%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU797^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:37:17 AM UTC 2026
% Result : Theorem 1.82s 1.50s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 361 ( 123 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 469 ( 50 ~; 41 |; 43 &; 316 @)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 130 ( 34 ^; 61 !; 35 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_10,type,
sK2: $i > $i ).
thf(func_def_12,type,
sK4: $i > $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
sK5: $i > $i ).
thf(func_def_18,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f46,f22]) ).
thf(f22,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( sK0
= ( sK2 @ sK3 ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK0
@ ( image1 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true )
& ( image1Equiv = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X0 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0
@ ( image1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
=> ( ? [X3: $i] :
( ( sK0
= ( sK2 @ X3 ) )
& ( ( in @ X3 @ sK1 )
= $true ) )
& ( ( in @ sK0
@ ( image1 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X3: $i] :
( ( sK0
= ( sK2 @ X3 ) )
& ( ( in @ X3 @ sK1 )
= $true ) )
=> ( ( sK0
= ( sK2 @ sK3 ) )
& ( ( in @ sK3 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X0 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0
@ ( image1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
& ( image1Equiv = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X0 )
& ( ( in @ X3 @ X1 )
= $true ) )
=> ( ( in @ X0
@ ( image1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( image1Equiv
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X0 )
& ( in @ X3 @ X1 ) )
=> ( in @ X0
@ ( image1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( image1Equiv
=> ! [X2: $i,X0: $i,X1: $i > $i] :
( ? [X3: $i] :
( ( ( X1 @ X3 )
= X2 )
& ( in @ X3 @ X0 ) )
=> ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( image1Equiv
=> ! [X2: $i,X0: $i,X1: $i > $i] :
( ? [X3: $i] :
( ( ( X1 @ X3 )
= X2 )
& ( in @ X3 @ X0 ) )
=> ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jkXUZKPcaH/DTF2THF_32428.p',image1I) ).
thf(f46,plain,
( ( in @ sK3 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( in @ sK3 @ sK1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f40,f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X0: $i > $i] :
( ( ( in @ ( X0 @ X3 ) @ ( image1 @ X2 @ X0 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X0: $i > $i] :
( ( ( in @ ( X0 @ X3 )
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X0: $i > $i] :
( ( ( in @ ( X0 @ X3 )
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X0: $i > $i,X1: $i] :
( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f20]) ).
thf(f20,plain,
image1Equiv = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X0: $i > $i,X1: $i] :
( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true )
| ( image1Equiv != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ! [X3: $i] :
( ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
& ( ( ( ( X0 @ ( sK4 @ X2 @ X1 @ X0 ) )
= X1 )
& ( ( in @ ( sK4 @ X2 @ X1 @ X0 ) @ X2 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) )
& ( ( image1Equiv = $true )
| ( ( ! [X8: $i] :
( ( sK6
!= ( sK5 @ X8 ) )
| ( $true
!= ( in @ X8 @ sK7 ) ) )
| ( ( in @ sK6
@ ( image1 @ sK7
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
!= $true ) )
& ( ( ( sK6
= ( sK5 @ sK8 ) )
& ( ( in @ sK8 @ sK7 )
= $true ) )
| ( ( in @ sK6
@ ( image1 @ sK7
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f18,f17,f16]) ).
thf(f16,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ? [X4: $i] :
( ( ( X0 @ X4 )
= X1 )
& ( ( in @ X4 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( sK4 @ X2 @ X1 @ X0 ) )
= X1 )
& ( ( in @ ( sK4 @ X2 @ X1 @ X0 ) @ X2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X5: $i > $i,X6: $i,X7: $i] :
( ( ! [X8: $i] :
( ( ( X5 @ X8 )
!= X6 )
| ( ( in @ X8 @ X7 )
!= $true ) )
| ( ( in @ X6
@ ( image1 @ X7
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
& ( ? [X9: $i] :
( ( ( X5 @ X9 )
= X6 )
& ( ( in @ X9 @ X7 )
= $true ) )
| ( ( in @ X6
@ ( image1 @ X7
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) ) )
=> ( ( ! [X8: $i] :
( ( sK6
!= ( sK5 @ X8 ) )
| ( $true
!= ( in @ X8 @ sK7 ) ) )
| ( ( in @ sK6
@ ( image1 @ sK7
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
!= $true ) )
& ( ? [X9: $i] :
( ( ( sK5 @ X9 )
= sK6 )
& ( ( in @ X9 @ sK7 )
= $true ) )
| ( ( in @ sK6
@ ( image1 @ sK7
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X9: $i] :
( ( ( sK5 @ X9 )
= sK6 )
& ( ( in @ X9 @ sK7 )
= $true ) )
=> ( ( sK6
= ( sK5 @ sK8 ) )
& ( ( in @ sK8 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ! [X3: $i] :
( ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
& ( ? [X4: $i] :
( ( ( X0 @ X4 )
= X1 )
& ( ( in @ X4 @ X2 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) )
& ( ( image1Equiv = $true )
| ? [X5: $i > $i,X6: $i,X7: $i] :
( ( ! [X8: $i] :
( ( ( X5 @ X8 )
!= X6 )
| ( ( in @ X8 @ X7 )
!= $true ) )
| ( ( in @ X6
@ ( image1 @ X7
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
& ( ? [X9: $i] :
( ( ( X5 @ X9 )
= X6 )
& ( ( in @ X9 @ X7 )
= $true ) )
| ( ( in @ X6
@ ( image1 @ X7
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ! [X3: $i] :
( ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
& ( ? [X3: $i] :
( ( ( X0 @ X3 )
= X1 )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) )
& ( ( image1Equiv = $true )
| ? [X0: $i > $i,X1: $i,X2: $i] :
( ( ! [X3: $i] :
( ( ( X0 @ X3 )
!= X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
& ( ? [X3: $i] :
( ( ( X0 @ X3 )
= X1 )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
<=> ? [X3: $i] :
( ( ( X0 @ X3 )
= X1 )
& ( ( in @ X3 @ X2 )
= $true ) ) )
<=> ( image1Equiv = $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( image1Equiv = $true )
<=> ! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( image1 @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
<=> ? [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
& ( ( X0 @ X4 )
= X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( image1Equiv
= ( ! [X0: $i > $i,X1: $i,X2: $i] :
( ( in @ X1
@ ( image1 @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
<=> ? [X4: $i] :
( ( in @ X4 @ X2 )
& ( ( X0 @ X4 )
= X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( image1Equiv
= ( ! [X1: $i > $i,X2: $i,X0: $i] :
( ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( X1 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jkXUZKPcaH/DTF2THF_32428.p',image1Equiv) ).
thf(f40,plain,
( ( in @ ( sK2 @ sK3 ) @ ( image1 @ sK1 @ sK2 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( in @ ( sK2 @ sK3 )
@ ( image1 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( sK0
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f21,plain,
( ( in @ sK0
@ ( image1 @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU797^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n019.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:34:24 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.42 ---- Original DTF file ---
% 0.19/0.42 thf(spec,logic,$$dhol).
% 0.19/0.42 %------------------------------------------------------------------------------
% 0.19/0.42 % File : SEU797^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.42 % Domain : Set Theory
% 0.19/0.42 % Problem : More about Functions - Images of Functions
% 0.19/0.42 % Version : Especial > Reduced > Especial.
% 0.19/0.42 % English : (! A:i.! f:i>i.! x:i.(? y:i.in y A & x = f y) ->
% 0.19/0.42 % in x (image1 A (^ y:i.f y)))
% 0.19/0.42
% 0.19/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.42 % Source : [Bro08]
% 0.19/0.42 % Names : ZFC299l [Bro08]
% 0.19/0.42
% 0.19/0.42 % Status : Theorem
% 0.19/0.42 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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, 0.00 v6.1.0, 0.14 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
% 0.19/0.42 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.19/0.42 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.19/0.42 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.42 % Number of connectives : 21 ( 0 ~; 0 |; 2 &; 16 @)
% 0.19/0.42 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.42 % Maximal formula depth : 10 ( 6 avg)
% 0.19/0.42 % Number of types : 2 ( 0 usr)
% 0.19/0.42 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.42 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.42 % Number of variables : 10 ( 2 ^; 6 !; 2 ?; 10 :)
% 0.19/0.42 % SPC : TH0_THM_EQU_NAR
% 0.19/0.42
% 0.19/0.42 % Comments : http://mathgate.info/detsetitem.php?id=420
% 0.19/0.42 %------------------------------------------------------------------------------
% 0.19/0.42 thf(in_type,type,
% 0.19/0.42 in: $i > $i > $o ).
% 0.19/0.42
% 0.19/0.42 thf(image1_type,type,
% 0.19/0.42 image1: $i > ( $i > $i ) > $i ).
% 0.19/0.42
% 0.19/0.42 thf(image1Equiv_type,type,
% 0.19/0.42 image1Equiv: $o ).
% 0.19/0.42
% 0.19/0.42 thf(image1Equiv,definition,
% 0.19/0.42 ( image1Equiv
% 0.19/0.42 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.19/0.42 ( ( in @ Xx
% 0.19/0.42 @ ( image1 @ A
% 0.19/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.19/0.42 <=> ? [Xy: $i] :
% 0.19/0.42 ( ( in @ Xy @ A )
% 0.19/0.42 & ( Xx
% 0.19/0.42 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.19/0.42
% 0.19/0.42 thf(image1I,conjecture,
% 0.19/0.42 ( image1Equiv
% 0.19/0.42 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.19/0.42 ( ? [Xy: $i] :
% 0.19/0.42 ( ( in @ Xy @ A )
% 0.19/0.42 & ( Xx
% 0.19/0.42 = ( Xf @ Xy ) ) )
% 0.19/0.42 => ( in @ Xx
% 0.19/0.42 @ ( image1 @ A
% 0.19/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ).
% 0.19/0.42
% 0.19/0.42 %------------------------------------------------------------------------------
% 0.19/0.42 ------------------------
% 1.67/1.46 ---- Embedded in THF ---
% 1.67/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.46 %%% Generated on Tue Feb 24 12:34:25 EST 2026
% 1.67/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.46 %%% Logic specification used:
% 1.67/1.46 %%% thf(spec, logic, $$dhol).
% 1.67/1.46
% 1.67/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jkXUZKPcaH/DTF2DTF32428.p
% See solution above
% 1.67/1.46 ------------------------
% 1.67/1.47 ---- Cleaned THF ---
% 1.67/1.47 thf(in_type,type,
% 1.67/1.47 in: $i > $i > $o ).
% 1.67/1.47
% 1.67/1.47 thf(image1_type,type,
% 1.67/1.47 image1: $i > ( $i > $i ) > $i ).
% 1.67/1.47
% 1.67/1.47 thf(image1Equiv_type,type,
% 1.67/1.47 image1Equiv: $o ).
% 1.67/1.47
% 1.67/1.47 thf(image1Equiv,definition,
% 1.67/1.47 ( image1Equiv
% 1.67/1.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 1.67/1.47 ( ( in @ Xx
% 1.67/1.47 @ ( image1 @ A
% 1.67/1.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 1.67/1.47 <=> ? [Xy: $i] :
% 1.67/1.47 ( ( in @ Xy @ A )
% 1.67/1.47 & ( Xx
% 1.67/1.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 1.67/1.47
% 1.67/1.47 thf(image1I,conjecture,
% 1.67/1.47 ( image1Equiv
% 1.67/1.47 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 1.67/1.47 ( ? [Xy: $i] :
% 1.67/1.47 ( ( in @ Xy @ A )
% 1.67/1.47 & ( Xx
% 1.67/1.47 = ( Xf @ Xy ) ) )
% 1.67/1.47 => ( in @ Xx
% 1.67/1.47 @ ( image1 @ A
% 1.67/1.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ).
% 1.67/1.47 ------------------------
% 1.67/1.49 % (32528)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32428 for (2999ds/2Mi)
% 1.67/1.49 % (32527)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_32428 for (2999ds/27Mi)
% 1.67/1.49 % (32531)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32428 for (2999ds/18Mi)
% 1.67/1.49 % (32530)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_32428 for (2999ds/275Mi)
% 1.67/1.49 % (32525)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32428 for (2999ds/183Mi)
% 1.67/1.49 % (32528)Instruction limit reached!
% 1.67/1.49 % (32528)------------------------------
% 1.67/1.49 % (32528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.49 % (32528)Termination reason: Unknown
% 1.67/1.49 % (32528)Termination phase: Preprocessing 1
% 1.67/1.49
% 1.67/1.49 % (32528)Memory used [KB]: 895
% 1.67/1.49 % (32528)Time elapsed: 0.003 s
% 1.67/1.49 % (32528)Instructions burned: 2 (million)
% 1.67/1.49 % (32528)------------------------------
% 1.67/1.49 % (32528)------------------------------
% 1.67/1.49 % (32526)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_32428 for (2999ds/4Mi)
% 1.67/1.49 % (32530)First to succeed.
% 1.67/1.50 % (32529)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_32428 for (2999ds/2Mi)
% 1.67/1.50 % (32529)Instruction limit reached!
% 1.67/1.50 % (32529)------------------------------
% 1.67/1.50 % (32529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.50 % (32529)Termination reason: Unknown
% 1.67/1.50 % (32529)Termination phase: shuffling
% 1.67/1.50
% 1.67/1.50 % (32529)Memory used [KB]: 895
% 1.67/1.50 % (32529)Time elapsed: 0.003 s
% 1.67/1.50 % (32529)Instructions burned: 2 (million)
% 1.82/1.50 % (32529)------------------------------
% 1.82/1.50 % (32529)------------------------------
% 1.82/1.50 % (32531)Also succeeded, but the first one will report.
% 1.82/1.50 % (32526)Instruction limit reached!
% 1.82/1.50 % (32526)------------------------------
% 1.82/1.50 % (32526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (32526)Termination reason: Unknown
% 1.82/1.50 % (32526)Termination phase: Saturation
% 1.82/1.50
% 1.82/1.50 % (32526)Memory used [KB]: 5500
% 1.82/1.50 % (32526)Time elapsed: 0.004 s
% 1.82/1.50 % (32526)Instructions burned: 4 (million)
% 1.82/1.50 % (32526)------------------------------
% 1.82/1.50 % (32526)------------------------------
% 1.82/1.50 % (32530)Refutation found. Thanks to Tanya!
% 1.82/1.50 % SZS status Theorem for DTF2THF_32428
% 1.82/1.50 % SZS output start Proof for DTF2THF_32428
% 1.82/1.50 thf(func_def_0, type, in: $i > $i > $o).
% 1.82/1.50 thf(func_def_1, type, image1: $i > ($i > $i) > $i).
% 1.82/1.50 thf(func_def_10, type, sK2: $i > $i).
% 1.82/1.50 thf(func_def_12, type, sK4: $i > $i > ($i > $i) > $i).
% 1.82/1.50 thf(func_def_13, type, sK5: $i > $i).
% 1.82/1.50 thf(func_def_18, type, ph10: !>[X0: $tType]:(X0)).
% 1.82/1.50 thf(f47,plain,(
% 1.82/1.50 $false),
% 1.82/1.50 inference(subsumption_resolution,[status(thm)],[f46,f22])).
% 1.82/1.50 thf(f22,plain,(
% 1.82/1.50 ((in @ sK3 @ sK1) = $true)),
% 1.82/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.82/1.50 thf(f13,plain,(
% 1.82/1.50 (((sK0 = (sK2 @ sK3)) & ((in @ sK3 @ sK1) = $true)) & ((in @ sK0 @ (image1 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true)) & (image1Equiv = $true)),
% 1.82/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11])).
% 1.82/1.50 thf(f11,plain,(
% 1.82/1.50 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((X2 @ X3) = X0) & ((in @ X3 @ X1) = $true)) & ((in @ X0 @ (image1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) => (? [X3 : $i] : ((sK0 = (sK2 @ X3)) & ((in @ X3 @ sK1) = $true)) & ((in @ sK0 @ (image1 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true))),
% 1.82/1.50 introduced(definition,[],[choice_axiom])).
% 1.82/1.50 thf(f12,plain,(
% 1.82/1.50 ? [X3 : $i] : ((sK0 = (sK2 @ X3)) & ((in @ X3 @ sK1) = $true)) => ((sK0 = (sK2 @ sK3)) & ((in @ sK3 @ sK1) = $true))),
% 1.82/1.50 introduced(definition,[],[choice_axiom])).
% 1.82/1.50 thf(f10,plain,(
% 1.82/1.50 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((X2 @ X3) = X0) & ((in @ X3 @ X1) = $true)) & ((in @ X0 @ (image1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) & (image1Equiv = $true)),
% 1.82/1.50 inference(ennf_transformation,[status(thm)],[f6])).
% 1.82/1.50 thf(f6,plain,(
% 1.82/1.50 ~((image1Equiv = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((X2 @ X3) = X0) & ((in @ X3 @ X1) = $true)) => ((in @ X0 @ (image1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))),
% 1.82/1.50 inference(fool_elimination,[status(thm)],[f5])).
% 1.82/1.50 thf(f5,plain,(
% 1.82/1.50 ~(image1Equiv => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((X2 @ X3) = X0) & (in @ X3 @ X1)) => (in @ X0 @ (image1 @ X1 @ (^[X4 : $i] : (X2 @ X4))))))),
% 1.82/1.50 inference(rectify,[status(thm)],[f3])).
% 1.82/1.50 thf(f3,negated_conjecture,(
% 1.82/1.50 ~(image1Equiv => ! [X2 : $i,X0 : $i,X1 : $i > $i] : (? [X3 : $i] : (((X1 @ X3) = X2) & (in @ X3 @ X0)) => (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3))))))),
% 1.82/1.50 inference(negated_conjecture,[status(cth)],[f2])).
% 1.82/1.50 thf(f2,conjecture,(
% 1.82/1.50 image1Equiv => ! [X2 : $i,X0 : $i,X1 : $i > $i] : (? [X3 : $i] : (((X1 @ X3) = X2) & (in @ X3 @ X0)) => (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3)))))),
% 1.82/1.50 file('/export/starexec/sandbox/tmp/tmp.jkXUZKPcaH/DTF2THF_32428.p',image1I)).
% 1.82/1.50 thf(f46,plain,(
% 1.82/1.50 ((in @ sK3 @ sK1) != $true)),
% 1.82/1.50 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.82/1.50 thf(f45,plain,(
% 1.82/1.50 ((in @ sK3 @ sK1) != $true) | ($true != $true)),
% 1.82/1.50 inference(superposition,[status(thm)],[f40,f44])).
% 1.82/1.50 thf(f44,plain,(
% 1.82/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i > $i] : (((in @ (X0 @ X3) @ (image1 @ X2 @ X0)) = $true) | ((in @ X3 @ X2) != $true)) )),
% 1.82/1.50 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.82/1.50 thf(f43,plain,(
% 1.82/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i > $i] : (((in @ (X0 @ X3) @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ((in @ X3 @ X2) != $true)) )),
% 1.82/1.50 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.82/1.50 thf(f37,plain,(
% 1.82/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i > $i] : (((in @ (X0 @ X3) @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ((in @ X3 @ X2) != $true) | ($true != $true)) )),
% 1.82/1.50 inference(equality_resolution,[status(thm)],[f31])).
% 1.82/1.50 thf(f31,plain,(
% 1.82/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i > $i,X1 : $i] : (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true) | ($true != $true)) )),
% 1.82/1.50 inference(definition_unfolding,[status(thm)],[f29,f20])).
% 1.82/1.50 thf(f20,plain,(
% 1.82/1.50 (image1Equiv = $true)),
% 1.82/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.82/1.50 thf(f29,plain,(
% 1.82/1.50 ( ! [X2 : $i,X3 : $i,X0 : $i > $i,X1 : $i] : (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true) | (image1Equiv != $true)) )),
% 1.82/1.50 inference(cnf_transformation,[status(thm)],[f19])).
% 1.82/1.50 thf(f19,plain,(
% 1.82/1.50 (! [X0 : $i > $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ! [X3 : $i] : (((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true))) & ((((X0 @ (sK4 @ X2 @ X1 @ X0)) = X1) & ((in @ (sK4 @ X2 @ X1 @ X0) @ X2) = $true)) | ((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))) | (image1Equiv != $true)) & ((image1Equiv = $true) | ((! [X8 : $i] : ((sK6 != (sK5 @ X8)) | ($true != (in @ X8 @ sK7))) | ((in @ sK6 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK5 @ Y0)))) != $true)) & (((sK6 = (sK5 @ sK8)) & ((in @ sK8 @ sK7) = $true)) | ((in @ sK6 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true))))),
% 1.82/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f15,f18,f17,f16])).
% 1.82/1.50 thf(f16,plain,(
% 1.82/1.50 ! [X0 : $i > $i,X1 : $i,X2 : $i] : (? [X4 : $i] : (((X0 @ X4) = X1) & ((in @ X4 @ X2) = $true)) => (((X0 @ (sK4 @ X2 @ X1 @ X0)) = X1) & ((in @ (sK4 @ X2 @ X1 @ X0) @ X2) = $true)))),
% 1.82/1.50 introduced(definition,[],[choice_axiom])).
% 1.82/1.50 thf(f17,plain,(
% 1.82/1.50 ? [X5 : $i > $i,X6 : $i,X7 : $i] : ((! [X8 : $i] : (((X5 @ X8) != X6) | ((in @ X8 @ X7) != $true)) | ((in @ X6 @ (image1 @ X7 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) & (? [X9 : $i] : (((X5 @ X9) = X6) & ((in @ X9 @ X7) = $true)) | ((in @ X6 @ (image1 @ X7 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true))) => ((! [X8 : $i] : ((sK6 != (sK5 @ X8)) | ($true != (in @ X8 @ sK7))) | ((in @ sK6 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK5 @ Y0)))) != $true)) & (? [X9 : $i] : (((sK5 @ X9) = sK6) & ((in @ X9 @ sK7) = $true)) | ((in @ sK6 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true)))),
% 1.82/1.50 introduced(definition,[],[choice_axiom])).
% 1.82/1.50 thf(f18,plain,(
% 1.82/1.50 ? [X9 : $i] : (((sK5 @ X9) = sK6) & ((in @ X9 @ sK7) = $true)) => ((sK6 = (sK5 @ sK8)) & ((in @ sK8 @ sK7) = $true))),
% 1.82/1.50 introduced(definition,[],[choice_axiom])).
% 1.82/1.50 thf(f15,plain,(
% 1.82/1.50 (! [X0 : $i > $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ! [X3 : $i] : (((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true))) & (? [X4 : $i] : (((X0 @ X4) = X1) & ((in @ X4 @ X2) = $true)) | ((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))) | (image1Equiv != $true)) & ((image1Equiv = $true) | ? [X5 : $i > $i,X6 : $i,X7 : $i] : ((! [X8 : $i] : (((X5 @ X8) != X6) | ((in @ X8 @ X7) != $true)) | ((in @ X6 @ (image1 @ X7 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) & (? [X9 : $i] : (((X5 @ X9) = X6) & ((in @ X9 @ X7) = $true)) | ((in @ X6 @ (image1 @ X7 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true))))),
% 1.82/1.50 inference(rectify,[status(thm)],[f14])).
% 1.82/1.50 thf(f14,plain,(
% 1.82/1.50 (! [X0 : $i > $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ! [X3 : $i] : (((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true))) & (? [X3 : $i] : (((X0 @ X3) = X1) & ((in @ X3 @ X2) = $true)) | ((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))) | (image1Equiv != $true)) & ((image1Equiv = $true) | ? [X0 : $i > $i,X1 : $i,X2 : $i] : ((! [X3 : $i] : (((X0 @ X3) != X1) | ((in @ X3 @ X2) != $true)) | ((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) & (? [X3 : $i] : (((X0 @ X3) = X1) & ((in @ X3 @ X2) = $true)) | ((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))))),
% 1.82/1.50 inference(nnf_transformation,[status(thm)],[f9])).
% 1.82/1.50 thf(f9,plain,(
% 1.82/1.50 ! [X0 : $i > $i,X1 : $i,X2 : $i] : (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) <=> ? [X3 : $i] : (((X0 @ X3) = X1) & ((in @ X3 @ X2) = $true))) <=> (image1Equiv = $true)),
% 1.82/1.50 inference(rectify,[status(thm)],[f8])).
% 1.82/1.50 thf(f8,plain,(
% 1.82/1.50 (image1Equiv = $true) <=> ! [X0 : $i > $i,X1 : $i,X2 : $i] : (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) <=> ? [X4 : $i] : (((in @ X4 @ X2) = $true) & ((X0 @ X4) = X1)))),
% 1.82/1.50 inference(fool_elimination,[status(thm)],[f7])).
% 1.82/1.50 thf(f7,plain,(
% 1.82/1.50 (image1Equiv = ! [X0 : $i > $i,X1 : $i,X2 : $i] : ((in @ X1 @ (image1 @ X2 @ (^[X3 : $i] : (X0 @ X3)))) <=> ? [X4 : $i] : ((in @ X4 @ X2) & ((X0 @ X4) = X1))))),
% 1.82/1.50 inference(rectify,[status(thm)],[f1])).
% 1.82/1.50 thf(f1,axiom,(
% 1.82/1.50 (image1Equiv = ! [X1 : $i > $i,X2 : $i,X0 : $i] : ((in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3)))) <=> ? [X3 : $i] : ((in @ X3 @ X0) & ((X1 @ X3) = X2))))),
% 1.82/1.50 file('/export/starexec/sandbox/tmp/tmp.jkXUZKPcaH/DTF2THF_32428.p',image1Equiv)).
% 1.82/1.50 thf(f40,plain,(
% 1.82/1.50 ((in @ (sK2 @ sK3) @ (image1 @ sK1 @ sK2)) != $true)),
% 1.82/1.50 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.82/1.50 thf(f30,plain,(
% 1.82/1.50 ((in @ (sK2 @ sK3) @ (image1 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true)),
% 1.82/1.50 inference(definition_unfolding,[status(thm)],[f21,f23])).
% 1.82/1.50 thf(f23,plain,(
% 1.82/1.50 (sK0 = (sK2 @ sK3))),
% 1.82/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.82/1.50 thf(f21,plain,(
% 1.82/1.50 ((in @ sK0 @ (image1 @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true)),
% 1.82/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.82/1.50 % SZS output end Proof for DTF2THF_32428
% 1.82/1.50 % (32530)------------------------------
% 1.82/1.50 % (32530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (32530)Termination reason: Refutation
% 1.82/1.50
% 1.82/1.50 % (32530)Memory used [KB]: 5500
% 1.82/1.50 % (32530)Time elapsed: 0.006 s
% 1.82/1.50 % (32530)Instructions burned: 3 (million)
% 1.82/1.50 % (32530)------------------------------
% 1.82/1.50 % (32530)------------------------------
% 1.82/1.50 % (32524)Success in time 0.02 s
%------------------------------------------------------------------------------