%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU823^2 : 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 : n009.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 09:37:31 AM UTC 2026
% Result : Theorem 0.31s 1.25s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 773 ( 223 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 667 ( 129 ~; 92 |; 55 &; 341 @)
% ( 7 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 114 ( 0 ^; 85 !; 29 ?; 114 :)
% 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(f103,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f95,f102]) ).
thf(f102,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f100,f43]) ).
thf(f43,plain,
( ( ordinal @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK0 @ sK1 )
= $true )
& ( ( ordinal @ sK0 )
= $true )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
=> ( ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ sK0 @ X1 )
= $true ) )
& ( ( ordinal @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( in @ sK0 @ X1 )
= $true ) )
=> ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( ordinalIrrefl = $true )
& ( ordinalTransSet = $true ) ),
inference(ennf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
~ ( ( ordinalTransSet = $true )
=> ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( ordinalTransSet = $true )
=> ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X2 @ X0 )
=> ~ ( in @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalNoCycle) ).
thf(f100,plain,
( ( ( ordinal @ sK0 )
!= $true )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $true != $true )
| ( ( ordinal @ sK0 )
!= $true )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f82,f45]) ).
thf(f45,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f82,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl7_2
<=> ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ sK1 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f95,plain,
spl7_2,
inference(avatar_split_clause,[status(thm)],[f94,f81]) ).
thf(f94,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ sK1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ sK1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f89,f44]) ).
thf(f44,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f89,plain,
! [X0: $i,X1: $i] :
( ( ( in @ sK0 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $i,X1: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ sK0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ sK0 @ X1 )
!= $true )
| ( ( ordinal @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f85,f64]) ).
thf(f64,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f41]) ).
thf(f41,plain,
ordinalTransSet = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f54,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ordinalTransSet != $true ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ( ( ( ordinal @ sK4 )
= $true )
& ( ( in @ sK5 @ sK6 )
= $true )
& ( ( in @ sK5 @ sK4 )
!= $true )
& ( ( in @ sK6 @ sK4 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f37,f39,f38]) ).
thf(f38,plain,
( ? [X3: $i] :
( ( ( ordinal @ X3 )
= $true )
& ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( ( in @ X4 @ X3 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) ) )
=> ( ( ( ordinal @ sK4 )
= $true )
& ? [X5: $i,X4: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( ( in @ X4 @ sK4 )
!= $true )
& ( ( in @ X5 @ sK4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f39,plain,
( ? [X5: $i,X4: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( ( in @ X4 @ sK4 )
!= $true )
& ( ( in @ X5 @ sK4 )
= $true ) )
=> ( ( ( in @ sK5 @ sK6 )
= $true )
& ( ( in @ sK5 @ sK4 )
!= $true )
& ( ( in @ sK6 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ? [X3: $i] :
( ( ( ordinal @ X3 )
= $true )
& ? [X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ( ( in @ X4 @ X3 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( ordinalTransSet = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( ordinal @ X0 )
!= $true ) )
<=> ( ordinalTransSet = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) )
<=> ( ordinalTransSet = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) )
= ordinalTransSet ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i] :
( ( ( ordinal @ X2 )
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) ) ) )
= ordinalTransSet ),
file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalTransSet) ).
thf(f85,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f84,f44]) ).
thf(f84,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( in @ sK0 @ X0 )
!= $true )
| ( ( in @ sK0 @ sK1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f71,f43]) ).
thf(f71,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( ( ordinal @ X0 )
!= $true )
| ( ( ordinal @ sK0 )
!= $true )
| ( ( in @ sK0 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( $true != $true )
| ( ( ordinal @ X0 )
!= $true )
| ( ( ordinal @ sK0 )
!= $true )
| ( ( in @ sK0 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f67,f45]) ).
thf(f67,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( ordinal @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( ordinal @ X1 )
!= $true )
| ( $true != $true )
| ( ( ordinal @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f65,f64]) ).
thf(f65,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( ordinal @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true )
| ( ( ordinal @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f42]) ).
thf(f42,plain,
ordinalIrrefl = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( ( ordinal @ X2 )
!= $true )
| ( ( in @ X3 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ordinalIrrefl != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ordinalIrrefl = $true )
| ( ( ( ordinal @ sK2 )
= $true )
& ( ( in @ sK3 @ sK3 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true ) ) )
& ( ! [X2: $i] :
( ( ( ordinal @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( ordinalIrrefl != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f32,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i] :
( ( ( in @ X1 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
=> ( ( ( ordinal @ sK2 )
= $true )
& ? [X1: $i] :
( ( ( in @ X1 @ X1 )
= $true )
& ( ( in @ X1 @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X1: $i] :
( ( ( in @ X1 @ X1 )
= $true )
& ( ( in @ X1 @ sK2 )
= $true ) )
=> ( ( ( in @ sK3 @ sK3 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ( ordinalIrrefl = $true )
| ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i] :
( ( ( in @ X1 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) )
& ( ! [X2: $i] :
( ( ( ordinal @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X3 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( ordinalIrrefl != $true ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ordinalIrrefl = $true )
| ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i] :
( ( ( in @ X1 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) )
& ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( in @ X1 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
| ( ordinalIrrefl != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ordinalIrrefl = $true )
<=> ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( in @ X1 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) )
<=> ( ordinalIrrefl = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) )
<=> ( ordinalIrrefl = $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) )
= ordinalIrrefl ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: $i] :
( ( ( ordinal @ X2 )
=> ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X0 ) ) )
= ordinalIrrefl ),
file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalIrrefl) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU823^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n009.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:34:55 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU823^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Ordinals
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! X:i.ordinal X -> (! A:i.in X A -> ~(in A X)))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC325l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% 0.28/0.47 % Number of atoms : 44 ( 7 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 5 ( 7 avg)
% 0.28/0.47 % Number of connectives : 85 ( 3 ~; 3 |; 6 &; 54 @)
% 0.28/0.47 % ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 10 ( 3 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 10 ( 9 usr; 2 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 19 ( 3 ^; 15 !; 1 ?; 19 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=520
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(transitiveset_type,type,
% 0.28/0.47 transitiveset: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(stricttotalorderedByIn_type,type,
% 0.28/0.47 stricttotalorderedByIn: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(stricttotalorderedByIn,definition,
% 0.28/0.47 ( stricttotalorderedByIn
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ A )
% 0.28/0.47 => ( ( ( in @ Xx @ X )
% 0.28/0.47 & ( in @ X @ Y ) )
% 0.28/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.28/0.47 & ! [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ A )
% 0.28/0.47 => ( ( X = Y )
% 0.28/0.47 | ( in @ X @ Y )
% 0.28/0.47 | ( in @ Y @ X ) ) ) )
% 0.28/0.47 & ! [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderedByIn_type,type,
% 0.28/0.47 wellorderedByIn: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderedByIn,definition,
% 0.28/0.47 ( wellorderedByIn
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ( ( stricttotalorderedByIn @ A )
% 0.28/0.47 & ! [X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( ( nonempty @ X )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ X )
% 0.28/0.47 & ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ X )
% 0.28/0.47 => ( ( Xx = Y )
% 0.28/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ordinal_type,type,
% 0.28/0.47 ordinal: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ordinal,definition,
% 0.28/0.47 ( ordinal
% 0.28/0.47 = ( ^ [Xx: $i] :
% 0.28/0.47 ( ( transitiveset @ Xx )
% 0.28/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ordinalTransSet_type,type,
% 0.28/0.47 ordinalTransSet: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ordinalTransSet,definition,
% 0.28/0.47 ( ordinalTransSet
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( ordinal @ X )
% 0.28/0.47 => ! [Xx: $i,A: $i] :
% 0.28/0.47 ( ( in @ A @ X )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ordinalIrrefl_type,type,
% 0.28/0.47 ordinalIrrefl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ordinalIrrefl,definition,
% 0.28/0.47 ( ordinalIrrefl
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( ordinal @ X )
% 0.28/0.47 => ! [A: $i] :
% 0.28/0.47 ( ( in @ A @ X )
% 0.28/0.47 => ~ ( in @ A @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ordinalNoCycle,conjecture,
% 0.28/0.47 ( ordinalTransSet
% 0.28/0.47 => ( ordinalIrrefl
% 0.28/0.47 => ! [X: $i] :
% 0.28/0.47 ( ( ordinal @ X )
% 0.28/0.47 => ! [A: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 => ~ ( in @ A @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 0.31/1.20 ---- Embedded in THF ---
% 0.31/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.20 %%% Generated on Tue Feb 24 12:34:56 EST 2026
% 0.31/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.20 %%% Logic specification used:
% 0.31/1.20 %%% thf(spec, logic, $$dhol).
% 0.31/1.20
% 0.31/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2DTF2942.p
% See solution above
% 0.31/1.20 ------------------------
% 0.31/1.21 ---- Cleaned THF ---
% 0.31/1.22 thf(in_type,type,
% 0.31/1.22 in: $i > $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(powerset_type,type,
% 0.31/1.22 powerset: $i > $i ).
% 0.31/1.22
% 0.31/1.22 thf(nonempty_type,type,
% 0.31/1.22 nonempty: $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(transitiveset_type,type,
% 0.31/1.22 transitiveset: $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(stricttotalorderedByIn_type,type,
% 0.31/1.22 stricttotalorderedByIn: $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(stricttotalorderedByIn,definition,
% 0.31/1.22 ( stricttotalorderedByIn
% 0.31/1.22 = ( ^ [A: $i] :
% 0.31/1.22 ( ! [Xx: $i] :
% 0.31/1.22 ( ( in @ Xx @ A )
% 0.31/1.22 => ! [X: $i] :
% 0.31/1.22 ( ( in @ X @ A )
% 0.31/1.22 => ! [Y: $i] :
% 0.31/1.22 ( ( in @ Y @ A )
% 0.31/1.22 => ( ( ( in @ Xx @ X )
% 0.31/1.22 & ( in @ X @ Y ) )
% 0.31/1.22 => ( in @ Xx @ Y ) ) ) ) )
% 0.31/1.22 & ! [X: $i] :
% 0.31/1.22 ( ( in @ X @ A )
% 0.31/1.22 => ! [Y: $i] :
% 0.31/1.22 ( ( in @ Y @ A )
% 0.31/1.22 => ( ( X = Y )
% 0.31/1.22 | ( in @ X @ Y )
% 0.31/1.22 | ( in @ Y @ X ) ) ) )
% 0.31/1.22 & ! [X: $i] :
% 0.31/1.22 ( ( in @ X @ A )
% 0.31/1.22 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.31/1.22
% 0.31/1.22 thf(wellorderedByIn_type,type,
% 0.31/1.22 wellorderedByIn: $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(wellorderedByIn,definition,
% 0.31/1.22 ( wellorderedByIn
% 0.31/1.22 = ( ^ [A: $i] :
% 0.31/1.22 ( ( stricttotalorderedByIn @ A )
% 0.31/1.22 & ! [X: $i] :
% 0.31/1.22 ( ( in @ X @ ( powerset @ A ) )
% 0.31/1.22 => ( ( nonempty @ X )
% 0.31/1.22 => ? [Xx: $i] :
% 0.31/1.22 ( ( in @ Xx @ X )
% 0.31/1.22 & ! [Y: $i] :
% 0.31/1.22 ( ( in @ Y @ X )
% 0.31/1.22 => ( ( Xx = Y )
% 0.31/1.22 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/1.22
% 0.31/1.22 thf(ordinal_type,type,
% 0.31/1.22 ordinal: $i > $o ).
% 0.31/1.22
% 0.31/1.22 thf(ordinal,definition,
% 0.31/1.22 ( ordinal
% 0.31/1.22 = ( ^ [Xx: $i] :
% 0.31/1.22 ( ( transitiveset @ Xx )
% 0.31/1.22 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.31/1.22
% 0.31/1.22 thf(ordinalTransSet_type,type,
% 0.31/1.22 ordinalTransSet: $o ).
% 0.31/1.22
% 0.31/1.22 thf(ordinalTransSet,definition,
% 0.31/1.22 ( ordinalTransSet
% 0.31/1.22 = ( ! [X: $i] :
% 0.31/1.22 ( ( ordinal @ X )
% 0.31/1.22 => ! [Xx: $i,A: $i] :
% 0.31/1.22 ( ( in @ A @ X )
% 0.31/1.22 => ( ( in @ Xx @ A )
% 0.31/1.22 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.31/1.22
% 0.31/1.22 thf(ordinalIrrefl_type,type,
% 0.31/1.22 ordinalIrrefl: $o ).
% 0.31/1.22
% 0.31/1.22 thf(ordinalIrrefl,definition,
% 0.31/1.22 ( ordinalIrrefl
% 0.31/1.22 = ( ! [X: $i] :
% 0.31/1.22 ( ( ordinal @ X )
% 0.31/1.22 => ! [A: $i] :
% 0.31/1.22 ( ( in @ A @ X )
% 0.31/1.22 => ~ ( in @ A @ A ) ) ) ) ) ).
% 0.31/1.22
% 0.31/1.22 thf(ordinalNoCycle,conjecture,
% 0.31/1.22 ( ordinalTransSet
% 0.31/1.22 => ( ordinalIrrefl
% 0.31/1.22 => ! [X: $i] :
% 0.31/1.22 ( ( ordinal @ X )
% 0.31/1.22 => ! [A: $i] :
% 0.31/1.22 ( ( in @ X @ A )
% 0.31/1.22 => ~ ( in @ A @ X ) ) ) ) ) ).
% 0.31/1.22 ------------------------
% 0.31/1.23 % (3039)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2942 for (2999ds/183Mi)
% 0.31/1.23 % (3040)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_2942 for (2999ds/4Mi)
% 0.31/1.24 % (3040)Instruction limit reached!
% 0.31/1.24 % (3040)------------------------------
% 0.31/1.24 % (3040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (3040)Termination reason: Unknown
% 0.31/1.24 % (3040)Termination phase: Function definition elimination
% 0.31/1.24
% 0.31/1.24 % (3040)Memory used [KB]: 1023
% 0.31/1.24 % (3040)Time elapsed: 0.003 s
% 0.31/1.24 % (3040)Instructions burned: 4 (million)
% 0.31/1.24 % (3040)------------------------------
% 0.31/1.24 % (3040)------------------------------
% 0.31/1.24 % (3045)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2942 for (2999ds/18Mi)
% 0.31/1.24 % (3044)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_2942 for (2999ds/275Mi)
% 0.31/1.24 % (3042)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2942 for (2999ds/2Mi)
% 0.31/1.24 % (3042)Instruction limit reached!
% 0.31/1.24 % (3042)------------------------------
% 0.31/1.24 % (3042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (3042)Termination reason: Unknown
% 0.31/1.24 % (3042)Termination phase: shuffling
% 0.31/1.24
% 0.31/1.24 % (3042)Memory used [KB]: 895
% 0.31/1.24 % (3042)Time elapsed: 0.002 s
% 0.31/1.24 % (3042)Instructions burned: 2 (million)
% 0.31/1.24 % (3042)------------------------------
% 0.31/1.24 % (3042)------------------------------
% 0.31/1.24 % (3043)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_2942 for (2999ds/2Mi)
% 0.31/1.24 % (3043)Instruction limit reached!
% 0.31/1.24 % (3043)------------------------------
% 0.31/1.24 % (3043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.24 % (3043)Termination reason: Unknown
% 0.31/1.24 % (3043)Termination phase: shuffling
% 0.31/1.24
% 0.31/1.24 % (3043)Memory used [KB]: 1023
% 0.31/1.24 % (3043)Time elapsed: 0.003 s
% 0.31/1.24 % (3043)Instructions burned: 2 (million)
% 0.31/1.24 % (3043)------------------------------
% 0.31/1.24 % (3043)------------------------------
% 0.31/1.24 % (3041)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_2942 for (2999ds/27Mi)
% 0.31/1.24 % (3044)First to succeed.
% 0.31/1.25 % (3044)Refutation found. Thanks to Tanya!
% 0.31/1.25 % SZS status Theorem for DTF2THF_2942
% 0.31/1.25 % SZS output start Proof for DTF2THF_2942
% 0.31/1.25 thf(func_def_0, type, in: $i > $i > $o).
% 0.31/1.25 thf(func_def_1, type, powerset: $i > $i).
% 0.31/1.25 thf(func_def_2, type, nonempty: $i > $o).
% 0.31/1.25 thf(func_def_3, type, transitiveset: $i > $o).
% 0.31/1.25 thf(func_def_4, type, stricttotalorderedByIn: $i > $o).
% 0.31/1.25 thf(func_def_6, type, wellorderedByIn: $i > $o).
% 0.31/1.25 thf(func_def_7, type, ordinal: $i > $o).
% 0.31/1.25 thf(f103,plain,(
% 0.31/1.25 $false),
% 0.31/1.25 inference(avatar_sat_refutation,[status(thm)],[f95,f102])).
% 0.31/1.25 thf(f102,plain,(
% 0.31/1.25 ~spl7_2),
% 0.31/1.25 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 0.31/1.25 thf(f101,plain,(
% 0.31/1.25 $false | ~spl7_2),
% 0.31/1.25 inference(subsumption_resolution,[status(thm)],[f100,f43])).
% 0.31/1.25 thf(f43,plain,(
% 0.31/1.25 ((ordinal @ sK0) = $true)),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.25 thf(f30,plain,(
% 0.31/1.25 ((((in @ sK1 @ sK0) = $true) & ((in @ sK0 @ sK1) = $true)) & ((ordinal @ sK0) = $true)) & (ordinalIrrefl = $true) & (ordinalTransSet = $true)),
% 0.31/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f29,f28])).
% 0.31/1.25 thf(f28,plain,(
% 0.31/1.25 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true)) & ((ordinal @ X0) = $true)) => (? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((in @ sK0 @ X1) = $true)) & ((ordinal @ sK0) = $true))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f29,plain,(
% 0.31/1.25 ? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((in @ sK0 @ X1) = $true)) => (((in @ sK1 @ sK0) = $true) & ((in @ sK0 @ sK1) = $true))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f24,plain,(
% 0.31/1.25 ? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true)) & ((ordinal @ X0) = $true)) & (ordinalIrrefl = $true) & (ordinalTransSet = $true)),
% 0.31/1.25 inference(flattening,[status(thm)],[f23])).
% 0.31/1.25 thf(f23,plain,(
% 0.31/1.25 (? [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true)) & ((ordinal @ X0) = $true)) & (ordinalIrrefl = $true)) & (ordinalTransSet = $true)),
% 0.31/1.25 inference(ennf_transformation,[status(thm)],[f21])).
% 0.31/1.25 thf(f21,plain,(
% 0.31/1.25 ~((ordinalTransSet = $true) => ((ordinalIrrefl = $true) => ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X0 @ X1) = $true) => ((in @ X1 @ X0) != $true)))))),
% 0.31/1.25 inference(flattening,[status(thm)],[f16])).
% 0.31/1.25 thf(f16,plain,(
% 0.31/1.25 ~((ordinalTransSet = $true) => ((ordinalIrrefl = $true) => ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X0 @ X1) = $true) => ~((in @ X1 @ X0) = $true)))))),
% 0.31/1.25 inference(fool_elimination,[status(thm)],[f15])).
% 0.31/1.25 thf(f15,plain,(
% 0.31/1.25 ~(ordinalTransSet => (ordinalIrrefl => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)))))),
% 0.31/1.25 inference(rectify,[status(thm)],[f7])).
% 0.31/1.25 thf(f7,negated_conjecture,(
% 0.31/1.25 ~(ordinalTransSet => (ordinalIrrefl => ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X2 @ X0) => ~(in @ X0 @ X2)))))),
% 0.31/1.25 inference(negated_conjecture,[status(cth)],[f6])).
% 0.31/1.25 thf(f6,conjecture,(
% 0.31/1.25 ordinalTransSet => (ordinalIrrefl => ! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X2 @ X0) => ~(in @ X0 @ X2))))),
% 0.31/1.25 file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalNoCycle)).
% 0.31/1.25 thf(f100,plain,(
% 0.31/1.25 ((ordinal @ sK0) != $true) | ~spl7_2),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 0.31/1.25 thf(f96,plain,(
% 0.31/1.25 ($true != $true) | ((ordinal @ sK0) != $true) | ~spl7_2),
% 0.31/1.25 inference(superposition,[status(thm)],[f82,f45])).
% 0.31/1.25 thf(f45,plain,(
% 0.31/1.25 ((in @ sK1 @ sK0) = $true)),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.25 thf(f82,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((in @ sK1 @ X0) != $true) | ((ordinal @ X0) != $true)) ) | ~spl7_2),
% 0.31/1.25 inference(avatar_component_clause,[status(thm)],[f81])).
% 0.31/1.25 thf(f81,definition,(
% 0.31/1.25 spl7_2 <=> ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK1 @ X0) != $true))),
% 0.31/1.25 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 0.31/1.25 thf(f95,plain,(
% 0.31/1.25 spl7_2),
% 0.31/1.25 inference(avatar_split_clause,[status(thm)],[f94,f81])).
% 0.31/1.25 thf(f94,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK1 @ X0) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 0.31/1.25 thf(f91,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ($true != $true) | ((in @ sK1 @ X0) != $true)) )),
% 0.31/1.25 inference(superposition,[status(thm)],[f89,f44])).
% 0.31/1.25 thf(f44,plain,(
% 0.31/1.25 ((in @ sK0 @ sK1) = $true)),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.25 thf(f89,plain,(
% 0.31/1.25 ( ! [X0 : $i,X1 : $i] : (((in @ sK0 @ X1) != $true) | ((in @ X1 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 0.31/1.25 thf(f88,plain,(
% 0.31/1.25 ( ! [X0 : $i,X1 : $i] : (((ordinal @ X0) != $true) | ((in @ sK0 @ X1) != $true) | ($true != $true) | ((in @ X1 @ X0) != $true)) )),
% 0.31/1.25 inference(duplicate_literal_removal,[status(thm)],[f87])).
% 0.31/1.25 thf(f87,plain,(
% 0.31/1.25 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ sK0 @ X1) != $true) | ((ordinal @ X0) != $true) | ((ordinal @ X0) != $true) | ($true != $true)) )),
% 0.31/1.25 inference(superposition,[status(thm)],[f85,f64])).
% 0.31/1.25 thf(f64,plain,(
% 0.31/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.31/1.25 thf(f59,plain,(
% 0.31/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((ordinal @ X0) != $true) | ((in @ X2 @ X0) != $true) | ((in @ X1 @ X2) != $true) | ($true != $true) | ((in @ X1 @ X0) = $true)) )),
% 0.31/1.25 inference(definition_unfolding,[status(thm)],[f54,f41])).
% 0.31/1.25 thf(f41,plain,(
% 0.31/1.25 (ordinalTransSet = $true)),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.25 thf(f54,plain,(
% 0.31/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((ordinal @ X0) != $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X2 @ X0) != $true) | (ordinalTransSet != $true)) )),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f40])).
% 0.31/1.25 thf(f40,plain,(
% 0.31/1.25 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X2 @ X0) != $true))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | (((ordinal @ sK4) = $true) & (((in @ sK5 @ sK6) = $true) & ((in @ sK5 @ sK4) != $true) & ((in @ sK6 @ sK4) = $true))))),
% 0.31/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f37,f39,f38])).
% 0.31/1.25 thf(f38,plain,(
% 0.31/1.25 ? [X3 : $i] : (((ordinal @ X3) = $true) & ? [X4 : $i,X5 : $i] : (((in @ X4 @ X5) = $true) & ((in @ X4 @ X3) != $true) & ((in @ X5 @ X3) = $true))) => (((ordinal @ sK4) = $true) & ? [X5 : $i,X4 : $i] : (((in @ X4 @ X5) = $true) & ((in @ X4 @ sK4) != $true) & ((in @ X5 @ sK4) = $true)))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f39,plain,(
% 0.31/1.25 ? [X5 : $i,X4 : $i] : (((in @ X4 @ X5) = $true) & ((in @ X4 @ sK4) != $true) & ((in @ X5 @ sK4) = $true)) => (((in @ sK5 @ sK6) = $true) & ((in @ sK5 @ sK4) != $true) & ((in @ sK6 @ sK4) = $true))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f37,plain,(
% 0.31/1.25 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X2 @ X0) != $true))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | ? [X3 : $i] : (((ordinal @ X3) = $true) & ? [X4 : $i,X5 : $i] : (((in @ X4 @ X5) = $true) & ((in @ X4 @ X3) != $true) & ((in @ X5 @ X3) = $true))))),
% 0.31/1.25 inference(rectify,[status(thm)],[f36])).
% 0.31/1.25 thf(f36,plain,(
% 0.31/1.25 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X2 @ X0) != $true))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true) & ((in @ X2 @ X0) = $true))))),
% 0.31/1.25 inference(nnf_transformation,[status(thm)],[f27])).
% 0.31/1.25 thf(f27,plain,(
% 0.31/1.25 ! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i,X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X2 @ X0) != $true))) <=> (ordinalTransSet = $true)),
% 0.31/1.25 inference(flattening,[status(thm)],[f26])).
% 0.31/1.25 thf(f26,plain,(
% 0.31/1.25 ! [X0 : $i] : (! [X1 : $i,X2 : $i] : ((((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true)) | ((in @ X2 @ X0) != $true)) | ((ordinal @ X0) != $true)) <=> (ordinalTransSet = $true)),
% 0.31/1.25 inference(ennf_transformation,[status(thm)],[f18])).
% 0.31/1.25 thf(f18,plain,(
% 0.31/1.25 ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) => (((in @ X1 @ X2) = $true) => ((in @ X1 @ X0) = $true)))) <=> (ordinalTransSet = $true)),
% 0.31/1.25 inference(fool_elimination,[status(thm)],[f17])).
% 0.31/1.25 thf(f17,plain,(
% 0.31/1.25 (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0)))) = ordinalTransSet)),
% 0.31/1.25 inference(rectify,[status(thm)],[f4])).
% 0.31/1.25 thf(f4,axiom,(
% 0.31/1.25 (! [X2 : $i] : ((ordinal @ X2) => ! [X1 : $i,X0 : $i] : ((in @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2)))) = ordinalTransSet)),
% 0.31/1.25 file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalTransSet)).
% 0.31/1.25 thf(f85,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.31/1.25 inference(subsumption_resolution,[status(thm)],[f84,f44])).
% 0.31/1.25 thf(f84,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK0 @ X0) != $true) | ((in @ sK0 @ sK1) != $true)) )),
% 0.31/1.25 inference(subsumption_resolution,[status(thm)],[f71,f43])).
% 0.31/1.25 thf(f71,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ((ordinal @ X0) != $true) | ((ordinal @ sK0) != $true) | ((in @ sK0 @ sK1) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 0.31/1.25 thf(f69,plain,(
% 0.31/1.25 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ($true != $true) | ((ordinal @ X0) != $true) | ((ordinal @ sK0) != $true) | ((in @ sK0 @ sK1) != $true)) )),
% 0.31/1.25 inference(superposition,[status(thm)],[f67,f45])).
% 0.31/1.25 thf(f67,plain,(
% 0.31/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X0 @ X1) != $true) | ((ordinal @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((ordinal @ X0) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 0.31/1.25 thf(f66,plain,(
% 0.31/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X2 @ X0) != $true) | ((ordinal @ X1) != $true) | ($true != $true) | ((ordinal @ X0) != $true) | ((in @ X0 @ X1) != $true)) )),
% 0.31/1.25 inference(superposition,[status(thm)],[f65,f64])).
% 0.31/1.25 thf(f65,plain,(
% 0.31/1.25 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X3) != $true) | ((in @ X3 @ X2) != $true) | ((ordinal @ X2) != $true)) )),
% 0.31/1.25 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 0.31/1.25 thf(f58,plain,(
% 0.31/1.25 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X3) != $true) | ((in @ X3 @ X2) != $true) | ($true != $true) | ((ordinal @ X2) != $true)) )),
% 0.31/1.25 inference(definition_unfolding,[status(thm)],[f46,f42])).
% 0.31/1.25 thf(f42,plain,(
% 0.31/1.25 (ordinalIrrefl = $true)),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 0.31/1.25 thf(f46,plain,(
% 0.31/1.25 ( ! [X2 : $i,X3 : $i] : (((ordinal @ X2) != $true) | ((in @ X3 @ X3) != $true) | ((in @ X3 @ X2) != $true) | (ordinalIrrefl != $true)) )),
% 0.31/1.25 inference(cnf_transformation,[status(thm)],[f35])).
% 0.31/1.25 thf(f35,plain,(
% 0.31/1.25 ((ordinalIrrefl = $true) | (((ordinal @ sK2) = $true) & (((in @ sK3 @ sK3) = $true) & ((in @ sK3 @ sK2) = $true)))) & (! [X2 : $i] : (((ordinal @ X2) != $true) | ! [X3 : $i] : (((in @ X3 @ X3) != $true) | ((in @ X3 @ X2) != $true))) | (ordinalIrrefl != $true))),
% 0.31/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f32,f34,f33])).
% 0.31/1.25 thf(f33,plain,(
% 0.31/1.25 ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i] : (((in @ X1 @ X1) = $true) & ((in @ X1 @ X0) = $true))) => (((ordinal @ sK2) = $true) & ? [X1 : $i] : (((in @ X1 @ X1) = $true) & ((in @ X1 @ sK2) = $true)))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f34,plain,(
% 0.31/1.25 ? [X1 : $i] : (((in @ X1 @ X1) = $true) & ((in @ X1 @ sK2) = $true)) => (((in @ sK3 @ sK3) = $true) & ((in @ sK3 @ sK2) = $true))),
% 0.31/1.25 introduced(definition,[],[choice_axiom])).
% 0.31/1.25 thf(f32,plain,(
% 0.31/1.25 ((ordinalIrrefl = $true) | ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i] : (((in @ X1 @ X1) = $true) & ((in @ X1 @ X0) = $true)))) & (! [X2 : $i] : (((ordinal @ X2) != $true) | ! [X3 : $i] : (((in @ X3 @ X3) != $true) | ((in @ X3 @ X2) != $true))) | (ordinalIrrefl != $true))),
% 0.31/1.25 inference(rectify,[status(thm)],[f31])).
% 0.31/1.25 thf(f31,plain,(
% 0.31/1.25 ((ordinalIrrefl = $true) | ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i] : (((in @ X1 @ X1) = $true) & ((in @ X1 @ X0) = $true)))) & (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((in @ X1 @ X1) != $true) | ((in @ X1 @ X0) != $true))) | (ordinalIrrefl != $true))),
% 0.31/1.25 inference(nnf_transformation,[status(thm)],[f25])).
% 0.31/1.25 thf(f25,plain,(
% 0.31/1.25 (ordinalIrrefl = $true) <=> ! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((in @ X1 @ X1) != $true) | ((in @ X1 @ X0) != $true)))),
% 0.31/1.25 inference(ennf_transformation,[status(thm)],[f22])).
% 0.31/1.25 thf(f22,plain,(
% 0.31/1.25 ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((in @ X1 @ X1) != $true))) <=> (ordinalIrrefl = $true)),
% 0.31/1.25 inference(flattening,[status(thm)],[f14])).
% 0.31/1.25 thf(f14,plain,(
% 0.31/1.25 ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ~((in @ X1 @ X1) = $true))) <=> (ordinalIrrefl = $true)),
% 0.31/1.25 inference(fool_elimination,[status(thm)],[f13])).
% 0.31/1.25 thf(f13,plain,(
% 0.31/1.25 (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ~(in @ X1 @ X1))) = ordinalIrrefl)),
% 0.31/1.25 inference(rectify,[status(thm)],[f5])).
% 0.31/1.25 thf(f5,axiom,(
% 0.31/1.25 (! [X2 : $i] : ((ordinal @ X2) => ! [X0 : $i] : ((in @ X0 @ X2) => ~(in @ X0 @ X0))) = ordinalIrrefl)),
% 0.31/1.25 file('/export/starexec/sandbox2/tmp/tmp.FY37k977jX/DTF2THF_2942.p',ordinalIrrefl)).
% 0.31/1.25 % SZS output end Proof for DTF2THF_2942
% 0.31/1.25 % (3044)------------------------------
% 0.31/1.25 % (3044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.25 % (3044)Termination reason: Refutation
% 0.31/1.25
% 0.31/1.25 % (3044)Memory used [KB]: 5500
% 0.31/1.25 % (3044)Time elapsed: 0.008 s
% 0.31/1.25 % (3044)Instructions burned: 8 (million)
% 0.31/1.25 % (3044)------------------------------
% 0.31/1.25 % (3044)------------------------------
% 0.31/1.25 % (3038)Success in time 0.024 s
%------------------------------------------------------------------------------