%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU818^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 09:37:28 AM UTC 2026
% Result : Theorem 1.55s 1.29s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 670 ( 197 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 615 ( 94 ~; 76 |; 54 &; 349 @)
% ( 5 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 11 con; 0-2 aty)
% Number of variables : 120 ( 0 ^; 89 !; 31 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_9,type,
wellorderedByIn: $i > $o ).
thf(func_def_10,type,
ordinal: $i > $o ).
thf(func_def_33,type,
sK7: $i > $i > $i ).
thf(f83,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f82,f49]) ).
thf(f49,plain,
( ( in @ sK4 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ordinalTransSet = $true )
& ( subsetI1 = $true )
& ( ( ordinal @ sK3 )
= $true )
& ( ( subset @ sK4 @ sK3 )
!= $true )
& ( ( in @ sK4 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f37,f36]) ).
thf(f36,plain,
( ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
=> ( ( ( ordinal @ sK3 )
= $true )
& ? [X1: $i] :
( ( $true
!= ( subset @ X1 @ sK3 ) )
& ( ( in @ X1 @ sK3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X1: $i] :
( ( $true
!= ( subset @ X1 @ sK3 ) )
& ( ( in @ X1 @ sK3 )
= $true ) )
=> ( ( ( subset @ sK4 @ sK3 )
!= $true )
& ( ( in @ sK4 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ordinalTransSet = $true )
& ( subsetI1 = $true )
& ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ordinalTransSet = $true )
& ( subsetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( ( subsetI1 = $true )
=> ( ( ordinalTransSet = $true )
=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
~ ( subsetI1
=> ( ordinalTransSet
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( subsetI1
=> ( ordinalTransSet
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( subsetI1
=> ( ordinalTransSet
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( subset @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',ordinalTransSet1) ).
thf(f82,plain,
( ( in @ sK4 @ sK3 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f81,f51]) ).
thf(f51,plain,
( ( ordinal @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f81,plain,
( ( ( ordinal @ sK3 )
!= $true )
| ( ( in @ sK4 @ sK3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $true != $true )
| ( ( in @ sK4 @ sK3 )
!= $true )
| ( ( ordinal @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f50,f78]) ).
thf(f78,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( ( ordinal @ X1 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: $i,X1: $i] :
( ( ( ordinal @ X1 )
!= $true )
| ( $true
= ( subset @ X0 @ X1 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( $true
= ( subset @ X0 @ X1 ) )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( ordinal @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f74,f69]) ).
thf(f69,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f55,f52]) ).
thf(f52,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f55,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( subsetI1 = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK6 )
!= $true )
| ( ( in @ X2 @ sK5 )
= $true ) )
& ( $true
!= ( subset @ sK6 @ sK5 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) )
| ( ( subset @ X4 @ X3 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f40,f42,f41]) ).
thf(f41,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( subset @ X1 @ X0 )
!= $true ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK6 )
!= $true )
| ( ( in @ X2 @ sK5 )
= $true ) )
& ( $true
!= ( subset @ sK6 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X5 @ X3 )
!= $true ) )
=> ( ( ( in @ ( sK7 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X5 @ X3 )
!= $true ) )
| ( ( subset @ X4 @ X3 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
( subsetI1
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetI1
= ( ! [X2: $i,X1: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',subsetI1) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK7 @ X0 @ X1 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( subset @ X0 @ X1 ) )
| ( ( ordinal @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( subset @ X0 @ X1 ) )
| ( ( ordinal @ X1 )
!= $true )
| ( ( in @ ( sK7 @ X0 @ X1 ) @ X2 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f67,f68]) ).
thf(f68,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( ordinal @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f48,f53]) ).
thf(f53,plain,
ordinalTransSet = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f48,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( ordinal @ X0 ) )
| ( ordinalTransSet != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( ordinal @ X0 ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ( ( ( in @ sK2 @ sK0 )
!= $true )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( ordinal @ sK0 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f32,f34,f33]) ).
thf(f33,plain,
( ? [X3: $i] :
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X4 @ X3 )
= $true ) )
& ( ( ordinal @ X3 )
= $true ) )
=> ( ? [X5: $i,X4: $i] :
( ( ( in @ X5 @ sK0 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) )
& ( $true
= ( in @ X4 @ sK0 ) ) )
& ( ( ordinal @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X5: $i,X4: $i] :
( ( ( in @ X5 @ sK0 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) )
& ( $true
= ( in @ X4 @ sK0 ) ) )
=> ( ( ( in @ sK2 @ sK0 )
!= $true )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( ( in @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( ordinal @ X0 ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ? [X3: $i] :
( ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) )
& ( ( in @ X4 @ X3 )
= $true ) )
& ( ( ordinal @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( ordinal @ X0 ) ) )
| ( ordinalTransSet != $true ) )
& ( ( ordinalTransSet = $true )
| ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ X1 ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( $true
= ( ordinal @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( ordinal @ X0 ) ) )
<=> ( ordinalTransSet = $true ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ordinalTransSet = $true )
<=> ! [X0: $i] :
( ! [X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( ordinal @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ordinalTransSet = $true )
<=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) )
= ordinalTransSet ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X3: $i] :
( ( ( ordinal @ X3 )
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X3 ) ) ) )
= ordinalTransSet ),
file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',ordinalTransSet) ).
thf(f67,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( $true != $true )
| ( ( subset @ X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f54,f52]) ).
thf(f54,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK7 @ X4 @ X3 ) @ X3 )
!= $true )
| ( ( subset @ X4 @ X3 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f50,plain,
( ( subset @ sK4 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU818^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:35:16 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEU818^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : Ordinals
% 0.29/0.47 % Version : Especial > Reduced > Especial.
% 0.29/0.47 % English : (! X:i.ordinal X -> (! A:i.in A X -> subset A X))
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.47 % Source : [Bro08]
% 0.29/0.47 % Names : ZFC320l [Bro08]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.33 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
% 0.29/0.47 % Syntax : Number of formulae : 19 ( 7 unt; 11 typ; 7 def)
% 0.29/0.47 % Number of atoms : 51 ( 10 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 5 ( 6 avg)
% 0.29/0.47 % Number of connectives : 90 ( 2 ~; 3 |; 6 &; 59 @)
% 0.29/0.47 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 9 ( 2 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 12 ( 11 usr; 3 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 23 ( 5 ^; 17 !; 1 ?; 23 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : http://mathgate.info/detsetitem.php?id=514
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(in_type,type,
% 0.29/0.47 in: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset_type,type,
% 0.29/0.47 emptyset: $i ).
% 0.29/0.47
% 0.29/0.47 thf(powerset_type,type,
% 0.29/0.47 powerset: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(nonempty_type,type,
% 0.29/0.47 nonempty: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonempty,definition,
% 0.29/0.47 ( nonempty
% 0.29/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset_type,type,
% 0.29/0.47 subset: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1_type,type,
% 0.29/0.47 subsetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1,definition,
% 0.29/0.47 ( subsetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(transitiveset_type,type,
% 0.29/0.47 transitiveset: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(transitiveset,definition,
% 0.29/0.47 ( transitiveset
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(stricttotalorderedByIn_type,type,
% 0.29/0.47 stricttotalorderedByIn: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(stricttotalorderedByIn,definition,
% 0.29/0.47 ( stricttotalorderedByIn
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ A )
% 0.29/0.47 => ( ( ( in @ Xx @ X )
% 0.29/0.47 & ( in @ X @ Y ) )
% 0.29/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ A )
% 0.29/0.47 => ( ( X = Y )
% 0.29/0.47 | ( in @ X @ Y )
% 0.29/0.47 | ( in @ Y @ X ) ) ) )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderedByIn_type,type,
% 0.29/0.47 wellorderedByIn: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderedByIn,definition,
% 0.29/0.47 ( wellorderedByIn
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ( ( stricttotalorderedByIn @ A )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ( ( nonempty @ X )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ X )
% 0.29/0.47 & ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ X )
% 0.29/0.47 => ( ( Xx = Y )
% 0.29/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ordinal_type,type,
% 0.29/0.47 ordinal: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(ordinal,definition,
% 0.29/0.47 ( ordinal
% 0.29/0.47 = ( ^ [Xx: $i] :
% 0.29/0.47 ( ( transitiveset @ Xx )
% 0.29/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ordinalTransSet_type,type,
% 0.29/0.47 ordinalTransSet: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ordinalTransSet,definition,
% 0.29/0.47 ( ordinalTransSet
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( ordinal @ X )
% 0.29/0.47 => ! [Xx: $i,A: $i] :
% 0.29/0.47 ( ( in @ A @ X )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ordinalTransSet1,conjecture,
% 0.29/0.47 ( subsetI1
% 0.29/0.47 => ( ordinalTransSet
% 0.29/0.47 => ! [X: $i] :
% 0.29/0.47 ( ( ordinal @ X )
% 0.29/0.47 => ! [A: $i] :
% 0.29/0.47 ( ( in @ A @ X )
% 0.29/0.47 => ( subset @ A @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.55/1.24 ---- Embedded in THF ---
% 1.55/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.24 %%% Generated on Tue Feb 24 12:35:17 EST 2026
% 1.55/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.24 %%% Logic specification used:
% 1.55/1.24 %%% thf(spec, logic, $$dhol).
% 1.55/1.24
% 1.55/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2DTF26684.p
% See solution above
% 1.55/1.24 ------------------------
% 1.55/1.25 ---- Cleaned THF ---
% 1.55/1.25 thf(in_type,type,
% 1.55/1.25 in: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(emptyset_type,type,
% 1.55/1.25 emptyset: $i ).
% 1.55/1.25
% 1.55/1.25 thf(powerset_type,type,
% 1.55/1.25 powerset: $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(nonempty_type,type,
% 1.55/1.25 nonempty: $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(nonempty,definition,
% 1.55/1.25 ( nonempty
% 1.55/1.25 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(subset_type,type,
% 1.55/1.25 subset: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1_type,type,
% 1.55/1.25 subsetI1: $o ).
% 1.55/1.25
% 1.55/1.25 thf(subsetI1,definition,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 = ( ! [A: $i,B: $i] :
% 1.55/1.25 ( ! [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ B ) )
% 1.55/1.25 => ( subset @ A @ B ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(transitiveset_type,type,
% 1.55/1.25 transitiveset: $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(transitiveset,definition,
% 1.55/1.25 ( transitiveset
% 1.55/1.25 = ( ^ [A: $i] :
% 1.55/1.25 ! [X: $i] :
% 1.55/1.25 ( ( in @ X @ A )
% 1.55/1.25 => ( subset @ X @ A ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(stricttotalorderedByIn_type,type,
% 1.55/1.25 stricttotalorderedByIn: $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(stricttotalorderedByIn,definition,
% 1.55/1.25 ( stricttotalorderedByIn
% 1.55/1.25 = ( ^ [A: $i] :
% 1.55/1.25 ( ! [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ A )
% 1.55/1.25 => ! [X: $i] :
% 1.55/1.25 ( ( in @ X @ A )
% 1.55/1.25 => ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ A )
% 1.55/1.25 => ( ( ( in @ Xx @ X )
% 1.55/1.25 & ( in @ X @ Y ) )
% 1.55/1.25 => ( in @ Xx @ Y ) ) ) ) )
% 1.55/1.25 & ! [X: $i] :
% 1.55/1.25 ( ( in @ X @ A )
% 1.55/1.25 => ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ A )
% 1.55/1.25 => ( ( X = Y )
% 1.55/1.25 | ( in @ X @ Y )
% 1.55/1.25 | ( in @ Y @ X ) ) ) )
% 1.55/1.25 & ! [X: $i] :
% 1.55/1.25 ( ( in @ X @ A )
% 1.55/1.25 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(wellorderedByIn_type,type,
% 1.55/1.25 wellorderedByIn: $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(wellorderedByIn,definition,
% 1.55/1.25 ( wellorderedByIn
% 1.55/1.25 = ( ^ [A: $i] :
% 1.55/1.25 ( ( stricttotalorderedByIn @ A )
% 1.55/1.25 & ! [X: $i] :
% 1.55/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.25 => ( ( nonempty @ X )
% 1.55/1.25 => ? [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ X )
% 1.55/1.25 & ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ X )
% 1.55/1.25 => ( ( Xx = Y )
% 1.55/1.25 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(ordinal_type,type,
% 1.55/1.25 ordinal: $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(ordinal,definition,
% 1.55/1.25 ( ordinal
% 1.55/1.25 = ( ^ [Xx: $i] :
% 1.55/1.25 ( ( transitiveset @ Xx )
% 1.55/1.25 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(ordinalTransSet_type,type,
% 1.55/1.25 ordinalTransSet: $o ).
% 1.55/1.25
% 1.55/1.25 thf(ordinalTransSet,definition,
% 1.55/1.25 ( ordinalTransSet
% 1.55/1.25 = ( ! [X: $i] :
% 1.55/1.25 ( ( ordinal @ X )
% 1.55/1.25 => ! [Xx: $i,A: $i] :
% 1.55/1.25 ( ( in @ A @ X )
% 1.55/1.25 => ( ( in @ Xx @ A )
% 1.55/1.25 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(ordinalTransSet1,conjecture,
% 1.55/1.25 ( subsetI1
% 1.55/1.25 => ( ordinalTransSet
% 1.55/1.25 => ! [X: $i] :
% 1.55/1.25 ( ( ordinal @ X )
% 1.55/1.25 => ! [A: $i] :
% 1.55/1.25 ( ( in @ A @ X )
% 1.55/1.25 => ( subset @ A @ X ) ) ) ) ) ).
% 1.55/1.25 ------------------------
% 1.55/1.26 % (26783)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_26684 for (2999ds/27Mi)
% 1.55/1.26 % (26785)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_26684 for (2999ds/2Mi)
% 1.55/1.26 % (26782)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_26684 for (2999ds/4Mi)
% 1.55/1.26 % (26785)Instruction limit reached!
% 1.55/1.26 % (26785)------------------------------
% 1.55/1.26 % (26785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (26785)Termination reason: Unknown
% 1.55/1.26 % (26785)Termination phase: Property scanning
% 1.55/1.26
% 1.55/1.26 % (26785)Memory used [KB]: 1023
% 1.55/1.26 % (26785)Time elapsed: 0.002 s
% 1.55/1.26 % (26785)Instructions burned: 3 (million)
% 1.55/1.26 % (26785)------------------------------
% 1.55/1.26 % (26785)------------------------------
% 1.55/1.26 % (26782)Instruction limit reached!
% 1.55/1.26 % (26782)------------------------------
% 1.55/1.26 % (26782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (26782)Termination reason: Unknown
% 1.55/1.26 % (26782)Termination phase: Saturation
% 1.55/1.26
% 1.55/1.26 % (26782)Memory used [KB]: 1023
% 1.55/1.26 % (26782)Time elapsed: 0.003 s
% 1.55/1.26 % (26782)Instructions burned: 6 (million)
% 1.55/1.26 % (26782)------------------------------
% 1.55/1.26 % (26782)------------------------------
% 1.55/1.27 % (26787)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/18Mi)
% 1.55/1.27 % (26781)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/183Mi)
% 1.55/1.27 % (26783)Instruction limit reached!
% 1.55/1.27 % (26783)------------------------------
% 1.55/1.27 % (26783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (26783)Termination reason: Unknown
% 1.55/1.27 % (26783)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.27 % (26783)Memory used [KB]: 5628
% 1.55/1.27 % (26783)Time elapsed: 0.010 s
% 1.55/1.27 % (26783)Instructions burned: 30 (million)
% 1.55/1.27 % (26783)------------------------------
% 1.55/1.27 % (26783)------------------------------
% 1.55/1.27 % (26788)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/3Mi)
% 1.55/1.27 % (26788)Instruction limit reached!
% 1.55/1.27 % (26788)------------------------------
% 1.55/1.27 % (26788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (26788)Termination reason: Unknown
% 1.55/1.27 % (26788)Termination phase: Property scanning
% 1.55/1.27
% 1.55/1.27 % (26788)Memory used [KB]: 1023
% 1.55/1.27 % (26788)Time elapsed: 0.003 s
% 1.55/1.27 % (26788)Instructions burned: 3 (million)
% 1.55/1.27 % (26788)------------------------------
% 1.55/1.27 % (26788)------------------------------
% 1.55/1.27 % (26789)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/37Mi)
% 1.55/1.27 % (26787)Instruction limit reached!
% 1.55/1.27 % (26787)------------------------------
% 1.55/1.27 % (26787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (26787)Termination reason: Unknown
% 1.55/1.27 % (26787)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.28 % (26787)Memory used [KB]: 5500
% 1.55/1.28 % (26787)Time elapsed: 0.010 s
% 1.55/1.28 % (26787)Instructions burned: 18 (million)
% 1.55/1.28 % (26787)------------------------------
% 1.55/1.28 % (26787)------------------------------
% 1.55/1.28 % (26790)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/15Mi)
% 1.55/1.28 % (26786)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_26684 for (2999ds/275Mi)
% 1.55/1.28 % (26784)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/2Mi)
% 1.55/1.28 % (26784)Instruction limit reached!
% 1.55/1.28 % (26784)------------------------------
% 1.55/1.28 % (26784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (26784)Termination reason: Unknown
% 1.55/1.28 % (26784)Termination phase: shuffling
% 1.55/1.28
% 1.55/1.28 % (26784)Memory used [KB]: 1023
% 1.55/1.28 % (26784)Time elapsed: 0.003 s
% 1.55/1.28 % (26784)Instructions burned: 2 (million)
% 1.55/1.28 % (26784)------------------------------
% 1.55/1.28 % (26784)------------------------------
% 1.55/1.28 % (26790)Instruction limit reached!
% 1.55/1.28 % (26790)------------------------------
% 1.55/1.28 % (26790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (26790)Termination reason: Unknown
% 1.55/1.28 % (26790)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (26790)Memory used [KB]: 5628
% 1.55/1.28 % (26790)Time elapsed: 0.006 s
% 1.55/1.28 % (26790)Instructions burned: 17 (million)
% 1.55/1.28 % (26790)------------------------------
% 1.55/1.28 % (26790)------------------------------
% 1.55/1.28 % (26791)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26684 for (2999ds/3Mi)
% 1.55/1.28 % (26786)First to succeed.
% 1.55/1.28 % (26791)Instruction limit reached!
% 1.55/1.28 % (26791)------------------------------
% 1.55/1.28 % (26791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (26791)Termination reason: Unknown
% 1.55/1.29 % (26791)Termination phase: Property scanning
% 1.55/1.29
% 1.55/1.29 % (26791)Memory used [KB]: 1023
% 1.55/1.29 % (26791)Time elapsed: 0.003 s
% 1.55/1.29 % (26791)Instructions burned: 4 (million)
% 1.55/1.29 % (26791)------------------------------
% 1.55/1.29 % (26791)------------------------------
% 1.55/1.29 % (26789)Instruction limit reached!
% 1.55/1.29 % (26789)------------------------------
% 1.55/1.29 % (26789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (26789)Termination reason: Unknown
% 1.55/1.29 % (26789)Termination phase: Saturation
% 1.55/1.29
% 1.55/1.29 % (26789)Memory used [KB]: 5628
% 1.55/1.29 % (26789)Time elapsed: 0.013 s
% 1.55/1.29 % (26789)Instructions burned: 39 (million)
% 1.55/1.29 % (26789)------------------------------
% 1.55/1.29 % (26789)------------------------------
% 1.55/1.29 % (26786)Refutation found. Thanks to Tanya!
% 1.55/1.29 % SZS status Theorem for DTF2THF_26684
% 1.55/1.29 % SZS output start Proof for DTF2THF_26684
% 1.55/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.29 thf(func_def_2, type, powerset: $i > $i).
% 1.55/1.29 thf(func_def_3, type, nonempty: $i > $o).
% 1.55/1.29 thf(func_def_4, type, subset: $i > $i > $o).
% 1.55/1.29 thf(func_def_7, type, transitiveset: $i > $o).
% 1.55/1.29 thf(func_def_8, type, stricttotalorderedByIn: $i > $o).
% 1.55/1.29 thf(func_def_9, type, wellorderedByIn: $i > $o).
% 1.55/1.29 thf(func_def_10, type, ordinal: $i > $o).
% 1.55/1.29 thf(func_def_33, type, sK7: $i > $i > $i).
% 1.55/1.29 thf(f83,plain,(
% 1.55/1.29 $false),
% 1.55/1.29 inference(subsumption_resolution,[status(thm)],[f82,f49])).
% 1.55/1.29 thf(f49,plain,(
% 1.55/1.29 ((in @ sK4 @ sK3) = $true)),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.29 thf(f38,plain,(
% 1.55/1.29 (ordinalTransSet = $true) & (subsetI1 = $true) & (((ordinal @ sK3) = $true) & (((subset @ sK4 @ sK3) != $true) & ((in @ sK4 @ sK3) = $true)))),
% 1.55/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f37,f36])).
% 1.55/1.29 thf(f36,plain,(
% 1.55/1.29 ? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ X0) = $true))) => (((ordinal @ sK3) = $true) & ? [X1 : $i] : (($true != (subset @ X1 @ sK3)) & ((in @ X1 @ sK3) = $true)))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f37,plain,(
% 1.55/1.29 ? [X1 : $i] : (($true != (subset @ X1 @ sK3)) & ((in @ X1 @ sK3) = $true)) => (((subset @ sK4 @ sK3) != $true) & ((in @ sK4 @ sK3) = $true))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f29,plain,(
% 1.55/1.29 (ordinalTransSet = $true) & (subsetI1 = $true) & ? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ X0) = $true)))),
% 1.55/1.29 inference(flattening,[status(thm)],[f28])).
% 1.55/1.29 thf(f28,plain,(
% 1.55/1.29 (? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ X0) = $true))) & (ordinalTransSet = $true)) & (subsetI1 = $true)),
% 1.55/1.29 inference(ennf_transformation,[status(thm)],[f25])).
% 1.55/1.29 thf(f25,plain,(
% 1.55/1.29 ~((subsetI1 = $true) => ((ordinalTransSet = $true) => ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((subset @ X1 @ X0) = $true)))))),
% 1.55/1.29 inference(fool_elimination,[status(thm)],[f24])).
% 1.55/1.29 thf(f24,plain,(
% 1.55/1.29 ~(subsetI1 => (ordinalTransSet => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 1.55/1.29 inference(rectify,[status(thm)],[f9])).
% 1.55/1.29 thf(f9,negated_conjecture,(
% 1.55/1.29 ~(subsetI1 => (ordinalTransSet => ! [X3 : $i] : ((ordinal @ X3) => ! [X1 : $i] : ((in @ X1 @ X3) => (subset @ X1 @ X3)))))),
% 1.55/1.29 inference(negated_conjecture,[status(cth)],[f8])).
% 1.55/1.29 thf(f8,conjecture,(
% 1.55/1.29 subsetI1 => (ordinalTransSet => ! [X3 : $i] : ((ordinal @ X3) => ! [X1 : $i] : ((in @ X1 @ X3) => (subset @ X1 @ X3))))),
% 1.55/1.29 file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',ordinalTransSet1)).
% 1.55/1.29 thf(f82,plain,(
% 1.55/1.29 ((in @ sK4 @ sK3) != $true)),
% 1.55/1.29 inference(subsumption_resolution,[status(thm)],[f81,f51])).
% 1.55/1.29 thf(f51,plain,(
% 1.55/1.29 ((ordinal @ sK3) = $true)),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.29 thf(f81,plain,(
% 1.55/1.29 ((ordinal @ sK3) != $true) | ((in @ sK4 @ sK3) != $true)),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.55/1.29 thf(f80,plain,(
% 1.55/1.29 ($true != $true) | ((in @ sK4 @ sK3) != $true) | ((ordinal @ sK3) != $true)),
% 1.55/1.29 inference(superposition,[status(thm)],[f50,f78])).
% 1.55/1.29 thf(f78,plain,(
% 1.55/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | ((ordinal @ X1) != $true) | ((in @ X0 @ X1) != $true)) )),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.55/1.29 thf(f77,plain,(
% 1.55/1.29 ( ! [X0 : $i,X1 : $i] : (((ordinal @ X1) != $true) | ($true = (subset @ X0 @ X1)) | ((in @ X0 @ X1) != $true) | ($true != $true)) )),
% 1.55/1.29 inference(duplicate_literal_removal,[status(thm)],[f75])).
% 1.55/1.29 thf(f75,plain,(
% 1.55/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | ($true = (subset @ X0 @ X1)) | ((in @ X0 @ X1) != $true) | ((ordinal @ X1) != $true) | ($true != $true)) )),
% 1.55/1.29 inference(superposition,[status(thm)],[f74,f69])).
% 1.55/1.29 thf(f69,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.55/1.29 thf(f65,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((subset @ X4 @ X3) = $true) | ((in @ (sK7 @ X4 @ X3) @ X4) = $true)) )),
% 1.55/1.29 inference(definition_unfolding,[status(thm)],[f55,f52])).
% 1.55/1.29 thf(f52,plain,(
% 1.55/1.29 (subsetI1 = $true)),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.29 thf(f55,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X4) = $true) | ((subset @ X4 @ X3) = $true) | (subsetI1 != $true)) )),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f43])).
% 1.55/1.29 thf(f43,plain,(
% 1.55/1.29 ((subsetI1 = $true) | (! [X2 : $i] : (((in @ X2 @ sK6) != $true) | ((in @ X2 @ sK5) = $true)) & ($true != (subset @ sK6 @ sK5)))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK7 @ X4 @ X3) @ X4) = $true) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI1 != $true))),
% 1.55/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f40,f42,f41])).
% 1.55/1.29 thf(f41,plain,(
% 1.55/1.29 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true)) => (! [X2 : $i] : (((in @ X2 @ sK6) != $true) | ((in @ X2 @ sK5) = $true)) & ($true != (subset @ sK6 @ sK5)))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f42,plain,(
% 1.55/1.29 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ((in @ X5 @ X3) != $true)) => (((in @ (sK7 @ X4 @ X3) @ X4) = $true) & ((in @ (sK7 @ X4 @ X3) @ X3) != $true)))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f40,plain,(
% 1.55/1.29 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ((in @ X5 @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI1 != $true))),
% 1.55/1.29 inference(rectify,[status(thm)],[f39])).
% 1.55/1.29 thf(f39,plain,(
% 1.55/1.29 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true))),
% 1.55/1.29 inference(nnf_transformation,[status(thm)],[f30])).
% 1.55/1.29 thf(f30,plain,(
% 1.55/1.29 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true))),
% 1.55/1.29 inference(ennf_transformation,[status(thm)],[f19])).
% 1.55/1.29 thf(f19,plain,(
% 1.55/1.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true)) <=> (subsetI1 = $true)),
% 1.55/1.29 inference(fool_elimination,[status(thm)],[f18])).
% 1.55/1.29 thf(f18,plain,(
% 1.55/1.29 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 1.55/1.29 inference(rectify,[status(thm)],[f2])).
% 1.55/1.29 thf(f2,axiom,(
% 1.55/1.29 (subsetI1 = ! [X2 : $i,X1 : $i] : (! [X0 : $i] : ((in @ X0 @ X1) => (in @ X0 @ X2)) => (subset @ X1 @ X2)))),
% 1.55/1.29 file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',subsetI1)).
% 1.55/1.29 thf(f74,plain,(
% 1.55/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK7 @ X0 @ X1) @ X2) != $true) | ($true != (in @ X2 @ X1)) | ($true = (subset @ X0 @ X1)) | ((ordinal @ X1) != $true)) )),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.55/1.29 thf(f73,plain,(
% 1.55/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ X1)) | ($true = (subset @ X0 @ X1)) | ((ordinal @ X1) != $true) | ((in @ (sK7 @ X0 @ X1) @ X2) != $true) | ($true != $true)) )),
% 1.55/1.29 inference(superposition,[status(thm)],[f67,f68])).
% 1.55/1.29 thf(f68,plain,(
% 1.55/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ($true != (ordinal @ X0)) | ((in @ X1 @ X0) != $true)) )),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.55/1.29 thf(f58,plain,(
% 1.55/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true != $true) | ((in @ X1 @ X0) != $true) | ($true != (ordinal @ X0)) | ($true != (in @ X2 @ X1))) )),
% 1.55/1.29 inference(definition_unfolding,[status(thm)],[f48,f53])).
% 1.55/1.29 thf(f53,plain,(
% 1.55/1.29 (ordinalTransSet = $true)),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.29 thf(f48,plain,(
% 1.55/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ((in @ X1 @ X0) != $true) | ($true != (ordinal @ X0)) | (ordinalTransSet != $true)) )),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f35])).
% 1.55/1.29 thf(f35,plain,(
% 1.55/1.29 (! [X0 : $i] : (! [X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ((in @ X1 @ X0) != $true)) | ($true != (ordinal @ X0))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | ((((in @ sK2 @ sK0) != $true) & ($true = (in @ sK2 @ sK1)) & ((in @ sK1 @ sK0) = $true)) & ((ordinal @ sK0) = $true)))),
% 1.55/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f32,f34,f33])).
% 1.55/1.29 thf(f33,plain,(
% 1.55/1.29 ? [X3 : $i] : (? [X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ($true = (in @ X5 @ X4)) & ((in @ X4 @ X3) = $true)) & ((ordinal @ X3) = $true)) => (? [X5 : $i,X4 : $i] : (((in @ X5 @ sK0) != $true) & ($true = (in @ X5 @ X4)) & ($true = (in @ X4 @ sK0))) & ((ordinal @ sK0) = $true))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f34,plain,(
% 1.55/1.29 ? [X5 : $i,X4 : $i] : (((in @ X5 @ sK0) != $true) & ($true = (in @ X5 @ X4)) & ($true = (in @ X4 @ sK0))) => (((in @ sK2 @ sK0) != $true) & ($true = (in @ sK2 @ sK1)) & ((in @ sK1 @ sK0) = $true))),
% 1.55/1.29 introduced(definition,[],[choice_axiom])).
% 1.55/1.29 thf(f32,plain,(
% 1.55/1.29 (! [X0 : $i] : (! [X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ((in @ X1 @ X0) != $true)) | ($true != (ordinal @ X0))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | ? [X3 : $i] : (? [X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) & ($true = (in @ X5 @ X4)) & ((in @ X4 @ X3) = $true)) & ((ordinal @ X3) = $true)))),
% 1.55/1.29 inference(rectify,[status(thm)],[f31])).
% 1.55/1.29 thf(f31,plain,(
% 1.55/1.29 (! [X0 : $i] : (! [X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ((in @ X1 @ X0) != $true)) | ($true != (ordinal @ X0))) | (ordinalTransSet != $true)) & ((ordinalTransSet = $true) | ? [X0 : $i] : (? [X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ X1)) & ((in @ X1 @ X0) = $true)) & ($true = (ordinal @ X0))))),
% 1.55/1.29 inference(nnf_transformation,[status(thm)],[f27])).
% 1.55/1.29 thf(f27,plain,(
% 1.55/1.29 ! [X0 : $i] : (! [X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1)) | ((in @ X1 @ X0) != $true)) | ($true != (ordinal @ X0))) <=> (ordinalTransSet = $true)),
% 1.55/1.29 inference(flattening,[status(thm)],[f26])).
% 1.55/1.29 thf(f26,plain,(
% 1.55/1.29 (ordinalTransSet = $true) <=> ! [X0 : $i] : (! [X1 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ X1))) | ((in @ X1 @ X0) != $true)) | ($true != (ordinal @ X0)))),
% 1.55/1.29 inference(ennf_transformation,[status(thm)],[f13])).
% 1.55/1.29 thf(f13,plain,(
% 1.55/1.29 (ordinalTransSet = $true) <=> ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (($true = (in @ X2 @ X1)) => ((in @ X2 @ X0) = $true))))),
% 1.55/1.29 inference(fool_elimination,[status(thm)],[f12])).
% 1.55/1.29 thf(f12,plain,(
% 1.55/1.29 (! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))) = ordinalTransSet)),
% 1.55/1.29 inference(rectify,[status(thm)],[f7])).
% 1.55/1.29 thf(f7,axiom,(
% 1.55/1.29 (! [X3 : $i] : ((ordinal @ X3) => ! [X1 : $i,X0 : $i] : ((in @ X1 @ X3) => ((in @ X0 @ X1) => (in @ X0 @ X3)))) = ordinalTransSet)),
% 1.55/1.29 file('/export/starexec/sandbox/tmp/tmp.BTrDb3Lodq/DTF2THF_26684.p',ordinalTransSet)).
% 1.55/1.29 thf(f67,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.55/1.29 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.55/1.29 thf(f66,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ($true != $true) | ((subset @ X4 @ X3) = $true)) )),
% 1.55/1.29 inference(definition_unfolding,[status(thm)],[f54,f52])).
% 1.55/1.29 thf(f54,plain,(
% 1.55/1.29 ( ! [X3 : $i,X4 : $i] : (((in @ (sK7 @ X4 @ X3) @ X3) != $true) | ((subset @ X4 @ X3) = $true) | (subsetI1 != $true)) )),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f43])).
% 1.55/1.29 thf(f50,plain,(
% 1.55/1.29 ((subset @ sK4 @ sK3) != $true)),
% 1.55/1.29 inference(cnf_transformation,[status(thm)],[f38])).
% 1.55/1.29 % SZS output end Proof for DTF2THF_26684
% 1.55/1.29 % (26786)------------------------------
% 1.55/1.29 % (26786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (26786)Termination reason: Refutation
% 1.55/1.29
% 1.55/1.29 % (26786)Memory used [KB]: 5500
% 1.55/1.29 % (26786)Time elapsed: 0.009 s
% 1.55/1.29 % (26786)Instructions burned: 8 (million)
% 1.55/1.29 % (26786)------------------------------
% 1.55/1.29 % (26786)------------------------------
% 1.55/1.29 % (26780)Success in time 0.032 s
%------------------------------------------------------------------------------