%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU796^2 : 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 : n015.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 09:37:16 AM UTC 2026
% Result : Theorem 1.48s 1.27s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 94 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 437 ( 19 ~; 17 |; 27 &; 331 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 7 con; 0-3 aty)
% ( 18 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 127 ( 49 ^; 65 !; 13 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK2: $i > $i ).
thf(func_def_21,type,
sK4: $i > $i > ( $i > $i ) > $i ).
thf(func_def_22,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f18,f42]) ).
thf(f42,plain,
( ( in @ sK1 @ ( image1 @ sK0 @ sK2 ) )
= $false ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( sK1 != X0 )
| ( ( in @ X0 @ ( image1 @ sK0 @ sK2 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i] :
( ( sK1 != X0 )
| ( ( in @ X0 @ ( image1 @ sK0 @ sK2 ) )
= $false )
| ( ( in @ X0 @ ( image1 @ sK0 @ sK2 ) )
= $false ) ),
inference(superposition,[status(thm)],[f39,f37]) ).
thf(f37,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) )
= X1 )
| ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false )
| ( $true
= ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) )
= X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false )
| ( $true
= ( ( ( X2 @ ( sK4 @ X3 @ X1 @ X2 ) )
= X1 )
& ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( X2 @ Y0 )
= X1 )
& ( in @ Y0 @ X3 ) )
@ ( sK4 @ X3 @ X1 @ X2 ) )
= $true )
| ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( X2 @ Y0 )
= X1 )
& ( in @ Y0 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( X2 @ Y0 )
= X1 )
& ( in @ Y0 @ X3 ) ) )
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( X2 @ Y0 )
= X1 )
& ( in @ Y0 @ X3 ) ) )
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( X2 @ Y1 )
= X1 )
& ( in @ Y1 @ Y0 ) ) )
= ( in @ X1 @ ( image1 @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( X2 @ Y1 )
= X1 )
& ( in @ Y1 @ Y0 ) ) )
= ( in @ X1 @ ( image1 @ Y0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 )
= X1 )
& ( in @ Y2 @ Y1 ) ) )
= ( in @ X1 @ ( image1 @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 )
= X1 )
& ( in @ Y2 @ Y1 ) ) )
= ( in @ X1 @ ( image1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 )
= Y0 )
& ( in @ Y3 @ Y2 ) ) )
= ( in @ Y0 @ ( image1 @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 )
= Y0 )
& ( in @ Y3 @ Y2 ) ) )
= ( in @ Y0 @ ( image1 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 )
= Y0 )
& ( in @ Y3 @ Y2 ) ) )
= ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f14,f13]) ).
thf(f13,plain,
( image1Equiv
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 )
= Y0 )
& ( in @ Y3 @ Y2 ) ) )
= ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( image1Equiv
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y3 )
= Y0 )
& ( in @ Y3 @ Y2 ) ) )
= ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i > $i,X2: $i] :
( ( ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( X1 @ X3 )
= X2 ) )
<=> ( in @ X2
@ ( image1 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) )
= image1Equiv ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i > $i,X2: $i] :
( ( ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( X1 @ X3 )
= X2 ) )
<=> ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) )
= image1Equiv ),
file('/export/starexec/sandbox2/tmp/tmp.gwb3Z5KESq/DTF2THF_23582.p',image1Equiv) ).
thf(f14,plain,
image1Equiv = $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X3: $i] :
( ( sK1
!= ( sK2 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ sK1
@ ( image1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) )
& ( image1Equiv = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true
= ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
=> ( ! [X3: $i] :
( ( sK1
!= ( sK2 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK0 ) ) )
& ( $true
= ( in @ sK1
@ ( image1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true
= ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
& ( image1Equiv = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
= ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X2 @ X3 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
= ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( X2 @ X4 )
= X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( image1Equiv
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( in @ X1
@ ( image1 @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( ( X2 @ X4 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( image1Equiv
=> ! [X0: $i,X2: $i,X1: $i > $i] :
( ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( X1 @ X3 )
= X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( image1Equiv
=> ! [X0: $i,X2: $i,X1: $i > $i] :
( ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ( ( X1 @ X3 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gwb3Z5KESq/DTF2THF_23582.p',image1E) ).
thf(f39,plain,
! [X0: $i,X1: $i > $i] :
( ( sK1
!= ( sK2 @ ( sK4 @ sK0 @ X0 @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( image1 @ sK0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $i,X1: $i > $i] :
( ( $false
= ( in @ X0 @ ( image1 @ sK0 @ X1 ) ) )
| ( sK1
!= ( sK2 @ ( sK4 @ sK0 @ X0 @ X1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f35]) ).
thf(f35,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f16,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK0 ) )
| ( sK1
!= ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f18,plain,
( ( in @ sK1 @ ( image1 @ sK0 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( in @ sK1
@ ( image1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU796^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:34:31 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEU796^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : More about Functions - Images of Functions
% 0.17/0.44 % Version : Especial > Reduced > Especial.
% 0.17/0.44 % English : (! A:i.! f:i>i.! x:i.in x (image1 A (^ y:i.f y)) ->
% 0.17/0.44 % (? y:i.in y A & x = f y))
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.44 % Source : [Bro08]
% 0.17/0.44 % Names : ZFC298l [Bro08]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % 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 v5.1.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.17/0.44 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.17/0.44 % Number of atoms : 9 ( 3 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 4 ( 4 avg)
% 0.17/0.44 % Number of connectives : 21 ( 0 ~; 0 |; 2 &; 16 @)
% 0.17/0.44 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 10 ( 6 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.17/0.44 % Number of variables : 10 ( 2 ^; 6 !; 2 ?; 10 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : http://mathgate.info/detsetitem.php?id=419
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(in_type,type,
% 0.17/0.44 in: $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(image1_type,type,
% 0.17/0.44 image1: $i > ( $i > $i ) > $i ).
% 0.17/0.44
% 0.17/0.44 thf(image1Equiv_type,type,
% 0.17/0.44 image1Equiv: $o ).
% 0.17/0.44
% 0.17/0.44 thf(image1Equiv,definition,
% 0.17/0.44 ( image1Equiv
% 0.17/0.44 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx
% 0.17/0.44 @ ( image1 @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.44 <=> ? [Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ A )
% 0.17/0.44 & ( Xx
% 0.17/0.44 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(image1E,conjecture,
% 0.17/0.44 ( image1Equiv
% 0.17/0.44 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx
% 0.17/0.44 @ ( image1 @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.44 => ? [Xy: $i] :
% 0.17/0.44 ( ( in @ Xy @ A )
% 0.17/0.44 & ( Xx
% 0.17/0.44 = ( Xf @ Xy ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.48/1.23 ---- Embedded in THF ---
% 1.48/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.23 %%% Generated on Tue Feb 24 12:34:32 EST 2026
% 1.48/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.23 %%% Logic specification used:
% 1.48/1.23 %%% thf(spec, logic, $$dhol).
% 1.48/1.23
% 1.48/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gwb3Z5KESq/DTF2DTF23582.p
% See solution above
% 1.48/1.23 ------------------------
% 1.48/1.24 ---- Cleaned THF ---
% 1.48/1.24 thf(in_type,type,
% 1.48/1.24 in: $i > $i > $o ).
% 1.48/1.24
% 1.48/1.24 thf(image1_type,type,
% 1.48/1.24 image1: $i > ( $i > $i ) > $i ).
% 1.48/1.24
% 1.48/1.24 thf(image1Equiv_type,type,
% 1.48/1.24 image1Equiv: $o ).
% 1.48/1.24
% 1.48/1.24 thf(image1Equiv,definition,
% 1.48/1.24 ( image1Equiv
% 1.48/1.24 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 1.48/1.24 ( ( in @ Xx
% 1.48/1.24 @ ( image1 @ A
% 1.48/1.24 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 1.48/1.24 <=> ? [Xy: $i] :
% 1.48/1.24 ( ( in @ Xy @ A )
% 1.48/1.24 & ( Xx
% 1.48/1.24 = ( Xf @ Xy ) ) ) ) ) ) ).
% 1.48/1.24
% 1.48/1.24 thf(image1E,conjecture,
% 1.48/1.24 ( image1Equiv
% 1.48/1.24 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 1.48/1.24 ( ( in @ Xx
% 1.48/1.24 @ ( image1 @ A
% 1.48/1.24 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 1.48/1.24 => ? [Xy: $i] :
% 1.48/1.24 ( ( in @ Xy @ A )
% 1.48/1.24 & ( Xx
% 1.48/1.24 = ( Xf @ Xy ) ) ) ) ) ).
% 1.48/1.24 ------------------------
% 1.48/1.26 % (23800)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23582 for (2999ds/183Mi)
% 1.48/1.26 % (23806)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23582 for (2999ds/18Mi)
% 1.48/1.26 % (23801)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_23582 for (2999ds/4Mi)
% 1.48/1.26 % (23806)Instruction limit reached!
% 1.48/1.26 % (23806)------------------------------
% 1.48/1.26 % (23806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (23806)Termination reason: Unknown
% 1.48/1.26 % (23806)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (23806)Memory used [KB]: 5628
% 1.48/1.26 % (23806)Time elapsed: 0.008 s
% 1.48/1.26 % (23806)Instructions burned: 20 (million)
% 1.48/1.26 % (23806)------------------------------
% 1.48/1.26 % (23806)------------------------------
% 1.48/1.26 % (23802)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_23582 for (2999ds/27Mi)
% 1.48/1.26 % (23803)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23582 for (2999ds/2Mi)
% 1.48/1.26 % (23804)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_23582 for (2999ds/2Mi)
% 1.48/1.26 % (23805)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_23582 for (2999ds/275Mi)
% 1.48/1.26 % (23803)Instruction limit reached!
% 1.48/1.26 % (23803)------------------------------
% 1.48/1.26 % (23803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (23803)Termination reason: Unknown
% 1.48/1.26 % (23803)Termination phase: shuffling
% 1.48/1.26
% 1.48/1.26 % (23803)Memory used [KB]: 895
% 1.48/1.26 % (23803)Time elapsed: 0.003 s
% 1.48/1.26 % (23803)Instructions burned: 2 (million)
% 1.48/1.26 % (23803)------------------------------
% 1.48/1.26 % (23803)------------------------------
% 1.48/1.26 % (23804)Instruction limit reached!
% 1.48/1.26 % (23804)------------------------------
% 1.48/1.26 % (23804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (23804)Termination reason: Unknown
% 1.48/1.26 % (23804)Termination phase: Naming
% 1.48/1.26
% 1.48/1.26 % (23804)Memory used [KB]: 895
% 1.48/1.26 % (23804)Time elapsed: 0.003 s
% 1.48/1.26 % (23804)Instructions burned: 2 (million)
% 1.48/1.26 % (23804)------------------------------
% 1.48/1.26 % (23804)------------------------------
% 1.48/1.27 % (23801)Instruction limit reached!
% 1.48/1.27 % (23801)------------------------------
% 1.48/1.27 % (23801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (23801)Termination reason: Unknown
% 1.48/1.27 % (23801)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (23801)Memory used [KB]: 5500
% 1.48/1.27 % (23801)Time elapsed: 0.005 s
% 1.48/1.27 % (23801)Instructions burned: 4 (million)
% 1.48/1.27 % (23801)------------------------------
% 1.48/1.27 % (23801)------------------------------
% 1.48/1.27 % (23802)First to succeed.
% 1.48/1.27 % (23805)Also succeeded, but the first one will report.
% 1.48/1.27 % (23800)Also succeeded, but the first one will report.
% 1.48/1.27 % (23802)Refutation found. Thanks to Tanya!
% 1.48/1.27 % SZS status Theorem for DTF2THF_23582
% 1.48/1.27 % SZS output start Proof for DTF2THF_23582
% 1.48/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.48/1.27 thf(func_def_1, type, image1: $i > ($i > $i) > $i).
% 1.48/1.27 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.27 thf(func_def_19, type, sK2: $i > $i).
% 1.48/1.27 thf(func_def_21, type, sK4: $i > $i > ($i > $i) > $i).
% 1.48/1.27 thf(func_def_22, type, ph5: !>[X0: $tType]:(X0)).
% 1.48/1.27 thf(f47,plain,(
% 1.48/1.27 $false),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.48/1.27 thf(f43,plain,(
% 1.48/1.27 ($true = $false)),
% 1.48/1.27 inference(backward_demodulation,[status(thm)],[f18,f42])).
% 1.48/1.27 thf(f42,plain,(
% 1.48/1.27 ((in @ sK1 @ (image1 @ sK0 @ sK2)) = $false)),
% 1.48/1.27 inference(equality_resolution,[status(thm)],[f41])).
% 1.48/1.27 thf(f41,plain,(
% 1.48/1.27 ( ! [X0 : $i] : ((sK1 != X0) | ((in @ X0 @ (image1 @ sK0 @ sK2)) = $false)) )),
% 1.48/1.27 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.48/1.27 thf(f40,plain,(
% 1.48/1.27 ( ! [X0 : $i] : ((sK1 != X0) | ((in @ X0 @ (image1 @ sK0 @ sK2)) = $false) | ((in @ X0 @ (image1 @ sK0 @ sK2)) = $false)) )),
% 1.48/1.27 inference(superposition,[status(thm)],[f39,f37])).
% 1.48/1.27 thf(f37,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (((X2 @ (sK4 @ X3 @ X1 @ X2)) = X1) | ((in @ X1 @ (image1 @ X3 @ X2)) = $false)) )),
% 1.48/1.27 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.48/1.27 thf(f36,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (((in @ X1 @ (image1 @ X3 @ X2)) = $false) | ($true = ((X2 @ (sK4 @ X3 @ X1 @ X2)) = X1))) )),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.48/1.27 thf(f34,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (((in @ X1 @ (image1 @ X3 @ X2)) = $false) | ($true = (((X2 @ (sK4 @ X3 @ X1 @ X2)) = X1) & (in @ (sK4 @ X3 @ X1 @ X2) @ X3)))) )),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.48/1.27 thf(f33,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((X2 @ Y0) = X1) & (in @ Y0 @ X3))) @ (sK4 @ X3 @ X1 @ X2)) = $true) | ((in @ X1 @ (image1 @ X3 @ X2)) = $false)) )),
% 1.48/1.27 inference(sigma_clausification,[status(thm)],[f27])).
% 1.48/1.27 thf(f27,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (((in @ X1 @ (image1 @ X3 @ X2)) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((X2 @ Y0) = X1) & (in @ Y0 @ X3)))) = $true)) )),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.48/1.27 thf(f26,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: (((X2 @ Y0) = X1) & (in @ Y0 @ X3)))) = (in @ X1 @ (image1 @ X3 @ X2)))) )),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.48/1.27 thf(f25,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: (((X2 @ Y0) = X1) & (in @ Y0 @ X3)))) = (in @ X1 @ (image1 @ X3 @ X2))) = $true)) )),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.48/1.27 thf(f24,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((X2 @ Y1) = X1) & (in @ Y1 @ Y0)))) = (in @ X1 @ (image1 @ Y0 @ X2)))) @ X3))) )),
% 1.48/1.27 inference(pi_clausification,[status(thm)],[f23])).
% 1.48/1.27 thf(f23,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((X2 @ Y1) = X1) & (in @ Y1 @ Y0)))) = (in @ X1 @ (image1 @ Y0 @ X2))))))) )),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.48/1.27 thf(f22,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X1 : $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((Y0 @ Y2) = X1) & (in @ Y2 @ Y1)))) = (in @ X1 @ (image1 @ Y1 @ Y0)))))) @ X2))) )),
% 1.48/1.27 inference(pi_clausification,[status(thm)],[f21])).
% 1.48/1.27 thf(f21,plain,(
% 1.48/1.27 ( ! [X1 : $i] : (($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((Y0 @ Y2) = X1) & (in @ Y2 @ Y1)))) = (in @ X1 @ (image1 @ Y1 @ Y0))))))))) )),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.48/1.27 thf(f20,plain,(
% 1.48/1.27 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) = Y0) & (in @ Y3 @ Y2)))) = (in @ Y0 @ (image1 @ Y2 @ Y1)))))))) @ X1))) )),
% 1.48/1.27 inference(pi_clausification,[status(thm)],[f19])).
% 1.48/1.27 thf(f19,plain,(
% 1.48/1.27 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) = Y0) & (in @ Y3 @ Y2)))) = (in @ Y0 @ (image1 @ Y2 @ Y1))))))))))),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.48/1.27 thf(f17,plain,(
% 1.48/1.27 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) = Y0) & (in @ Y3 @ Y2)))) = (in @ Y0 @ (image1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))),
% 1.48/1.27 inference(definition_unfolding,[status(thm)],[f14,f13])).
% 1.48/1.27 thf(f13,plain,(
% 1.48/1.27 (image1Equiv = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) = Y0) & (in @ Y3 @ Y2)))) = (in @ Y0 @ (image1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.27 thf(f8,plain,(
% 1.48/1.27 (image1Equiv = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((?? @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) = Y0) & (in @ Y3 @ Y2)))) = (in @ Y0 @ (image1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.27 thf(f7,plain,(
% 1.48/1.27 (! [X0 : $i,X1 : $i > $i,X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ((X1 @ X3) = X2)) <=> (in @ X2 @ (image1 @ X0 @ (^[X4 : $i] : (X1 @ X4))))) = image1Equiv)),
% 1.48/1.27 inference(rectify,[status(thm)],[f1])).
% 1.48/1.27 thf(f1,axiom,(
% 1.48/1.27 (! [X0 : $i,X1 : $i > $i,X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ((X1 @ X3) = X2)) <=> (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3))))) = image1Equiv)),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.gwb3Z5KESq/DTF2THF_23582.p',image1Equiv)).
% 1.48/1.27 thf(f14,plain,(
% 1.48/1.27 (image1Equiv = $true)),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 thf(f12,plain,(
% 1.48/1.27 (! [X3 : $i] : ((sK1 != (sK2 @ X3)) | ($true != (in @ X3 @ sK0))) & ($true = (in @ sK1 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0)))))) & (image1Equiv = $true)),
% 1.48/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.48/1.27 thf(f11,plain,(
% 1.48/1.27 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true)) & ($true = (in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (! [X3 : $i] : ((sK1 != (sK2 @ X3)) | ($true != (in @ X3 @ sK0))) & ($true = (in @ sK1 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))))),
% 1.48/1.27 introduced(definition,[],[choice_axiom])).
% 1.48/1.27 thf(f10,plain,(
% 1.48/1.27 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true)) & ($true = (in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) & (image1Equiv = $true)),
% 1.48/1.27 inference(ennf_transformation,[status(thm)],[f9])).
% 1.48/1.27 thf(f9,plain,(
% 1.48/1.27 ~((image1Equiv = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (($true = (in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((X2 @ X3) = X1))))),
% 1.48/1.27 inference(rectify,[status(thm)],[f6])).
% 1.48/1.27 thf(f6,plain,(
% 1.48/1.27 ~((image1Equiv = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (($true = (in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((X2 @ X4) = X1))))),
% 1.48/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.27 thf(f5,plain,(
% 1.48/1.27 ~(image1Equiv => ! [X0 : $i,X1 : $i,X2 : $i > $i] : ((in @ X1 @ (image1 @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => ? [X4 : $i] : ((in @ X4 @ X0) & ((X2 @ X4) = X1))))),
% 1.48/1.27 inference(rectify,[status(thm)],[f3])).
% 1.48/1.27 thf(f3,negated_conjecture,(
% 1.48/1.27 ~(image1Equiv => ! [X0 : $i,X2 : $i,X1 : $i > $i] : ((in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => ? [X3 : $i] : ((in @ X3 @ X0) & ((X1 @ X3) = X2))))),
% 1.48/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.27 thf(f2,conjecture,(
% 1.48/1.27 image1Equiv => ! [X0 : $i,X2 : $i,X1 : $i > $i] : ((in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => ? [X3 : $i] : ((in @ X3 @ X0) & ((X1 @ X3) = X2)))),
% 1.48/1.27 file('/export/starexec/sandbox2/tmp/tmp.gwb3Z5KESq/DTF2THF_23582.p',image1E)).
% 1.48/1.27 thf(f39,plain,(
% 1.48/1.27 ( ! [X0 : $i,X1 : $i > $i] : ((sK1 != (sK2 @ (sK4 @ sK0 @ X0 @ X1))) | ($false = (in @ X0 @ (image1 @ sK0 @ X1)))) )),
% 1.48/1.27 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.48/1.27 thf(f38,plain,(
% 1.48/1.27 ( ! [X0 : $i,X1 : $i > $i] : (($false = (in @ X0 @ (image1 @ sK0 @ X1))) | (sK1 != (sK2 @ (sK4 @ sK0 @ X0 @ X1))) | ($true != $true)) )),
% 1.48/1.27 inference(superposition,[status(thm)],[f16,f35])).
% 1.48/1.27 thf(f35,plain,(
% 1.48/1.27 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (($true = (in @ (sK4 @ X3 @ X1 @ X2) @ X3)) | ((in @ X1 @ (image1 @ X3 @ X2)) = $false)) )),
% 1.48/1.27 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.48/1.27 thf(f16,plain,(
% 1.48/1.27 ( ! [X3 : $i] : (($true != (in @ X3 @ sK0)) | (sK1 != (sK2 @ X3))) )),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 thf(f18,plain,(
% 1.48/1.27 ((in @ sK1 @ (image1 @ sK0 @ sK2)) = $true)),
% 1.48/1.27 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.48/1.27 thf(f15,plain,(
% 1.48/1.27 ($true = (in @ sK1 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0)))))),
% 1.48/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.27 % SZS output end Proof for DTF2THF_23582
% 1.48/1.27 % (23802)------------------------------
% 1.48/1.27 % (23802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (23802)Termination reason: Refutation
% 1.48/1.27
% 1.48/1.27 % (23802)Memory used [KB]: 5500
% 1.48/1.27 % (23802)Time elapsed: 0.008 s
% 1.48/1.27 % (23802)Instructions burned: 7 (million)
% 1.48/1.27 % (23802)------------------------------
% 1.48/1.27 % (23802)------------------------------
% 1.48/1.27 % (23799)Success in time 0.023 s
%------------------------------------------------------------------------------