%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU812^2 : 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 : n020.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 09:37:25 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 36 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 148 ( 11 ~; 2 |; 10 &; 103 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 29 ( 10 ^; 13 !; 6 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
transitiveset: $i > $o ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f15,f23]) ).
thf(f23,plain,
( $false
= ( in @ sK1 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( $false
= ( in @ sK1 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f14,f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( subset @ X1 @ sK0 )
= $true )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[status(thm)],[f16,f13]) ).
thf(f13,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
file('/export/starexec/sandbox2/tmp/tmp.Ih7b9nvnk0/DTF2THF_19512.p',transitiveset) ).
thf(f16,plain,
( ( transitiveset @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( transitiveset @ sK0 )
= $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( subset @ sK1 @ sK0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) )
=> ( ( ( transitiveset @ sK0 )
= $true )
& ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( subset @ X1 @ sK0 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $true )
& ( ( subset @ X1 @ sK0 )
!= $true ) )
=> ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( subset @ sK1 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i] :
( ( transitiveset @ X1 )
=> ! [X0: $i] :
( ( in @ X0 @ X1 )
=> ( subset @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i] :
( ( transitiveset @ X1 )
=> ! [X0: $i] :
( ( in @ X0 @ X1 )
=> ( subset @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih7b9nvnk0/DTF2THF_19512.p',transitivesetOp1) ).
thf(f14,plain,
( ( subset @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f15,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU812^2 : 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 : n020.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 12:34:57 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU812^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Transitive Sets
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! X:i.transitiveset X -> (! A:i.in A X -> subset A X))
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC314l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.31/0.46 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.31/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 0 &; 9 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=500
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(in_type,type,
% 0.31/0.46 in: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(subset_type,type,
% 0.31/0.46 subset: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(transitiveset_type,type,
% 0.31/0.46 transitiveset: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(transitiveset,definition,
% 0.31/0.46 ( transitiveset
% 0.31/0.46 = ( ^ [A: $i] :
% 0.31/0.46 ! [X: $i] :
% 0.31/0.46 ( ( in @ X @ A )
% 0.31/0.46 => ( subset @ X @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(transitivesetOp1,conjecture,
% 0.31/0.46 ! [X: $i] :
% 0.31/0.46 ( ( transitiveset @ X )
% 0.31/0.46 => ! [A: $i] :
% 0.31/0.46 ( ( in @ A @ X )
% 0.31/0.46 => ( subset @ A @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 12:34:58 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ih7b9nvnk0/DTF2DTF19512.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(in_type,type,
% 1.48/1.27 in: $i > $i > $o ).
% 1.48/1.27
% 1.48/1.27 thf(subset_type,type,
% 1.48/1.27 subset: $i > $i > $o ).
% 1.48/1.27
% 1.48/1.27 thf(transitiveset_type,type,
% 1.48/1.27 transitiveset: $i > $o ).
% 1.48/1.27
% 1.48/1.27 thf(transitiveset,definition,
% 1.48/1.27 ( transitiveset
% 1.48/1.27 = ( ^ [A: $i] :
% 1.48/1.27 ! [X: $i] :
% 1.48/1.27 ( ( in @ X @ A )
% 1.48/1.27 => ( subset @ X @ A ) ) ) ) ).
% 1.48/1.27
% 1.48/1.27 thf(transitivesetOp1,conjecture,
% 1.48/1.27 ! [X: $i] :
% 1.48/1.27 ( ( transitiveset @ X )
% 1.48/1.27 => ! [A: $i] :
% 1.48/1.27 ( ( in @ A @ X )
% 1.48/1.27 => ( subset @ A @ X ) ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.28 % (19737)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19512 for (2999ds/18Mi)
% 1.48/1.28 % (19735)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_19512 for (2999ds/2Mi)
% 1.48/1.28 % (19737)First to succeed.
% 1.48/1.28 % (19735)Instruction limit reached!
% 1.48/1.28 % (19735)------------------------------
% 1.48/1.28 % (19735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19735)Termination reason: Unknown
% 1.48/1.28 % (19735)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (19735)Memory used [KB]: 5500
% 1.48/1.28 % (19735)Time elapsed: 0.002 s
% 1.48/1.28 % (19735)Instructions burned: 2 (million)
% 1.48/1.28 % (19735)------------------------------
% 1.48/1.28 % (19735)------------------------------
% 1.48/1.28 % (19737)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_19512
% 1.48/1.28 % SZS output start Proof for DTF2THF_19512
% 1.48/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.48/1.28 thf(func_def_1, type, subset: $i > $i > $o).
% 1.48/1.28 thf(func_def_2, type, transitiveset: $i > $o).
% 1.48/1.28 thf(f25,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.48/1.28 thf(f24,plain,(
% 1.48/1.28 ($false = $true)),
% 1.48/1.28 inference(backward_demodulation,[status(thm)],[f15,f23])).
% 1.48/1.28 thf(f23,plain,(
% 1.48/1.28 ($false = (in @ sK1 @ sK0))),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.48/1.28 thf(f22,plain,(
% 1.48/1.28 ($true != $true) | ($false = (in @ sK1 @ sK0))),
% 1.48/1.28 inference(superposition,[status(thm)],[f14,f21])).
% 1.48/1.28 thf(f21,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (((subset @ X1 @ sK0) = $true) | ((in @ X1 @ sK0) = $false)) )),
% 1.48/1.28 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.48/1.28 thf(f20,plain,(
% 1.48/1.28 ( ! [X1 : $i] : ((((in @ X1 @ sK0) => (subset @ X1 @ sK0)) = $true)) )),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))) @ X1) = $true)) )),
% 1.48/1.28 inference(pi_clausification,[status(thm)],[f18])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0)))) = $true)),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK0) = $true)),
% 1.48/1.28 inference(definition_unfolding,[status(thm)],[f16,f13])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 1.48/1.28 inference(rectify,[status(thm)],[f1])).
% 1.48/1.28 thf(f1,axiom,(
% 1.48/1.28 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.Ih7b9nvnk0/DTF2THF_19512.p',transitiveset)).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ((transitiveset @ sK0) = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ((transitiveset @ sK0) = $true) & (((in @ sK1 @ sK0) = $true) & ((subset @ sK1 @ sK0) != $true))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ? [X0 : $i] : (($true = (transitiveset @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((subset @ X1 @ X0) != $true))) => (((transitiveset @ sK0) = $true) & ? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((subset @ X1 @ sK0) != $true)))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ? [X1 : $i] : (((in @ X1 @ sK0) = $true) & ((subset @ X1 @ sK0) != $true)) => (((in @ sK1 @ sK0) = $true) & ((subset @ sK1 @ sK0) != $true))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ? [X0 : $i] : (($true = (transitiveset @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((subset @ X1 @ X0) != $true)))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ~! [X0 : $i] : (($true = (transitiveset @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((subset @ X1 @ X0) = $true)))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))),
% 1.48/1.28 inference(rectify,[status(thm)],[f3])).
% 1.48/1.28 thf(f3,negated_conjecture,(
% 1.48/1.28 ~! [X1 : $i] : ((transitiveset @ X1) => ! [X0 : $i] : ((in @ X0 @ X1) => (subset @ X0 @ X1)))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.28 thf(f2,conjecture,(
% 1.48/1.28 ! [X1 : $i] : ((transitiveset @ X1) => ! [X0 : $i] : ((in @ X0 @ X1) => (subset @ X0 @ X1)))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.Ih7b9nvnk0/DTF2THF_19512.p',transitivesetOp1)).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ((subset @ sK1 @ sK0) != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ((in @ sK1 @ sK0) = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_19512
% 1.48/1.28 % (19737)------------------------------
% 1.48/1.28 % (19737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (19737)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (19737)Memory used [KB]: 5500
% 1.48/1.28 % (19737)Time elapsed: 0.003 s
% 1.48/1.28 % (19737)Instructions burned: 2 (million)
% 1.48/1.28 % (19737)------------------------------
% 1.48/1.28 % (19737)------------------------------
% 1.48/1.28 % (19730)Success in time 0.012 s
%------------------------------------------------------------------------------