%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU538^2 : 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 : n021.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 09:35:09 AM UTC 2026
% Result : Theorem 0.22s 1.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 128 ( 27 ~; 6 |; 15 &; 68 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 20 !; 13 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_5,type,
sK1: $i > $o ).
thf(f16,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f15,f12]) ).
thf(f12,plain,
( ( sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
| ( ( sK1 @ X2 )
!= $true ) )
& ( ( sK1 @ sK2 )
= $true )
& ( ( in @ sK2 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( $true
= ( X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
| ( ( sK1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( sK1 @ X3 )
= $true )
& ( ( in @ X3 @ sK0 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: $i] :
( ( ( sK1 @ X3 )
= $true )
& ( ( in @ X3 @ sK0 )
= $true ) )
=> ( ( ( sK1 @ sK2 )
= $true )
& ( ( in @ sK2 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( $true
= ( X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
!= ( X1 @ X3 ) ) ) ),
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 )
=> ( $true
!= ( X1 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ~ ( X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lskjLqKs83/DTF2THF_10145.p',quantDeMorgan3) ).
thf(f15,plain,
( ( sK1 @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( sK1 @ sK2 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f11]) ).
thf(f11,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
| ( ( sK1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU538^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n021.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:26:08 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SEU538^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.40 % Domain : Set Theory
% 0.16/0.40 % Problem : Preliminary Notions - Bounded Quantifier Laws
% 0.16/0.40 % Version : Especial > Reduced > Especial.
% 0.16/0.40 % English : (! A:i.! phi:i>o.~(? x:i.in x A & phi x) -> (! x:i.in x A ->
% 0.16/0.40 % ~(phi x)))
% 0.16/0.40
% 0.16/0.40 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.40 % Source : [Bro08]
% 0.16/0.40 % Names : ZFC040l [Bro08]
% 0.16/0.40 % : ZFC044l [Bro08]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % 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
% 0.16/0.40 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.40 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.40 % Number of connectives : 11 ( 2 ~; 0 |; 1 &; 6 @)
% 0.16/0.40 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 9 ( 9 avg)
% 0.16/0.40 % Number of types : 2 ( 0 usr)
% 0.16/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.16/0.40 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.16/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : http://mathgate.info/detsetitem.php?id=451
% 0.16/0.40 % : http://mathgate.info/detsetitem.php?id=118
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(in,type,
% 0.16/0.40 in: $i > $i > $o ).
% 0.16/0.40
% 0.16/0.40 thf(quantDeMorgan3,conjecture,
% 0.16/0.40 ! [A: $i,Xphi: $i > $o] :
% 0.16/0.40 ( ~ ? [Xx: $i] :
% 0.16/0.40 ( ( in @ Xx @ A )
% 0.16/0.40 & ( Xphi @ Xx ) )
% 0.16/0.40 => ! [Xx: $i] :
% 0.16/0.40 ( ( in @ Xx @ A )
% 0.16/0.40 => ~ ( Xphi @ Xx ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 0.22/1.30 ---- Embedded in THF ---
% 0.22/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.22/1.30 %%% Generated on Tue Feb 24 12:26:09 EST 2026
% 0.22/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.22/1.30 %%% Logic specification used:
% 0.22/1.30 %%% thf(spec, logic, $$dhol).
% 0.22/1.30
% 0.22/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lskjLqKs83/DTF2DTF10145.p
% See solution above
% 0.22/1.30 ------------------------
% 0.22/1.31 ---- Cleaned THF ---
% 0.22/1.31 thf(in,type,
% 0.22/1.31 in: $i > $i > $o ).
% 0.22/1.31
% 0.22/1.31 thf(quantDeMorgan3,conjecture,
% 0.22/1.31 ! [A: $i,Xphi: $i > $o] :
% 0.22/1.31 ( ~ ? [Xx: $i] :
% 0.22/1.31 ( ( in @ Xx @ A )
% 0.22/1.31 & ( Xphi @ Xx ) )
% 0.22/1.31 => ! [Xx: $i] :
% 0.22/1.31 ( ( in @ Xx @ A )
% 0.22/1.31 => ~ ( Xphi @ Xx ) ) ) ).
% 0.22/1.31 ------------------------
% 0.22/1.33 % (10246)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10145 for (3000ds/2Mi)
% 0.22/1.33 % (10243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10145 for (3000ds/183Mi)
% 0.22/1.33 % (10249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10145 for (3000ds/18Mi)
% 0.22/1.33 % (10245)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_10145 for (3000ds/27Mi)
% 0.22/1.33 % (10248)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_10145 for (3000ds/275Mi)
% 0.22/1.33 % (10244)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_10145 for (3000ds/4Mi)
% 0.22/1.33 % (10247)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_10145 for (3000ds/2Mi)
% 0.22/1.33 % (10248)First to succeed.
% 0.22/1.33 % (10247)Instruction limit reached!
% 0.22/1.33 % (10247)------------------------------
% 0.22/1.33 % (10247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (10247)Termination reason: Unknown
% 0.22/1.33 % (10247)Termination phase: Saturation
% 0.22/1.33
% 0.22/1.33 % (10247)Memory used [KB]: 5500
% 0.22/1.33 % (10247)Time elapsed: 0.003 s
% 0.22/1.33 % (10247)Instructions burned: 2 (million)
% 0.22/1.33 % (10247)------------------------------
% 0.22/1.33 % (10247)------------------------------
% 0.22/1.33 % (10243)Also succeeded, but the first one will report.
% 0.22/1.33 % (10249)Also succeeded, but the first one will report.
% 0.22/1.33 % (10248)Refutation found. Thanks to Tanya!
% 0.22/1.33 % SZS status Theorem for DTF2THF_10145
% 0.22/1.33 % SZS output start Proof for DTF2THF_10145
% 0.22/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/1.33 thf(func_def_5, type, sK1: $i > $o).
% 0.22/1.33 thf(f16,plain,(
% 0.22/1.33 $false),
% 0.22/1.33 inference(subsumption_resolution,[status(thm)],[f15,f12])).
% 0.22/1.33 thf(f12,plain,(
% 0.22/1.33 ((sK1 @ sK2) = $true)),
% 0.22/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 0.22/1.33 thf(f10,plain,(
% 0.22/1.33 ! [X2 : $i] : (((in @ X2 @ sK0) != $true) | ((sK1 @ X2) != $true)) & (((sK1 @ sK2) = $true) & ((in @ sK2 @ sK0) = $true))),
% 0.22/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 0.22/1.33 thf(f8,plain,(
% 0.22/1.33 ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) != $true)) & ? [X3 : $i] : (($true = (X1 @ X3)) & ((in @ X3 @ X0) = $true))) => (! [X2 : $i] : (((in @ X2 @ sK0) != $true) | ((sK1 @ X2) != $true)) & ? [X3 : $i] : (((sK1 @ X3) = $true) & ((in @ X3 @ sK0) = $true)))),
% 0.22/1.33 introduced(definition,[],[choice_axiom])).
% 0.22/1.33 thf(f9,plain,(
% 0.22/1.33 ? [X3 : $i] : (((sK1 @ X3) = $true) & ((in @ X3 @ sK0) = $true)) => (((sK1 @ sK2) = $true) & ((in @ sK2 @ sK0) = $true))),
% 0.22/1.33 introduced(definition,[],[choice_axiom])).
% 0.22/1.33 thf(f7,plain,(
% 0.22/1.33 ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) != $true)) & ? [X3 : $i] : (($true = (X1 @ X3)) & ((in @ X3 @ X0) = $true)))),
% 0.22/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 0.22/1.33 thf(f6,plain,(
% 0.22/1.33 ~! [X0 : $i,X1 : $i > $o] : (~? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ($true != (X1 @ X3))))),
% 0.22/1.33 inference(flattening,[status(thm)],[f5])).
% 0.22/1.33 thf(f5,plain,(
% 0.22/1.33 ~! [X0 : $i,X1 : $i > $o] : (~? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ~($true = (X1 @ X3))))),
% 0.22/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.22/1.33 thf(f4,plain,(
% 0.22/1.33 ~! [X0 : $i,X1 : $i > $o] : (~? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ~(X1 @ X3)))),
% 0.22/1.33 inference(rectify,[status(thm)],[f2])).
% 0.22/1.33 thf(f2,negated_conjecture,(
% 0.22/1.33 ~! [X0 : $i,X1 : $i > $o] : (~? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)))),
% 0.22/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/1.33 thf(f1,conjecture,(
% 0.22/1.33 ! [X0 : $i,X1 : $i > $o] : (~? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ~(X1 @ X2)))),
% 0.22/1.33 file('/export/starexec/sandbox/tmp/tmp.lskjLqKs83/DTF2THF_10145.p',quantDeMorgan3)).
% 0.22/1.33 thf(f15,plain,(
% 0.22/1.33 ((sK1 @ sK2) != $true)),
% 0.22/1.33 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 0.22/1.33 thf(f14,plain,(
% 0.22/1.33 ((sK1 @ sK2) != $true) | ($true != $true)),
% 0.22/1.33 inference(superposition,[status(thm)],[f13,f11])).
% 0.22/1.33 thf(f11,plain,(
% 0.22/1.33 ((in @ sK2 @ sK0) = $true)),
% 0.22/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 0.22/1.33 thf(f13,plain,(
% 0.22/1.33 ( ! [X2 : $i] : (((in @ X2 @ sK0) != $true) | ((sK1 @ X2) != $true)) )),
% 0.22/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 0.22/1.33 % SZS output end Proof for DTF2THF_10145
% 0.22/1.33 % (10248)------------------------------
% 0.22/1.33 % (10248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.22/1.33 % (10248)Termination reason: Refutation
% 0.22/1.33
% 0.22/1.33 % (10248)Memory used [KB]: 5500
% 0.22/1.33 % (10248)Time elapsed: 0.003 s
% 0.22/1.33 % (10248)Instructions burned: 1 (million)
% 0.22/1.33 % (10248)------------------------------
% 0.22/1.33 % (10248)------------------------------
% 0.22/1.33 % (10242)Success in time 0.006 s
%------------------------------------------------------------------------------