%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU539^2 : 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 : n023.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 09:35:10 AM UTC 2026
% Result : Theorem 1.37s 1.30s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 39 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 139 ( 29 ~; 7 |; 17 &; 74 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 21 !; 16 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f13]) ).
thf(f13,plain,
( ( sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( in @ sK2 @ sK1 )
= $true )
& ( ( sK0 @ sK2 )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ sK1 )
= $true )
& ( ( sK0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ sK1 )
= $true )
& ( ( sK0 @ X2 )
!= $true ) )
=> ( ( ( in @ sK2 @ sK1 )
= $true )
& ( ( sK0 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: $i > $o,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: $i > $o,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iBn2dxi99G/DTF2THF_16980.p',quantDeMorgan4) ).
thf(f16,plain,
( ( sK0 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( $true
= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU539^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n023.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:26:49 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU539^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Preliminary Notions - Bounded Quantifier Laws
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.! phi:i>o.(? x:i.in x A & ~(phi x)) -> ~(! x:i.in x A ->
% 0.18/0.38 % phi x))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC041l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.38 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 2 ( 2 avg)
% 0.18/0.38 % Number of connectives : 11 ( 2 ~; 0 |; 1 &; 6 @)
% 0.18/0.38 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.38 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.18/0.38 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=452
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan4,conjecture,
% 0.18/0.38 ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ~ ( Xphi @ Xx ) )
% 0.18/0.38 => ~ ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.37/1.26 ---- Embedded in THF ---
% 1.37/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.26 %%% Generated on Tue Feb 24 12:26:50 EST 2026
% 1.37/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.26 %%% Logic specification used:
% 1.37/1.26 %%% thf(spec, logic, $$dhol).
% 1.37/1.26
% 1.37/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.iBn2dxi99G/DTF2DTF16980.p
% See solution above
% 1.37/1.26 ------------------------
% 1.37/1.27 ---- Cleaned THF ---
% 1.37/1.27 thf(in,type,
% 1.37/1.27 in: $i > $i > $o ).
% 1.37/1.27
% 1.37/1.27 thf(quantDeMorgan4,conjecture,
% 1.37/1.27 ! [A: $i,Xphi: $i > $o] :
% 1.37/1.27 ( ? [Xx: $i] :
% 1.37/1.27 ( ( in @ Xx @ A )
% 1.37/1.27 & ~ ( Xphi @ Xx ) )
% 1.37/1.27 => ~ ! [Xx: $i] :
% 1.37/1.27 ( ( in @ Xx @ A )
% 1.37/1.27 => ( Xphi @ Xx ) ) ) ).
% 1.37/1.27 ------------------------
% 1.37/1.29 % (17080)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_16980 for (3000ds/27Mi)
% 1.37/1.29 % (17078)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16980 for (3000ds/183Mi)
% 1.37/1.29 % (17081)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16980 for (3000ds/2Mi)
% 1.37/1.29 % (17079)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_16980 for (3000ds/4Mi)
% 1.37/1.29 % (17082)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_16980 for (3000ds/2Mi)
% 1.37/1.29 % (17083)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_16980 for (3000ds/275Mi)
% 1.37/1.29 % (17084)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16980 for (3000ds/18Mi)
% 1.37/1.29 % (17081)Instruction limit reached!
% 1.37/1.29 % (17081)------------------------------
% 1.37/1.29 % (17081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.29 % (17083)First to succeed.
% 1.37/1.29 % (17081)Termination reason: Unknown
% 1.37/1.29 % (17081)Termination phase: Saturation
% 1.37/1.29
% 1.37/1.29 % (17081)Memory used [KB]: 5500
% 1.37/1.29 % (17081)Time elapsed: 0.003 s
% 1.37/1.29 % (17081)Instructions burned: 2 (million)
% 1.37/1.29 % (17081)------------------------------
% 1.37/1.29 % (17081)------------------------------
% 1.37/1.29 % (17082)Instruction limit reached!
% 1.37/1.29 % (17082)------------------------------
% 1.37/1.29 % (17082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.29 % (17082)Termination reason: Unknown
% 1.37/1.29 % (17082)Termination phase: Saturation
% 1.37/1.29
% 1.37/1.29 % (17082)Memory used [KB]: 5500
% 1.37/1.29 % (17082)Time elapsed: 0.003 s
% 1.37/1.29 % (17082)Instructions burned: 2 (million)
% 1.37/1.29 % (17082)------------------------------
% 1.37/1.29 % (17082)------------------------------
% 1.37/1.29 % (17078)Also succeeded, but the first one will report.
% 1.37/1.30 % (17083)Refutation found. Thanks to Tanya!
% 1.37/1.30 % SZS status Theorem for DTF2THF_16980
% 1.37/1.30 % SZS output start Proof for DTF2THF_16980
% 1.37/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.37/1.30 thf(func_def_4, type, sK0: $i > $o).
% 1.37/1.30 thf(f17,plain,(
% 1.37/1.30 $false),
% 1.37/1.30 inference(subsumption_resolution,[status(thm)],[f16,f13])).
% 1.37/1.30 thf(f13,plain,(
% 1.37/1.30 ((sK0 @ sK2) != $true)),
% 1.37/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.37/1.30 thf(f11,plain,(
% 1.37/1.30 (((in @ sK2 @ sK1) = $true) & ((sK0 @ sK2) != $true)) & ! [X3 : $i] : (((in @ X3 @ sK1) != $true) | ($true = (sK0 @ X3)))),
% 1.37/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.37/1.30 thf(f9,plain,(
% 1.37/1.30 ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((X0 @ X2) != $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((X0 @ X3) = $true))) => (? [X2 : $i] : (((in @ X2 @ sK1) = $true) & ((sK0 @ X2) != $true)) & ! [X3 : $i] : (((in @ X3 @ sK1) != $true) | ($true = (sK0 @ X3))))),
% 1.37/1.30 introduced(definition,[],[choice_axiom])).
% 1.37/1.30 thf(f10,plain,(
% 1.37/1.30 ? [X2 : $i] : (((in @ X2 @ sK1) = $true) & ((sK0 @ X2) != $true)) => (((in @ sK2 @ sK1) = $true) & ((sK0 @ sK2) != $true))),
% 1.37/1.30 introduced(definition,[],[choice_axiom])).
% 1.37/1.30 thf(f8,plain,(
% 1.37/1.30 ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((X0 @ X2) != $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((X0 @ X3) = $true)))),
% 1.37/1.30 inference(rectify,[status(thm)],[f7])).
% 1.37/1.30 thf(f7,plain,(
% 1.37/1.30 ? [X1 : $i > $o,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) != $true)) & ! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((X1 @ X3) = $true)))),
% 1.37/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.37/1.30 thf(f6,plain,(
% 1.37/1.30 ~! [X1 : $i > $o,X0 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) != $true)) => ~! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((X1 @ X3) = $true)))),
% 1.37/1.30 inference(flattening,[status(thm)],[f5])).
% 1.37/1.30 thf(f5,plain,(
% 1.37/1.30 ~! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ~((X1 @ X2) = $true)) => ~! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((X1 @ X3) = $true)))),
% 1.37/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.37/1.30 thf(f4,plain,(
% 1.37/1.30 ~! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~! [X3 : $i] : ((in @ X3 @ X0) => (X1 @ X3)))),
% 1.37/1.30 inference(rectify,[status(thm)],[f2])).
% 1.37/1.30 thf(f2,negated_conjecture,(
% 1.37/1.30 ~! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2)))),
% 1.37/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.37/1.30 thf(f1,conjecture,(
% 1.37/1.30 ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & ~(X1 @ X2)) => ~! [X2 : $i] : ((in @ X2 @ X0) => (X1 @ X2)))),
% 1.37/1.30 file('/export/starexec/sandbox/tmp/tmp.iBn2dxi99G/DTF2THF_16980.p',quantDeMorgan4)).
% 1.37/1.30 thf(f16,plain,(
% 1.37/1.30 ((sK0 @ sK2) = $true)),
% 1.37/1.30 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.37/1.30 thf(f15,plain,(
% 1.37/1.30 ((sK0 @ sK2) = $true) | ($true != $true)),
% 1.37/1.30 inference(superposition,[status(thm)],[f12,f14])).
% 1.37/1.30 thf(f14,plain,(
% 1.37/1.30 ((in @ sK2 @ sK1) = $true)),
% 1.37/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.37/1.30 thf(f12,plain,(
% 1.37/1.30 ( ! [X3 : $i] : (((in @ X3 @ sK1) != $true) | ($true = (sK0 @ X3))) )),
% 1.37/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.37/1.30 % SZS output end Proof for DTF2THF_16980
% 1.37/1.30 % (17083)------------------------------
% 1.37/1.30 % (17083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.30 % (17083)Termination reason: Refutation
% 1.37/1.30
% 1.37/1.30 % (17083)Memory used [KB]: 5500
% 1.37/1.30 % (17083)Time elapsed: 0.003 s
% 1.37/1.30 % (17083)Instructions burned: 1 (million)
% 1.37/1.30 % (17083)------------------------------
% 1.37/1.30 % (17083)------------------------------
% 1.37/1.30 % (17077)Success in time 0.017 s
%------------------------------------------------------------------------------