%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU822^2 : 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 : n008.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 09:37:30 AM UTC 2026
% Result : Theorem 1.36s 1.13s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 86 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 244 ( 47 ~; 26 |; 21 &; 126 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 29 !; 10 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
nonempty: $i > $o ).
thf(func_def_3,type,
transitiveset: $i > $o ).
thf(func_def_4,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_6,type,
wellorderedByIn: $i > $o ).
thf(func_def_7,type,
ordinal: $i > $o ).
thf(f45,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44,f30]) ).
thf(f30,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ordinalIrrefl = $true )
& ( $true
= ( ordinal @ sK0 ) )
& ( $true
= ( in @ sK0 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ( ( in @ X0 @ X0 )
= $true ) )
=> ( ( $true
= ( ordinal @ sK0 ) )
& ( $true
= ( in @ sK0 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ordinalIrrefl = $true )
& ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ( ( in @ X0 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ordinalIrrefl
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ~ ( in @ X2 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ordinalIrrefl
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ~ ( in @ X2 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWvNvh0n5Y/DTF2THF_21335.p',ordinalIrrefl2) ).
thf(f44,plain,
( $true
!= ( ordinal @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( $true
!= ( ordinal @ sK0 ) ) ),
inference(superposition,[status(thm)],[f42,f29]) ).
thf(f29,plain,
( $true
= ( in @ sK0 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f42,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f40,f29]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f31]) ).
thf(f31,plain,
ordinalIrrefl = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( ordinal @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X1 ) )
| ( ordinalIrrefl != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i] :
( ( $true
!= ( ordinal @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X1 ) ) ) )
| ( ordinalIrrefl != $true ) )
& ( ( ordinalIrrefl = $true )
| ( ( $true
= ( ordinal @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f25,f27,f26]) ).
thf(f26,plain,
( ? [X2: $i] :
( ( ( ordinal @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X3 )
= $true ) ) )
=> ( ( $true
= ( ordinal @ sK1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ X3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( ( in @ X3 @ X3 )
= $true ) )
=> ( ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i] :
( ( $true
!= ( ordinal @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X1 ) ) ) )
| ( ordinalIrrefl != $true ) )
& ( ( ordinalIrrefl = $true )
| ? [X2: $i] :
( ( ( ordinal @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X3 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i] :
( ( $true
!= ( ordinal @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X1 ) ) ) )
| ( ordinalIrrefl != $true ) )
& ( ( ordinalIrrefl = $true )
| ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X1 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X0: $i] :
( ( $true
!= ( ordinal @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X1 @ X1 ) ) ) )
<=> ( ordinalIrrefl = $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ordinalIrrefl = $true )
<=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
!= ( in @ X1 @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
!= ( in @ X1 @ X1 ) ) ) )
<=> ( ordinalIrrefl = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) )
= ordinalIrrefl ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i] :
( ( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X0 ) ) )
= ordinalIrrefl ),
file('/export/starexec/sandbox2/tmp/tmp.HWvNvh0n5Y/DTF2THF_21335.p',ordinalIrrefl) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU822^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:35:09 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEU822^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : Ordinals
% 0.16/0.42 % Version : Especial > Reduced > Especial.
% 0.16/0.42 % English : (! X:i.ordinal X -> ~(in X X))
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.42 % Source : [Bro08]
% 0.16/0.42 % Names : ZFC324l [Bro08]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.16/0.42 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.16/0.42 % Number of atoms : 36 ( 6 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 3 ( 7 avg)
% 0.16/0.42 % Number of connectives : 71 ( 3 ~; 3 |; 6 &; 45 @)
% 0.16/0.42 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 7 ( 2 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 9 ( 8 usr; 1 con; 0-2 aty)
% 0.16/0.42 % Number of variables : 15 ( 3 ^; 11 !; 1 ?; 15 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : http://mathgate.info/detsetitem.php?id=519
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(in_type,type,
% 0.16/0.42 in: $i > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(powerset_type,type,
% 0.16/0.42 powerset: $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(nonempty_type,type,
% 0.16/0.42 nonempty: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(transitiveset_type,type,
% 0.16/0.42 transitiveset: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(stricttotalorderedByIn_type,type,
% 0.16/0.42 stricttotalorderedByIn: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(stricttotalorderedByIn,definition,
% 0.16/0.42 ( stricttotalorderedByIn
% 0.16/0.42 = ( ^ [A: $i] :
% 0.16/0.42 ( ! [Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ A )
% 0.16/0.42 => ! [X: $i] :
% 0.16/0.42 ( ( in @ X @ A )
% 0.16/0.42 => ! [Y: $i] :
% 0.16/0.42 ( ( in @ Y @ A )
% 0.16/0.42 => ( ( ( in @ Xx @ X )
% 0.16/0.42 & ( in @ X @ Y ) )
% 0.16/0.42 => ( in @ Xx @ Y ) ) ) ) )
% 0.16/0.42 & ! [X: $i] :
% 0.16/0.42 ( ( in @ X @ A )
% 0.16/0.42 => ! [Y: $i] :
% 0.16/0.42 ( ( in @ Y @ A )
% 0.16/0.42 => ( ( X = Y )
% 0.16/0.42 | ( in @ X @ Y )
% 0.16/0.42 | ( in @ Y @ X ) ) ) )
% 0.16/0.42 & ! [X: $i] :
% 0.16/0.42 ( ( in @ X @ A )
% 0.16/0.42 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(wellorderedByIn_type,type,
% 0.16/0.42 wellorderedByIn: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(wellorderedByIn,definition,
% 0.16/0.42 ( wellorderedByIn
% 0.16/0.42 = ( ^ [A: $i] :
% 0.16/0.42 ( ( stricttotalorderedByIn @ A )
% 0.16/0.42 & ! [X: $i] :
% 0.16/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.16/0.42 => ( ( nonempty @ X )
% 0.16/0.42 => ? [Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ X )
% 0.16/0.42 & ! [Y: $i] :
% 0.16/0.42 ( ( in @ Y @ X )
% 0.16/0.42 => ( ( Xx = Y )
% 0.16/0.42 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(ordinal_type,type,
% 0.16/0.42 ordinal: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(ordinal,definition,
% 0.16/0.42 ( ordinal
% 0.16/0.42 = ( ^ [Xx: $i] :
% 0.16/0.42 ( ( transitiveset @ Xx )
% 0.16/0.42 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(ordinalIrrefl_type,type,
% 0.16/0.42 ordinalIrrefl: $o ).
% 0.16/0.42
% 0.16/0.42 thf(ordinalIrrefl,definition,
% 0.16/0.42 ( ordinalIrrefl
% 0.16/0.42 = ( ! [X: $i] :
% 0.16/0.42 ( ( ordinal @ X )
% 0.16/0.42 => ! [A: $i] :
% 0.16/0.42 ( ( in @ A @ X )
% 0.16/0.42 => ~ ( in @ A @ A ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(ordinalIrrefl2,conjecture,
% 0.16/0.42 ( ordinalIrrefl
% 0.16/0.42 => ! [X: $i] :
% 0.16/0.42 ( ( ordinal @ X )
% 0.16/0.42 => ~ ( in @ X @ X ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.17/1.10 ---- Embedded in THF ---
% 1.17/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.17/1.10 %%% Generated on Tue Feb 24 12:35:10 EST 2026
% 1.17/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.17/1.10 %%% Logic specification used:
% 1.17/1.10 %%% thf(spec, logic, $$dhol).
% 1.17/1.10
% 1.17/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HWvNvh0n5Y/DTF2DTF21335.p
% See solution above
% 1.17/1.10 ------------------------
% 1.17/1.11 ---- Cleaned THF ---
% 1.17/1.11 thf(in_type,type,
% 1.17/1.11 in: $i > $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(powerset_type,type,
% 1.17/1.11 powerset: $i > $i ).
% 1.17/1.11
% 1.17/1.11 thf(nonempty_type,type,
% 1.17/1.11 nonempty: $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(transitiveset_type,type,
% 1.17/1.11 transitiveset: $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(stricttotalorderedByIn_type,type,
% 1.17/1.11 stricttotalorderedByIn: $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(stricttotalorderedByIn,definition,
% 1.17/1.11 ( stricttotalorderedByIn
% 1.17/1.11 = ( ^ [A: $i] :
% 1.17/1.11 ( ! [Xx: $i] :
% 1.17/1.11 ( ( in @ Xx @ A )
% 1.17/1.11 => ! [X: $i] :
% 1.17/1.11 ( ( in @ X @ A )
% 1.17/1.11 => ! [Y: $i] :
% 1.17/1.11 ( ( in @ Y @ A )
% 1.17/1.11 => ( ( ( in @ Xx @ X )
% 1.17/1.11 & ( in @ X @ Y ) )
% 1.17/1.11 => ( in @ Xx @ Y ) ) ) ) )
% 1.17/1.11 & ! [X: $i] :
% 1.17/1.11 ( ( in @ X @ A )
% 1.17/1.11 => ! [Y: $i] :
% 1.17/1.11 ( ( in @ Y @ A )
% 1.17/1.11 => ( ( X = Y )
% 1.17/1.11 | ( in @ X @ Y )
% 1.17/1.11 | ( in @ Y @ X ) ) ) )
% 1.17/1.11 & ! [X: $i] :
% 1.17/1.11 ( ( in @ X @ A )
% 1.17/1.11 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.17/1.11
% 1.17/1.11 thf(wellorderedByIn_type,type,
% 1.17/1.11 wellorderedByIn: $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(wellorderedByIn,definition,
% 1.17/1.11 ( wellorderedByIn
% 1.17/1.11 = ( ^ [A: $i] :
% 1.17/1.11 ( ( stricttotalorderedByIn @ A )
% 1.17/1.11 & ! [X: $i] :
% 1.17/1.11 ( ( in @ X @ ( powerset @ A ) )
% 1.17/1.11 => ( ( nonempty @ X )
% 1.17/1.11 => ? [Xx: $i] :
% 1.17/1.11 ( ( in @ Xx @ X )
% 1.17/1.11 & ! [Y: $i] :
% 1.17/1.11 ( ( in @ Y @ X )
% 1.17/1.11 => ( ( Xx = Y )
% 1.17/1.11 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.11
% 1.17/1.11 thf(ordinal_type,type,
% 1.17/1.11 ordinal: $i > $o ).
% 1.17/1.11
% 1.17/1.11 thf(ordinal,definition,
% 1.17/1.11 ( ordinal
% 1.17/1.11 = ( ^ [Xx: $i] :
% 1.17/1.11 ( ( transitiveset @ Xx )
% 1.17/1.11 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.17/1.11
% 1.17/1.11 thf(ordinalIrrefl_type,type,
% 1.17/1.11 ordinalIrrefl: $o ).
% 1.17/1.11
% 1.17/1.11 thf(ordinalIrrefl,definition,
% 1.17/1.11 ( ordinalIrrefl
% 1.17/1.11 = ( ! [X: $i] :
% 1.17/1.11 ( ( ordinal @ X )
% 1.17/1.11 => ! [A: $i] :
% 1.17/1.11 ( ( in @ A @ X )
% 1.17/1.11 => ~ ( in @ A @ A ) ) ) ) ) ).
% 1.17/1.11
% 1.17/1.11 thf(ordinalIrrefl2,conjecture,
% 1.17/1.11 ( ordinalIrrefl
% 1.17/1.11 => ! [X: $i] :
% 1.17/1.11 ( ( ordinal @ X )
% 1.17/1.11 => ~ ( in @ X @ X ) ) ) ).
% 1.17/1.11 ------------------------
% 1.17/1.12 % (21435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21335 for (2999ds/183Mi)
% 1.36/1.13 % (21437)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_21335 for (2999ds/27Mi)
% 1.36/1.13 % (21439)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_21335 for (2999ds/2Mi)
% 1.36/1.13 % (21438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21335 for (2999ds/2Mi)
% 1.36/1.13 % (21440)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_21335 for (2999ds/275Mi)
% 1.36/1.13 % (21441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21335 for (2999ds/18Mi)
% 1.36/1.13 % (21436)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_21335 for (2999ds/4Mi)
% 1.36/1.13 % (21439)Instruction limit reached!
% 1.36/1.13 % (21439)------------------------------
% 1.36/1.13 % (21439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.13 % (21439)Termination reason: Unknown
% 1.36/1.13 % (21439)Termination phase: shuffling
% 1.36/1.13
% 1.36/1.13 % (21439)Memory used [KB]: 1023
% 1.36/1.13 % (21439)Time elapsed: 0.002 s
% 1.36/1.13 % (21439)Instructions burned: 2 (million)
% 1.36/1.13 % (21439)------------------------------
% 1.36/1.13 % (21439)------------------------------
% 1.36/1.13 % (21438)Instruction limit reached!
% 1.36/1.13 % (21438)------------------------------
% 1.36/1.13 % (21438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.13 % (21438)Termination reason: Unknown
% 1.36/1.13 % (21438)Termination phase: Function definition elimination
% 1.36/1.13
% 1.36/1.13 % (21438)Memory used [KB]: 1023
% 1.36/1.13 % (21438)Time elapsed: 0.003 s
% 1.36/1.13 % (21438)Instructions burned: 4 (million)
% 1.36/1.13 % (21438)------------------------------
% 1.36/1.13 % (21438)------------------------------
% 1.36/1.13 % (21436)Instruction limit reached!
% 1.36/1.13 % (21436)------------------------------
% 1.36/1.13 % (21436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.13 % (21436)Termination reason: Unknown
% 1.36/1.13 % (21436)Termination phase: Property scanning
% 1.36/1.13
% 1.36/1.13 % (21436)Memory used [KB]: 1023
% 1.36/1.13 % (21436)Time elapsed: 0.003 s
% 1.36/1.13 % (21436)Instructions burned: 4 (million)
% 1.36/1.13 % (21436)------------------------------
% 1.36/1.13 % (21436)------------------------------
% 1.36/1.13 % (21440)First to succeed.
% 1.36/1.13 % (21440)Refutation found. Thanks to Tanya!
% 1.36/1.13 % SZS status Theorem for DTF2THF_21335
% 1.36/1.13 % SZS output start Proof for DTF2THF_21335
% 1.36/1.13 thf(func_def_0, type, in: $i > $i > $o).
% 1.36/1.13 thf(func_def_1, type, powerset: $i > $i).
% 1.36/1.13 thf(func_def_2, type, nonempty: $i > $o).
% 1.36/1.13 thf(func_def_3, type, transitiveset: $i > $o).
% 1.36/1.13 thf(func_def_4, type, stricttotalorderedByIn: $i > $o).
% 1.36/1.13 thf(func_def_6, type, wellorderedByIn: $i > $o).
% 1.36/1.13 thf(func_def_7, type, ordinal: $i > $o).
% 1.36/1.13 thf(f45,plain,(
% 1.36/1.13 $false),
% 1.36/1.13 inference(subsumption_resolution,[status(thm)],[f44,f30])).
% 1.36/1.13 thf(f30,plain,(
% 1.36/1.13 ($true = (ordinal @ sK0))),
% 1.36/1.13 inference(cnf_transformation,[status(thm)],[f23])).
% 1.36/1.13 thf(f23,plain,(
% 1.36/1.13 (ordinalIrrefl = $true) & (($true = (ordinal @ sK0)) & ($true = (in @ sK0 @ sK0)))),
% 1.36/1.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22])).
% 1.36/1.13 thf(f22,plain,(
% 1.36/1.13 ? [X0 : $i] : (($true = (ordinal @ X0)) & ((in @ X0 @ X0) = $true)) => (($true = (ordinal @ sK0)) & ($true = (in @ sK0 @ sK0)))),
% 1.36/1.13 introduced(definition,[],[choice_axiom])).
% 1.36/1.13 thf(f21,plain,(
% 1.36/1.13 (ordinalIrrefl = $true) & ? [X0 : $i] : (($true = (ordinal @ X0)) & ((in @ X0 @ X0) = $true))),
% 1.36/1.13 inference(ennf_transformation,[status(thm)],[f18])).
% 1.36/1.13 thf(f18,plain,(
% 1.36/1.13 ~((ordinalIrrefl = $true) => ! [X0 : $i] : (($true = (ordinal @ X0)) => ((in @ X0 @ X0) != $true)))),
% 1.36/1.13 inference(flattening,[status(thm)],[f17])).
% 1.36/1.13 thf(f17,plain,(
% 1.36/1.13 ~((ordinalIrrefl = $true) => ! [X0 : $i] : (($true = (ordinal @ X0)) => ~((in @ X0 @ X0) = $true)))),
% 1.36/1.13 inference(fool_elimination,[status(thm)],[f16])).
% 1.36/1.13 thf(f16,plain,(
% 1.36/1.13 ~(ordinalIrrefl => ! [X0 : $i] : ((ordinal @ X0) => ~(in @ X0 @ X0)))),
% 1.36/1.13 inference(rectify,[status(thm)],[f6])).
% 1.36/1.13 thf(f6,negated_conjecture,(
% 1.36/1.13 ~(ordinalIrrefl => ! [X2 : $i] : ((ordinal @ X2) => ~(in @ X2 @ X2)))),
% 1.36/1.13 inference(negated_conjecture,[status(cth)],[f5])).
% 1.36/1.13 thf(f5,conjecture,(
% 1.36/1.13 ordinalIrrefl => ! [X2 : $i] : ((ordinal @ X2) => ~(in @ X2 @ X2))),
% 1.36/1.13 file('/export/starexec/sandbox2/tmp/tmp.HWvNvh0n5Y/DTF2THF_21335.p',ordinalIrrefl2)).
% 1.36/1.13 thf(f44,plain,(
% 1.36/1.13 ($true != (ordinal @ sK0))),
% 1.36/1.13 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.36/1.13 thf(f43,plain,(
% 1.36/1.13 ($true != $true) | ($true != (ordinal @ sK0))),
% 1.36/1.13 inference(superposition,[status(thm)],[f42,f29])).
% 1.36/1.13 thf(f29,plain,(
% 1.36/1.13 ($true = (in @ sK0 @ sK0))),
% 1.36/1.13 inference(cnf_transformation,[status(thm)],[f23])).
% 1.36/1.13 thf(f42,plain,(
% 1.36/1.13 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ($true != (ordinal @ X0))) )),
% 1.36/1.13 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.36/1.13 thf(f41,plain,(
% 1.36/1.13 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ($true != (ordinal @ X0)) | ($true != $true)) )),
% 1.36/1.13 inference(superposition,[status(thm)],[f40,f29])).
% 1.36/1.13 thf(f40,plain,(
% 1.36/1.13 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X1)) | ((in @ X1 @ X0) != $true) | ($true != (ordinal @ X0))) )),
% 1.36/1.13 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.36/1.13 thf(f36,plain,(
% 1.36/1.13 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X1)) | ((in @ X1 @ X0) != $true) | ($true != (ordinal @ X0)) | ($true != $true)) )),
% 1.36/1.13 inference(definition_unfolding,[status(thm)],[f35,f31])).
% 1.36/1.13 thf(f31,plain,(
% 1.36/1.13 (ordinalIrrefl = $true)),
% 1.36/1.13 inference(cnf_transformation,[status(thm)],[f23])).
% 1.36/1.13 thf(f35,plain,(
% 1.36/1.13 ( ! [X0 : $i,X1 : $i] : (($true != (ordinal @ X0)) | ((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X1)) | (ordinalIrrefl != $true)) )),
% 1.36/1.13 inference(cnf_transformation,[status(thm)],[f28])).
% 1.36/1.13 thf(f28,plain,(
% 1.36/1.13 (! [X0 : $i] : (($true != (ordinal @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X1)))) | (ordinalIrrefl != $true)) & ((ordinalIrrefl = $true) | (($true = (ordinal @ sK1)) & (($true = (in @ sK2 @ sK1)) & ($true = (in @ sK2 @ sK2)))))),
% 1.36/1.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f25,f27,f26])).
% 1.36/1.13 thf(f26,plain,(
% 1.36/1.13 ? [X2 : $i] : (((ordinal @ X2) = $true) & ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ X3 @ X3) = $true))) => (($true = (ordinal @ sK1)) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((in @ X3 @ X3) = $true)))),
% 1.36/1.13 introduced(definition,[],[choice_axiom])).
% 1.36/1.13 thf(f27,plain,(
% 1.36/1.13 ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ((in @ X3 @ X3) = $true)) => (($true = (in @ sK2 @ sK1)) & ($true = (in @ sK2 @ sK2)))),
% 1.36/1.13 introduced(definition,[],[choice_axiom])).
% 1.36/1.13 thf(f25,plain,(
% 1.36/1.13 (! [X0 : $i] : (($true != (ordinal @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X1)))) | (ordinalIrrefl != $true)) & ((ordinalIrrefl = $true) | ? [X2 : $i] : (((ordinal @ X2) = $true) & ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ X3 @ X3) = $true))))),
% 1.36/1.13 inference(rectify,[status(thm)],[f24])).
% 1.36/1.13 thf(f24,plain,(
% 1.36/1.13 (! [X0 : $i] : (($true != (ordinal @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X1)))) | (ordinalIrrefl != $true)) & ((ordinalIrrefl = $true) | ? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ($true = (in @ X1 @ X1)))))),
% 1.36/1.13 inference(nnf_transformation,[status(thm)],[f20])).
% 1.36/1.13 thf(f20,plain,(
% 1.36/1.13 ! [X0 : $i] : (($true != (ordinal @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ X1)))) <=> (ordinalIrrefl = $true)),
% 1.36/1.13 inference(ennf_transformation,[status(thm)],[f19])).
% 1.36/1.13 thf(f19,plain,(
% 1.36/1.13 (ordinalIrrefl = $true) <=> ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ($true != (in @ X1 @ X1))))),
% 1.36/1.13 inference(flattening,[status(thm)],[f15])).
% 1.36/1.13 thf(f15,plain,(
% 1.36/1.13 ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ~($true = (in @ X1 @ X1)))) <=> (ordinalIrrefl = $true)),
% 1.36/1.13 inference(fool_elimination,[status(thm)],[f14])).
% 1.36/1.13 thf(f14,plain,(
% 1.36/1.13 (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ~(in @ X1 @ X1))) = ordinalIrrefl)),
% 1.36/1.13 inference(rectify,[status(thm)],[f4])).
% 1.36/1.13 thf(f4,axiom,(
% 1.36/1.13 (! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X0 @ X2) => ~(in @ X0 @ X0))) = ordinalIrrefl)),
% 1.36/1.13 file('/export/starexec/sandbox2/tmp/tmp.HWvNvh0n5Y/DTF2THF_21335.p',ordinalIrrefl)).
% 1.36/1.13 % SZS output end Proof for DTF2THF_21335
% 1.36/1.13 % (21440)------------------------------
% 1.36/1.13 % (21440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.13 % (21440)Termination reason: Refutation
% 1.36/1.13
% 1.36/1.13 % (21440)Memory used [KB]: 5500
% 1.36/1.13 % (21440)Time elapsed: 0.004 s
% 1.36/1.13 % (21440)Instructions burned: 3 (million)
% 1.36/1.13 % (21440)------------------------------
% 1.36/1.13 % (21440)------------------------------
% 1.36/1.13 % (21434)Success in time 0.008 s
%------------------------------------------------------------------------------