%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU501^2 : 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 : n012.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 09:34:57 AM UTC 2026
% Result : Theorem 1.02s 0.90s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 76 ( 16 ~; 0 |; 6 &; 41 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 7 con; 0-2 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 23 ( 4 ^; 13 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f13,f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( ~ ( in @ X1 @ emptyset ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f16,f15]) ).
thf(f15,plain,
emptysetAx = $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( emptysetAx = $true )
& ( $true != sK1 )
& ( $true
= ( in @ sK0 @ emptyset ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i] :
( ? [X1: $o] : ( $true != X1 )
& ( ( in @ X0 @ emptyset )
= $true ) )
=> ( ? [X1: $o] : ( $true != X1 )
& ( $true
= ( in @ sK0 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X1: $o] : ( $true != X1 )
=> ( $true != sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( emptysetAx = $true )
& ? [X0: $i] :
( ? [X1: $o] : ( $true != X1 )
& ( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( emptysetAx = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( emptysetAx
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( emptysetAx
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( emptysetAx
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SDztlPePRl/DTF2THF_24062.p',emptysetE) ).
thf(f16,plain,
( emptysetAx
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( emptysetAx
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SDztlPePRl/DTF2THF_24062.p',emptysetAx) ).
thf(f13,plain,
( $true
= ( in @ sK0 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU501^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n012.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 12:24:15 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SEU501^2 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.31 % Domain : Set Theory
% 0.08/0.31 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.08/0.31 % Version : Especial > Reduced > Especial.
% 0.08/0.31 % English : (! x:i.in x emptyset -> (! phi:o.phi))
% 0.08/0.31
% 0.08/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.31 % Source : [Bro08]
% 0.08/0.31 % Names : ZFC003l [Bro08]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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
% 0.08/0.31 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.08/0.31 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 2 ( 2 avg)
% 0.08/0.31 % Number of connectives : 7 ( 1 ~; 0 |; 0 &; 4 @)
% 0.08/0.31 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 6 ( 4 avg)
% 0.08/0.31 % Number of types : 2 ( 0 usr)
% 0.08/0.31 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.08/0.31 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.08/0.31 % SPC : TH0_THM_EQU_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : http://mathgate.info/detsetitem.php?id=57
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(in_type,type,
% 0.08/0.31 in: $i > $i > $o ).
% 0.08/0.31
% 0.08/0.31 thf(emptyset_type,type,
% 0.08/0.31 emptyset: $i ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetAx_type,type,
% 0.08/0.31 emptysetAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetAx,definition,
% 0.08/0.31 ( emptysetAx
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetE,conjecture,
% 0.08/0.31 ( emptysetAx
% 0.08/0.31 => ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ emptyset )
% 0.08/0.31 => ! [Xphi: $o] : Xphi ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 0.85/0.88 ---- Embedded in THF ---
% 0.85/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.85/0.88 %%% Generated on Tue Feb 24 12:24:16 EST 2026
% 0.85/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.85/0.88 %%% Logic specification used:
% 0.85/0.88 %%% thf(spec, logic, $$dhol).
% 0.85/0.88
% 0.85/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SDztlPePRl/DTF2DTF24062.p
% See solution above
% 0.85/0.88 ------------------------
% 0.85/0.89 ---- Cleaned THF ---
% 0.85/0.89 thf(in_type,type,
% 0.85/0.89 in: $i > $i > $o ).
% 0.85/0.89
% 0.85/0.89 thf(emptyset_type,type,
% 0.85/0.89 emptyset: $i ).
% 0.85/0.89
% 0.85/0.89 thf(emptysetAx_type,type,
% 0.85/0.89 emptysetAx: $o ).
% 0.85/0.89
% 0.85/0.89 thf(emptysetAx,definition,
% 0.85/0.89 ( emptysetAx
% 0.85/0.89 = ( ! [Xx: $i] :
% 0.85/0.89 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.85/0.89
% 0.85/0.89 thf(emptysetE,conjecture,
% 0.85/0.89 ( emptysetAx
% 0.85/0.89 => ! [Xx: $i] :
% 0.85/0.89 ( ( in @ Xx @ emptyset )
% 0.85/0.89 => ! [Xphi: $o] : Xphi ) ) ).
% 0.85/0.89 ------------------------
% 1.02/0.90 % (24180)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_24062 for (3000ds/2Mi)
% 1.02/0.90 % (24177)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_24062 for (3000ds/4Mi)
% 1.02/0.90 % (24179)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24062 for (3000ds/2Mi)
% 1.02/0.90 % (24178)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_24062 for (3000ds/27Mi)
% 1.02/0.90 % (24176)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24062 for (3000ds/183Mi)
% 1.02/0.90 % (24181)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_24062 for (3000ds/275Mi)
% 1.02/0.90 % (24182)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24062 for (3000ds/18Mi)
% 1.02/0.90 % (24179)First to succeed.
% 1.02/0.90 % (24176)Also succeeded, but the first one will report.
% 1.02/0.90 % (24177)Also succeeded, but the first one will report.
% 1.02/0.90 % (24179)Refutation found. Thanks to Tanya!
% 1.02/0.90 % SZS status Theorem for DTF2THF_24062
% 1.02/0.90 % SZS output start Proof for DTF2THF_24062
% 1.02/0.90 thf(func_def_0, type, in: $i > $i > $o).
% 1.02/0.90 thf(f22,plain,(
% 1.02/0.90 $false),
% 1.02/0.90 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.02/0.90 thf(f21,plain,(
% 1.02/0.90 ($true = $false)),
% 1.02/0.90 inference(backward_demodulation,[status(thm)],[f13,f20])).
% 1.02/0.90 thf(f20,plain,(
% 1.02/0.90 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) )),
% 1.02/0.90 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.02/0.90 thf(f19,plain,(
% 1.02/0.90 ( ! [X1 : $i] : (($true = (~ (in @ X1 @ emptyset)))) )),
% 1.02/0.90 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.02/0.90 thf(f18,plain,(
% 1.02/0.90 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (in @ Y0 @ emptyset))) @ X1) = $true)) )),
% 1.02/0.90 inference(pi_clausification,[status(thm)],[f17])).
% 1.02/0.90 thf(f17,plain,(
% 1.02/0.90 ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) = $true)),
% 1.02/0.90 inference(definition_unfolding,[status(thm)],[f16,f15])).
% 1.02/0.90 thf(f15,plain,(
% 1.02/0.90 (emptysetAx = $true)),
% 1.02/0.90 inference(cnf_transformation,[status(thm)],[f12])).
% 1.02/0.90 thf(f12,plain,(
% 1.02/0.90 (emptysetAx = $true) & (($true != sK1) & ($true = (in @ sK0 @ emptyset)))),
% 1.02/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.02/0.90 thf(f10,plain,(
% 1.02/0.90 ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true)) => (? [X1 : $o] : ($true != X1) & ($true = (in @ sK0 @ emptyset)))),
% 1.02/0.90 introduced(definition,[],[choice_axiom])).
% 1.02/0.90 thf(f11,plain,(
% 1.02/0.90 ? [X1 : $o] : ($true != X1) => ($true != sK1)),
% 1.02/0.90 introduced(definition,[],[choice_axiom])).
% 1.02/0.90 thf(f9,plain,(
% 1.02/0.90 (emptysetAx = $true) & ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true))),
% 1.02/0.90 inference(ennf_transformation,[status(thm)],[f8])).
% 1.02/0.90 thf(f8,plain,(
% 1.02/0.90 ~((emptysetAx = $true) => ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1)))),
% 1.02/0.90 inference(fool_elimination,[status(thm)],[f7])).
% 1.02/0.90 thf(f7,plain,(
% 1.02/0.90 ~(emptysetAx => ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.02/0.90 inference(rectify,[status(thm)],[f3])).
% 1.02/0.90 thf(f3,negated_conjecture,(
% 1.02/0.90 ~(emptysetAx => ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.02/0.90 inference(negated_conjecture,[status(cth)],[f2])).
% 1.02/0.90 thf(f2,conjecture,(
% 1.02/0.90 emptysetAx => ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1)),
% 1.02/0.90 file('/export/starexec/sandbox2/tmp/tmp.SDztlPePRl/DTF2THF_24062.p',emptysetE)).
% 1.02/0.90 thf(f16,plain,(
% 1.02/0.90 (emptysetAx = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 1.02/0.90 inference(cnf_transformation,[status(thm)],[f6])).
% 1.02/0.90 thf(f6,plain,(
% 1.02/0.90 (emptysetAx = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 1.02/0.90 inference(fool_elimination,[status(thm)],[f5])).
% 1.02/0.90 thf(f5,plain,(
% 1.02/0.90 (emptysetAx = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.02/0.90 inference(rectify,[status(thm)],[f1])).
% 1.02/0.90 thf(f1,axiom,(
% 1.02/0.90 (emptysetAx = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.02/0.90 file('/export/starexec/sandbox2/tmp/tmp.SDztlPePRl/DTF2THF_24062.p',emptysetAx)).
% 1.02/0.90 thf(f13,plain,(
% 1.02/0.90 ($true = (in @ sK0 @ emptyset))),
% 1.02/0.90 inference(cnf_transformation,[status(thm)],[f12])).
% 1.02/0.90 % SZS output end Proof for DTF2THF_24062
% 1.02/0.90 % (24179)------------------------------
% 1.02/0.90 % (24179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.90 % (24179)Termination reason: Refutation
% 1.02/0.90
% 1.02/0.90 % (24179)Memory used [KB]: 5500
% 1.02/0.90 % (24179)Time elapsed: 0.002 s
% 1.02/0.90 % (24179)Instructions burned: 1 (million)
% 1.02/0.90 % (24179)------------------------------
% 1.02/0.90 % (24179)------------------------------
% 1.02/0.90 % (24175)Success in time 0.005 s
%------------------------------------------------------------------------------