ((in @ (sK1 @ X3) @ sK0) = $true)))),
% 1.54/1.29 introduced(definition,[],[choice_axiom])).
% 1.54/1.29 thf(f24,plain,(
% 1.54/1.29 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ((in @ (X1 @ X3) @ X0) = $true))) & (lamProp = $true)),
% 1.54/1.29 inference(ennf_transformation,[status(thm)],[f15])).
% 1.54/1.29 thf(f15,plain,(
% 1.54/1.29 ~((lamProp = $true) => ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2) = $true) => ((in @ (X1 @ X3) @ X0) = $true)) => ((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)))),
% 1.54/1.29 inference(fool_elimination,[status(thm)],[f14])).
% 1.54/1.29 thf(f14,plain,(
% 1.54/1.29 ~(lamProp => ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[X4 : $i] : (X1 @ X4))))))),
% 1.54/1.29 inference(rectify,[status(thm)],[f8])).
% 1.54/1.29 thf(f8,negated_conjecture,(
% 1.54/1.29 ~(lamProp => ! [X3 : $i,X7 : $i > $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (func @ X0 @ X3 @ (lam @ X0 @ X3 @ (^[X1 : $i] : (X7 @ X1))))))),
% 1.54/1.29 inference(negated_conjecture,[status(cth)],[f7])).
% 1.54/1.29 thf(f7,conjecture,(
% 1.54/1.29 lamProp => ! [X3 : $i,X7 : $i > $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (func @ X0 @ X3 @ (lam @ X0 @ X3 @ (^[X1 : $i] : (X7 @ X1)))))),
% 1.54/1.29 file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lamp)).
% 1.54/1.29 thf(f37,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true) | ((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true) | (lamProp != $true)) )),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f32])).
% 1.54/1.29 thf(f32,plain,(
% 1.54/1.29 ((lamProp = $true) | (((func @ sK5 @ sK4 @ (dpsetconstr @ sK5 @ sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK3 @ Y0) = Y1)))))) != $true) & ! [X3 : $i] : (((in @ (sK3 @ X3) @ sK4) = $true) | ((in @ X3 @ sK5) != $true)))) & (! [X4 : $i > $i,X5 : $i,X6 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true) | (((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true) & ((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true))) | (lamProp != $true))),
% 1.54/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f29,f31,f30])).
% 1.54/1.29 thf(f30,plain,(
% 1.54/1.29 ? [X0 : $i > $i,X1 : $i,X2 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) != $true) & ! [X3 : $i] : (((in @ (X0 @ X3) @ X1) = $true) | ((in @ X3 @ X2) != $true))) => (((func @ sK5 @ sK4 @ (dpsetconstr @ sK5 @ sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK3 @ Y0) = Y1)))))) != $true) & ! [X3 : $i] : (((in @ (sK3 @ X3) @ sK4) = $true) | ((in @ X3 @ sK5) != $true)))),
% 1.54/1.29 introduced(definition,[],[choice_axiom])).
% 1.54/1.29 thf(f31,plain,(
% 1.54/1.29 ! [X4 : $i > $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (((in @ (X4 @ X7) @ X5) != $true) & ((in @ X7 @ X6) = $true)) => (((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true) & ((in @ (sK6 @ X6 @ X5 @ X4) @ X6) = $true)))),
% 1.54/1.29 introduced(definition,[],[choice_axiom])).
% 1.54/1.29 thf(f29,plain,(
% 1.54/1.29 ((lamProp = $true) | ? [X0 : $i > $i,X1 : $i,X2 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) != $true) & ! [X3 : $i] : (((in @ (X0 @ X3) @ X1) = $true) | ((in @ X3 @ X2) != $true)))) & (! [X4 : $i > $i,X5 : $i,X6 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true) | ? [X7 : $i] : (((in @ (X4 @ X7) @ X5) != $true) & ((in @ X7 @ X6) = $true))) | (lamProp != $true))),
% 1.54/1.29 inference(rectify,[status(thm)],[f28])).
% 1.54/1.29 thf(f28,plain,(
% 1.54/1.29 ((lamProp = $true) | ? [X0 : $i > $i,X1 : $i,X2 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) != $true) & ! [X3 : $i] : (((in @ (X0 @ X3) @ X1) = $true) | ((in @ X3 @ X2) != $true)))) & (! [X0 : $i > $i,X1 : $i,X2 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) = $true) | ? [X3 : $i] : (((in @ (X0 @ X3) @ X1) != $true) & ((in @ X3 @ X2) = $true))) | (lamProp != $true))),
% 1.54/1.29 inference(nnf_transformation,[status(thm)],[f25])).
% 1.54/1.29 thf(f25,plain,(
% 1.54/1.29 (lamProp = $true) <=> ! [X0 : $i > $i,X1 : $i,X2 : $i] : (((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) = $true) | ? [X3 : $i] : (((in @ (X0 @ X3) @ X1) != $true) & ((in @ X3 @ X2) = $true)))),
% 1.54/1.29 inference(ennf_transformation,[status(thm)],[f19])).
% 1.54/1.29 thf(f19,plain,(
% 1.54/1.29 (lamProp = $true) <=> ! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2) = $true) => ((in @ (X0 @ X3) @ X1) = $true)) => ((func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X0 @ Y0) = Y1)))))) = $true))),
% 1.54/1.29 inference(fool_elimination,[status(thm)],[f18])).
% 1.54/1.29 thf(f18,plain,(
% 1.54/1.29 (! [X0 : $i > $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (func @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[X4 : $i, X5 : $i] : (((X0 @ X4) = X5)))))) = lamProp)),
% 1.54/1.29 inference(rectify,[status(thm)],[f5])).
% 1.54/1.29 thf(f5,axiom,(
% 1.54/1.29 (! [X7 : $i > $i,X3 : $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (func @ X0 @ X3 @ (dpsetconstr @ X0 @ X3 @ (^[X1 : $i, X6 : $i] : (((X7 @ X1) = X6)))))) = lamProp)),
% 1.54/1.29 file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lamProp)).
% 1.54/1.29 thf(f46,plain,(
% 1.54/1.29 ((func @ sK2 @ sK0 @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))) != $true)),
% 1.54/1.29 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.54/1.29 thf(f41,plain,(
% 1.54/1.29 ((func @ sK2 @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))) @ sK2 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) != $true)),
% 1.54/1.29 inference(definition_unfolding,[status(thm)],[f35,f36])).
% 1.54/1.29 thf(f36,plain,(
% 1.54/1.29 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f21])).
% 1.54/1.29 thf(f21,plain,(
% 1.54/1.29 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 1.54/1.29 inference(fool_elimination,[status(thm)],[f20])).
% 1.54/1.29 thf(f20,plain,(
% 1.54/1.29 ((^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))) = lam)),
% 1.54/1.29 inference(rectify,[status(thm)],[f6])).
% 1.54/1.29 thf(f6,axiom,(
% 1.54/1.29 ((^[X0 : $i, X3 : $i, X7 : $i > $i] : (dpsetconstr @ X0 @ X3 @ (^[X1 : $i, X6 : $i] : (((X7 @ X1) = X6))))) = lam)),
% 1.54/1.29 file('/export/starexec/sandbox2/tmp/tmp.mYAJHxF0vE/DTF2THF_20676.p',lam)).
% 1.54/1.29 thf(f35,plain,(
% 1.54/1.29 ((func @ sK2 @ sK0 @ (lam @ sK2 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) != $true)),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f27])).
% 1.54/1.29 thf(f56,plain,(
% 1.54/1.29 ((in @ (sK6 @ sK2 @ sK0 @ sK1) @ sK2) != $true)),
% 1.54/1.29 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.54/1.29 thf(f55,plain,(
% 1.54/1.29 ((in @ (sK6 @ sK2 @ sK0 @ sK1) @ sK2) != $true) | ($true != $true)),
% 1.54/1.29 inference(superposition,[status(thm)],[f54,f34])).
% 1.54/1.29 thf(f34,plain,(
% 1.54/1.29 ( ! [X3 : $i] : (((in @ (sK1 @ X3) @ sK0) = $true) | ((in @ X3 @ sK2) != $true)) )),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f27])).
% 1.54/1.29 thf(f54,plain,(
% 1.54/1.29 ((in @ (sK1 @ (sK6 @ sK2 @ sK0 @ sK1)) @ sK0) != $true)),
% 1.54/1.29 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.54/1.29 thf(f53,plain,(
% 1.54/1.29 ($true != $true) | ((in @ (sK1 @ (sK6 @ sK2 @ sK0 @ sK1)) @ sK0) != $true)),
% 1.54/1.29 inference(superposition,[status(thm)],[f46,f48])).
% 1.54/1.29 thf(f48,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: (= @ (X4 @ Y0))))) = $true) | ((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true)) )),
% 1.54/1.29 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.54/1.29 thf(f47,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true) | ((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true)) )),
% 1.54/1.29 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.54/1.29 thf(f44,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (($true != $true) | ((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true) | ((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true)) )),
% 1.54/1.29 inference(definition_unfolding,[status(thm)],[f38,f33])).
% 1.54/1.29 thf(f38,plain,(
% 1.54/1.29 ( ! [X6 : $i,X4 : $i > $i,X5 : $i] : (((func @ X6 @ X5 @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X4 @ Y0) = Y1)))))) = $true) | ((in @ (X4 @ (sK6 @ X6 @ X5 @ X4)) @ X5) != $true) | (lamProp != $true)) )),
% 1.54/1.29 inference(cnf_transformation,[status(thm)],[f32])).
% 1.54/1.29 % SZS output end Proof for DTF2THF_20676
% 1.54/1.29 % (20890)------------------------------
% 1.54/1.29 % (20890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.29 % (20890)Termination reason: Refutation
% 1.54/1.29
% 1.54/1.29 % (20890)Memory used [KB]: 5500
% 1.54/1.29 % (20890)Time elapsed: 0.005 s
% 1.54/1.29 % (20890)Instructions burned: 7 (million)
% 1.54/1.29 % (20890)------------------------------
% 1.54/1.29 % (20890)------------------------------
% 1.54/1.29 % (20884)Success in time 0.015 s
%------------------------------------------------------------------------------