%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU816^2 : 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 : n018.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 09:37:27 AM UTC 2026
% Result : Theorem 1.67s 1.36s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 353 ( 97 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 287 ( 42 ~; 25 |; 35 &; 161 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 6 ^; 28 !; 14 ?; 48 :)
% 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_5,type,
binintersect: $i > $i > $i ).
thf(func_def_6,type,
transitiveset: $i > $o ).
thf(func_def_9,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_10,type,
wellorderedByIn: $i > $o ).
thf(func_def_11,type,
ordinal: $i > $o ).
thf(f58,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f57,f52]) ).
thf(f52,plain,
( ( transitiveset @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( wellorderedByIn @ sK2 )
& ( transitiveset @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) )
@ sK2 )
= $true ),
inference(definition_unfolding,[status(thm)],[f39,f37]) ).
thf(f37,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',ordinal) ).
thf(f39,plain,
( $true
= ( ordinal @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( transitiveset @ ( binintersect @ sK2 @ sK3 ) )
!= $true )
& ( $true
= ( ordinal @ sK3 ) )
& ( $true
= ( ordinal @ sK2 ) )
& ( binintTransitive = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f31,f30]) ).
thf(f30,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( ordinal @ X1 )
= $true ) )
& ( $true
= ( ordinal @ X0 ) ) )
=> ( ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ sK2 @ X1 ) ) )
& ( ( ordinal @ X1 )
= $true ) )
& ( $true
= ( ordinal @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ sK2 @ X1 ) ) )
& ( ( ordinal @ X1 )
= $true ) )
=> ( ( ( transitiveset @ ( binintersect @ sK2 @ sK3 ) )
!= $true )
& ( $true
= ( ordinal @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( ordinal @ X1 )
= $true ) )
& ( $true
= ( ordinal @ X0 ) ) )
& ( binintTransitive = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( binintTransitive = $true )
=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( binintTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( binintTransitive
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ( transitiveset @ ( binintersect @ X2 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( binintTransitive
=> ! [X2: $i] :
( ( ordinal @ X2 )
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ( transitiveset @ ( binintersect @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',ordinalMinLem1) ).
thf(f57,plain,
( ( transitiveset @ sK2 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f56,f49]) ).
thf(f49,plain,
( ( transitiveset @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( wellorderedByIn @ sK3 )
& ( transitiveset @ sK3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) )
@ sK3 ) ),
inference(definition_unfolding,[status(thm)],[f40,f37]) ).
thf(f40,plain,
( $true
= ( ordinal @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f56,plain,
( ( ( transitiveset @ sK3 )
!= $true )
| ( ( transitiveset @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true != $true )
| ( ( transitiveset @ sK2 )
!= $true )
| ( ( transitiveset @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f41,f54]) ).
thf(f54,plain,
! [X2: $i,X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( ( transitiveset @ X2 )
!= $true )
| ( ( transitiveset @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( $true != $true )
| ( ( transitiveset @ X3 )
!= $true )
| ( ( transitiveset @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f38]) ).
thf(f38,plain,
binintTransitive = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f33,plain,
! [X2: $i,X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( ( transitiveset @ X3 )
!= $true )
| ( ( transitiveset @ X2 )
!= $true )
| ( binintTransitive != $true ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( binintTransitive = $true )
| ( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( transitiveset @ sK1 ) )
& ( $true
= ( transitiveset @ sK0 ) ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( ( transitiveset @ X3 )
!= $true ) )
| ( ( transitiveset @ X2 )
!= $true ) )
| ( binintTransitive != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f28,f27]) ).
thf(f27,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
=> ( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( $true
= ( transitiveset @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
=> ( ( $true
!= ( transitiveset @ ( binintersect @ sK0 @ sK1 ) ) )
& ( $true
= ( transitiveset @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ( binintTransitive = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
= $true )
| ( ( transitiveset @ X3 )
!= $true ) )
| ( ( transitiveset @ X2 )
!= $true ) )
| ( binintTransitive != $true ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( binintTransitive = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( transitiveset @ X1 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) ) )
& ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X1 )
!= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) )
| ( binintTransitive != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( binintTransitive = $true )
<=> ! [X0: $i] :
( ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( transitiveset @ X1 )
!= $true ) )
| ( ( transitiveset @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( binintTransitive = $true )
<=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( transitiveset @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) )
= binintTransitive ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i] :
( ( ( transitiveset @ X2 )
=> ! [X3: $i] :
( ( transitiveset @ X3 )
=> ( transitiveset @ ( binintersect @ X2 @ X3 ) ) ) )
= binintTransitive ),
file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',binintTransitive) ).
thf(f41,plain,
( ( transitiveset @ ( binintersect @ sK2 @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU816^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.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
% 0.17/0.34 % DateTime : Tue Feb 24 12:34:46 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU816^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Ordinals
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! X:i.ordinal X -> (! Y:i.ordinal Y ->
% 0.20/0.46 % transitiveset (binintersect X Y)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC318l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.20/0.46 % Number of atoms : 44 ( 9 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 4 ( 6 avg)
% 0.20/0.46 % Number of connectives : 78 ( 2 ~; 3 |; 6 &; 51 @)
% 0.20/0.46 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 9 ( 2 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 12 ( 11 usr; 2 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 19 ( 5 ^; 13 !; 1 ?; 19 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : http://mathgate.info/detsetitem.php?id=512
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(in_type,type,
% 0.20/0.47 in: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset_type,type,
% 0.20/0.47 emptyset: $i ).
% 0.20/0.47
% 0.20/0.47 thf(powerset_type,type,
% 0.20/0.47 powerset: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty_type,type,
% 0.20/0.47 nonempty: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty,definition,
% 0.20/0.47 ( nonempty
% 0.20/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset_type,type,
% 0.20/0.47 subset: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersect_type,type,
% 0.20/0.47 binintersect: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(transitiveset_type,type,
% 0.20/0.47 transitiveset: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(transitiveset,definition,
% 0.20/0.47 ( transitiveset
% 0.20/0.47 = ( ^ [A: $i] :
% 0.20/0.47 ! [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintTransitive_type,type,
% 0.20/0.47 binintTransitive: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintTransitive,definition,
% 0.20/0.47 ( binintTransitive
% 0.20/0.47 = ( ! [X: $i] :
% 0.20/0.47 ( ( transitiveset @ X )
% 0.20/0.47 => ! [Y: $i] :
% 0.20/0.47 ( ( transitiveset @ Y )
% 0.20/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(stricttotalorderedByIn_type,type,
% 0.20/0.47 stricttotalorderedByIn: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(stricttotalorderedByIn,definition,
% 0.20/0.47 ( stricttotalorderedByIn
% 0.20/0.47 = ( ^ [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 => ! [Y: $i] :
% 0.20/0.47 ( ( in @ Y @ A )
% 0.20/0.47 => ( ( ( in @ Xx @ X )
% 0.20/0.47 & ( in @ X @ Y ) )
% 0.20/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.20/0.47 & ! [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 => ! [Y: $i] :
% 0.20/0.47 ( ( in @ Y @ A )
% 0.20/0.47 => ( ( X = Y )
% 0.20/0.47 | ( in @ X @ Y )
% 0.20/0.47 | ( in @ Y @ X ) ) ) )
% 0.20/0.47 & ! [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderedByIn_type,type,
% 0.20/0.47 wellorderedByIn: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderedByIn,definition,
% 0.20/0.47 ( wellorderedByIn
% 0.20/0.47 = ( ^ [A: $i] :
% 0.20/0.47 ( ( stricttotalorderedByIn @ A )
% 0.20/0.47 & ! [X: $i] :
% 0.20/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.47 => ( ( nonempty @ X )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ X )
% 0.20/0.47 & ! [Y: $i] :
% 0.20/0.47 ( ( in @ Y @ X )
% 0.20/0.47 => ( ( Xx = Y )
% 0.20/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ordinal_type,type,
% 0.20/0.47 ordinal: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ordinal,definition,
% 0.20/0.47 ( ordinal
% 0.20/0.47 = ( ^ [Xx: $i] :
% 0.20/0.47 ( ( transitiveset @ Xx )
% 0.20/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ordinalMinLem1,conjecture,
% 0.20/0.47 ( binintTransitive
% 0.20/0.47 => ! [X: $i] :
% 0.20/0.47 ( ( ordinal @ X )
% 0.20/0.47 => ! [Y: $i] :
% 0.20/0.47 ( ( ordinal @ Y )
% 0.20/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.67/1.32 ---- Embedded in THF ---
% 1.67/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.32 %%% Generated on Tue Feb 24 12:34:47 EST 2026
% 1.67/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.32 %%% Logic specification used:
% 1.67/1.32 %%% thf(spec, logic, $$dhol).
% 1.67/1.32
% 1.67/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2DTF13541.p
% See solution above
% 1.67/1.32 ------------------------
% 1.67/1.33 ---- Cleaned THF ---
% 1.67/1.33 thf(in_type,type,
% 1.67/1.33 in: $i > $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(emptyset_type,type,
% 1.67/1.33 emptyset: $i ).
% 1.67/1.33
% 1.67/1.33 thf(powerset_type,type,
% 1.67/1.33 powerset: $i > $i ).
% 1.67/1.33
% 1.67/1.33 thf(nonempty_type,type,
% 1.67/1.33 nonempty: $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(nonempty,definition,
% 1.67/1.33 ( nonempty
% 1.67/1.33 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(subset_type,type,
% 1.67/1.33 subset: $i > $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(binintersect_type,type,
% 1.67/1.33 binintersect: $i > $i > $i ).
% 1.67/1.33
% 1.67/1.33 thf(transitiveset_type,type,
% 1.67/1.33 transitiveset: $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(transitiveset,definition,
% 1.67/1.33 ( transitiveset
% 1.67/1.33 = ( ^ [A: $i] :
% 1.67/1.33 ! [X: $i] :
% 1.67/1.33 ( ( in @ X @ A )
% 1.67/1.33 => ( subset @ X @ A ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(binintTransitive_type,type,
% 1.67/1.33 binintTransitive: $o ).
% 1.67/1.33
% 1.67/1.33 thf(binintTransitive,definition,
% 1.67/1.33 ( binintTransitive
% 1.67/1.33 = ( ! [X: $i] :
% 1.67/1.33 ( ( transitiveset @ X )
% 1.67/1.33 => ! [Y: $i] :
% 1.67/1.33 ( ( transitiveset @ Y )
% 1.67/1.33 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(stricttotalorderedByIn_type,type,
% 1.67/1.33 stricttotalorderedByIn: $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(stricttotalorderedByIn,definition,
% 1.67/1.33 ( stricttotalorderedByIn
% 1.67/1.33 = ( ^ [A: $i] :
% 1.67/1.33 ( ! [Xx: $i] :
% 1.67/1.33 ( ( in @ Xx @ A )
% 1.67/1.33 => ! [X: $i] :
% 1.67/1.33 ( ( in @ X @ A )
% 1.67/1.33 => ! [Y: $i] :
% 1.67/1.33 ( ( in @ Y @ A )
% 1.67/1.33 => ( ( ( in @ Xx @ X )
% 1.67/1.33 & ( in @ X @ Y ) )
% 1.67/1.33 => ( in @ Xx @ Y ) ) ) ) )
% 1.67/1.33 & ! [X: $i] :
% 1.67/1.33 ( ( in @ X @ A )
% 1.67/1.33 => ! [Y: $i] :
% 1.67/1.33 ( ( in @ Y @ A )
% 1.67/1.33 => ( ( X = Y )
% 1.67/1.33 | ( in @ X @ Y )
% 1.67/1.33 | ( in @ Y @ X ) ) ) )
% 1.67/1.33 & ! [X: $i] :
% 1.67/1.33 ( ( in @ X @ A )
% 1.67/1.33 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(wellorderedByIn_type,type,
% 1.67/1.33 wellorderedByIn: $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(wellorderedByIn,definition,
% 1.67/1.33 ( wellorderedByIn
% 1.67/1.33 = ( ^ [A: $i] :
% 1.67/1.33 ( ( stricttotalorderedByIn @ A )
% 1.67/1.33 & ! [X: $i] :
% 1.67/1.33 ( ( in @ X @ ( powerset @ A ) )
% 1.67/1.33 => ( ( nonempty @ X )
% 1.67/1.33 => ? [Xx: $i] :
% 1.67/1.33 ( ( in @ Xx @ X )
% 1.67/1.33 & ! [Y: $i] :
% 1.67/1.33 ( ( in @ Y @ X )
% 1.67/1.33 => ( ( Xx = Y )
% 1.67/1.33 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(ordinal_type,type,
% 1.67/1.33 ordinal: $i > $o ).
% 1.67/1.33
% 1.67/1.33 thf(ordinal,definition,
% 1.67/1.33 ( ordinal
% 1.67/1.33 = ( ^ [Xx: $i] :
% 1.67/1.33 ( ( transitiveset @ Xx )
% 1.67/1.33 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf(ordinalMinLem1,conjecture,
% 1.67/1.33 ( binintTransitive
% 1.67/1.33 => ! [X: $i] :
% 1.67/1.33 ( ( ordinal @ X )
% 1.67/1.33 => ! [Y: $i] :
% 1.67/1.33 ( ( ordinal @ Y )
% 1.67/1.33 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ).
% 1.67/1.33 ------------------------
% 1.67/1.34 % (13732)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_13541 for (2999ds/4Mi)
% 1.67/1.34 % (13732)Instruction limit reached!
% 1.67/1.34 % (13732)------------------------------
% 1.67/1.34 % (13732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (13732)Termination reason: Unknown
% 1.67/1.34 % (13732)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (13732)Memory used [KB]: 5500
% 1.67/1.34 % (13732)Time elapsed: 0.003 s
% 1.67/1.34 % (13732)Instructions burned: 6 (million)
% 1.67/1.34 % (13732)------------------------------
% 1.67/1.34 % (13732)------------------------------
% 1.67/1.34 % (13737)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13541 for (2999ds/18Mi)
% 1.67/1.35 % (13736)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_13541 for (2999ds/275Mi)
% 1.67/1.35 % (13731)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13541 for (2999ds/183Mi)
% 1.67/1.35 % (13737)Instruction limit reached!
% 1.67/1.35 % (13737)------------------------------
% 1.67/1.35 % (13737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (13737)Termination reason: Unknown
% 1.67/1.35 % (13737)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (13737)Memory used [KB]: 5628
% 1.67/1.35 % (13737)Time elapsed: 0.007 s
% 1.67/1.35 % (13737)Instructions burned: 20 (million)
% 1.67/1.35 % (13737)------------------------------
% 1.67/1.35 % (13737)------------------------------
% 1.67/1.35 % (13733)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_13541 for (2999ds/27Mi)
% 1.67/1.35 % (13736)First to succeed.
% 1.67/1.35 % (13735)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_13541 for (2999ds/2Mi)
% 1.67/1.35 % (13735)Instruction limit reached!
% 1.67/1.35 % (13735)------------------------------
% 1.67/1.35 % (13735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (13735)Termination reason: Unknown
% 1.67/1.35 % (13735)Termination phase: Property scanning
% 1.67/1.35
% 1.67/1.35 % (13735)Memory used [KB]: 1023
% 1.67/1.35 % (13735)Time elapsed: 0.002 s
% 1.67/1.35 % (13735)Instructions burned: 4 (million)
% 1.67/1.35 % (13735)------------------------------
% 1.67/1.35 % (13735)------------------------------
% 1.67/1.36 % (13736)Refutation found. Thanks to Tanya!
% 1.67/1.36 % SZS status Theorem for DTF2THF_13541
% 1.67/1.36 % SZS output start Proof for DTF2THF_13541
% 1.67/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.36 thf(func_def_2, type, powerset: $i > $i).
% 1.67/1.36 thf(func_def_3, type, nonempty: $i > $o).
% 1.67/1.36 thf(func_def_4, type, subset: $i > $i > $o).
% 1.67/1.36 thf(func_def_5, type, binintersect: $i > $i > $i).
% 1.67/1.36 thf(func_def_6, type, transitiveset: $i > $o).
% 1.67/1.36 thf(func_def_9, type, stricttotalorderedByIn: $i > $o).
% 1.67/1.36 thf(func_def_10, type, wellorderedByIn: $i > $o).
% 1.67/1.36 thf(func_def_11, type, ordinal: $i > $o).
% 1.67/1.36 thf(f58,plain,(
% 1.67/1.36 $false),
% 1.67/1.36 inference(subsumption_resolution,[status(thm)],[f57,f52])).
% 1.67/1.36 thf(f52,plain,(
% 1.67/1.36 ((transitiveset @ sK2) = $true)),
% 1.67/1.36 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.67/1.36 thf(f51,plain,(
% 1.67/1.36 (((wellorderedByIn @ sK2) & (transitiveset @ sK2)) = $true)),
% 1.67/1.36 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.67/1.36 thf(f47,plain,(
% 1.67/1.36 (((^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))) @ sK2) = $true)),
% 1.67/1.36 inference(definition_unfolding,[status(thm)],[f39,f37])).
% 1.67/1.36 thf(f37,plain,(
% 1.67/1.36 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f11])).
% 1.67/1.36 thf(f11,plain,(
% 1.67/1.36 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 1.67/1.36 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.36 thf(f10,plain,(
% 1.67/1.36 ((^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))) = ordinal)),
% 1.67/1.36 inference(rectify,[status(thm)],[f6])).
% 1.67/1.36 thf(f6,axiom,(
% 1.67/1.36 ((^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))) = ordinal)),
% 1.67/1.36 file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',ordinal)).
% 1.67/1.36 thf(f39,plain,(
% 1.67/1.36 ($true = (ordinal @ sK2))),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.67/1.36 thf(f32,plain,(
% 1.67/1.36 ((((transitiveset @ (binintersect @ sK2 @ sK3)) != $true) & ($true = (ordinal @ sK3))) & ($true = (ordinal @ sK2))) & (binintTransitive = $true)),
% 1.67/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f24,f31,f30])).
% 1.67/1.36 thf(f30,plain,(
% 1.67/1.36 ? [X0 : $i] : (? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((ordinal @ X1) = $true)) & ($true = (ordinal @ X0))) => (? [X1 : $i] : (($true != (transitiveset @ (binintersect @ sK2 @ X1))) & ((ordinal @ X1) = $true)) & ($true = (ordinal @ sK2)))),
% 1.67/1.36 introduced(definition,[],[choice_axiom])).
% 1.67/1.36 thf(f31,plain,(
% 1.67/1.36 ? [X1 : $i] : (($true != (transitiveset @ (binintersect @ sK2 @ X1))) & ((ordinal @ X1) = $true)) => (((transitiveset @ (binintersect @ sK2 @ sK3)) != $true) & ($true = (ordinal @ sK3)))),
% 1.67/1.36 introduced(definition,[],[choice_axiom])).
% 1.67/1.36 thf(f24,plain,(
% 1.67/1.36 ? [X0 : $i] : (? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((ordinal @ X1) = $true)) & ($true = (ordinal @ X0))) & (binintTransitive = $true)),
% 1.67/1.36 inference(ennf_transformation,[status(thm)],[f17])).
% 1.67/1.36 thf(f17,plain,(
% 1.67/1.36 ~((binintTransitive = $true) => ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i] : (((ordinal @ X1) = $true) => ((transitiveset @ (binintersect @ X0 @ X1)) = $true))))),
% 1.67/1.36 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.36 thf(f16,plain,(
% 1.67/1.36 ~(binintTransitive => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((ordinal @ X1) => (transitiveset @ (binintersect @ X0 @ X1)))))),
% 1.67/1.36 inference(rectify,[status(thm)],[f8])).
% 1.67/1.36 thf(f8,negated_conjecture,(
% 1.67/1.36 ~(binintTransitive => ! [X2 : $i] : ((ordinal @ X2) => ! [X3 : $i] : ((ordinal @ X3) => (transitiveset @ (binintersect @ X2 @ X3)))))),
% 1.67/1.36 inference(negated_conjecture,[status(cth)],[f7])).
% 1.67/1.36 thf(f7,conjecture,(
% 1.67/1.36 binintTransitive => ! [X2 : $i] : ((ordinal @ X2) => ! [X3 : $i] : ((ordinal @ X3) => (transitiveset @ (binintersect @ X2 @ X3))))),
% 1.67/1.36 file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',ordinalMinLem1)).
% 1.67/1.36 thf(f57,plain,(
% 1.67/1.36 ((transitiveset @ sK2) != $true)),
% 1.67/1.36 inference(subsumption_resolution,[status(thm)],[f56,f49])).
% 1.67/1.36 thf(f49,plain,(
% 1.67/1.36 ((transitiveset @ sK3) = $true)),
% 1.67/1.36 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.67/1.36 thf(f48,plain,(
% 1.67/1.36 (((wellorderedByIn @ sK3) & (transitiveset @ sK3)) = $true)),
% 1.67/1.36 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.67/1.36 thf(f46,plain,(
% 1.67/1.36 ($true = ((^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))) @ sK3))),
% 1.67/1.36 inference(definition_unfolding,[status(thm)],[f40,f37])).
% 1.67/1.36 thf(f40,plain,(
% 1.67/1.36 ($true = (ordinal @ sK3))),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.67/1.36 thf(f56,plain,(
% 1.67/1.36 ((transitiveset @ sK3) != $true) | ((transitiveset @ sK2) != $true)),
% 1.67/1.36 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.67/1.36 thf(f55,plain,(
% 1.67/1.36 ($true != $true) | ((transitiveset @ sK2) != $true) | ((transitiveset @ sK3) != $true)),
% 1.67/1.36 inference(superposition,[status(thm)],[f41,f54])).
% 1.67/1.36 thf(f54,plain,(
% 1.67/1.36 ( ! [X2 : $i,X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) = $true) | ((transitiveset @ X2) != $true) | ((transitiveset @ X3) != $true)) )),
% 1.67/1.36 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.67/1.36 thf(f45,plain,(
% 1.67/1.36 ( ! [X2 : $i,X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) = $true) | ($true != $true) | ((transitiveset @ X3) != $true) | ((transitiveset @ X2) != $true)) )),
% 1.67/1.36 inference(definition_unfolding,[status(thm)],[f33,f38])).
% 1.67/1.36 thf(f38,plain,(
% 1.67/1.36 (binintTransitive = $true)),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.67/1.36 thf(f33,plain,(
% 1.67/1.36 ( ! [X2 : $i,X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) = $true) | ((transitiveset @ X3) != $true) | ((transitiveset @ X2) != $true) | (binintTransitive != $true)) )),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f29])).
% 1.67/1.36 thf(f29,plain,(
% 1.67/1.36 ((binintTransitive = $true) | ((($true != (transitiveset @ (binintersect @ sK0 @ sK1))) & ($true = (transitiveset @ sK1))) & ($true = (transitiveset @ sK0)))) & (! [X2 : $i] : (! [X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) = $true) | ((transitiveset @ X3) != $true)) | ((transitiveset @ X2) != $true)) | (binintTransitive != $true))),
% 1.67/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f28,f27])).
% 1.67/1.36 thf(f27,plain,(
% 1.67/1.36 ? [X0 : $i] : (? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((transitiveset @ X1) = $true)) & ((transitiveset @ X0) = $true)) => (? [X1 : $i] : (((transitiveset @ (binintersect @ sK0 @ X1)) != $true) & ((transitiveset @ X1) = $true)) & ($true = (transitiveset @ sK0)))),
% 1.67/1.36 introduced(definition,[],[choice_axiom])).
% 1.67/1.36 thf(f28,plain,(
% 1.67/1.36 ? [X1 : $i] : (((transitiveset @ (binintersect @ sK0 @ X1)) != $true) & ((transitiveset @ X1) = $true)) => (($true != (transitiveset @ (binintersect @ sK0 @ sK1))) & ($true = (transitiveset @ sK1)))),
% 1.67/1.36 introduced(definition,[],[choice_axiom])).
% 1.67/1.36 thf(f26,plain,(
% 1.67/1.36 ((binintTransitive = $true) | ? [X0 : $i] : (? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((transitiveset @ X1) = $true)) & ((transitiveset @ X0) = $true))) & (! [X2 : $i] : (! [X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) = $true) | ((transitiveset @ X3) != $true)) | ((transitiveset @ X2) != $true)) | (binintTransitive != $true))),
% 1.67/1.36 inference(rectify,[status(thm)],[f25])).
% 1.67/1.36 thf(f25,plain,(
% 1.67/1.36 ((binintTransitive = $true) | ? [X0 : $i] : (? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((transitiveset @ X1) = $true)) & ((transitiveset @ X0) = $true))) & (! [X0 : $i] : (! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((transitiveset @ X1) != $true)) | ((transitiveset @ X0) != $true)) | (binintTransitive != $true))),
% 1.67/1.36 inference(nnf_transformation,[status(thm)],[f23])).
% 1.67/1.36 thf(f23,plain,(
% 1.67/1.36 (binintTransitive = $true) <=> ! [X0 : $i] : (! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((transitiveset @ X1) != $true)) | ((transitiveset @ X0) != $true))),
% 1.67/1.36 inference(ennf_transformation,[status(thm)],[f13])).
% 1.67/1.36 thf(f13,plain,(
% 1.67/1.36 (binintTransitive = $true) <=> ! [X0 : $i] : (((transitiveset @ X0) = $true) => ! [X1 : $i] : (((transitiveset @ X1) = $true) => ((transitiveset @ (binintersect @ X0 @ X1)) = $true)))),
% 1.67/1.36 inference(fool_elimination,[status(thm)],[f12])).
% 1.67/1.36 thf(f12,plain,(
% 1.67/1.36 (! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i] : ((transitiveset @ X1) => (transitiveset @ (binintersect @ X0 @ X1)))) = binintTransitive)),
% 1.67/1.36 inference(rectify,[status(thm)],[f3])).
% 1.67/1.36 thf(f3,axiom,(
% 1.67/1.36 (! [X2 : $i] : ((transitiveset @ X2) => ! [X3 : $i] : ((transitiveset @ X3) => (transitiveset @ (binintersect @ X2 @ X3)))) = binintTransitive)),
% 1.67/1.36 file('/export/starexec/sandbox/tmp/tmp.1mH8f9nJCx/DTF2THF_13541.p',binintTransitive)).
% 1.67/1.36 thf(f41,plain,(
% 1.67/1.36 ((transitiveset @ (binintersect @ sK2 @ sK3)) != $true)),
% 1.67/1.36 inference(cnf_transformation,[status(thm)],[f32])).
% 1.67/1.36 % SZS output end Proof for DTF2THF_13541
% 1.67/1.36 % (13736)------------------------------
% 1.67/1.36 % (13736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (13736)Termination reason: Refutation
% 1.67/1.36
% 1.67/1.36 % (13736)Memory used [KB]: 5500
% 1.67/1.36 % (13736)Time elapsed: 0.006 s
% 1.67/1.36 % (13736)Instructions burned: 4 (million)
% 1.67/1.36 % (13736)------------------------------
% 1.67/1.36 % (13736)------------------------------
% 1.67/1.36 % (13730)Success in time 0.01 s
%------------------------------------------------------------------------------