%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU568^2 : 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 : n003.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 09:35:19 AM UTC 2026
% Result : Theorem 1.66s 1.40s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 104 ( 21 ~; 0 |; 16 &; 46 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 15 !; 9 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f45,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f24]) ).
thf(f24,plain,
( $true
!= ( in @ sK1 @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f23,f22]) ).
thf(f22,plain,
sK2 = sK0,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( in @ sK1 @ sK2 ) )
& ( sK2 = sK0 )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( notsubsetI = $true )
& ( notequalI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( X0 = X2 )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( in @ sK1 @ sK2 ) )
& ( sK2 = sK0 )
& ( $true
= ( in @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( X0 = X2 )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( notsubsetI = $true )
& ( notequalI1 = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
& ( $true
!= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( notequalI1 = $true )
& ( notsubsetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( X0 != X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( X0 != X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( notsubsetI
=> ( notequalI1
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( X0 != X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( notsubsetI
=> ( notequalI1
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( X0 != X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( notsubsetI
=> ( notequalI1
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( X0 != X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NWvZmRhoKK/DTF2THF_11049.p',notequalI2) ).
thf(f23,plain,
( $true
!= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f21,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU568^2 : 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
% 0.15/0.34 % Computer : n003.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:26:55 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU568^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.30/0.47 % Version : Especial > Reduced > Especial.
% 0.30/0.47 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> ~(A = B))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC070l [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 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
% 0.30/0.47 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.30/0.47 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 5 ( 4 avg)
% 0.30/0.47 % Number of connectives : 25 ( 6 ~; 0 |; 0 &; 12 @)
% 0.30/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 11 ( 4 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=439
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(subset_type,type,
% 0.30/0.47 subset: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(notsubsetI_type,type,
% 0.30/0.47 notsubsetI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notsubsetI,definition,
% 0.30/0.47 ( notsubsetI
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI1_type,type,
% 0.30/0.47 notequalI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI1,definition,
% 0.30/0.47 ( notequalI1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ~ ( subset @ A @ B )
% 0.30/0.47 => ( A != B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI2,conjecture,
% 0.30/0.47 ( notsubsetI
% 0.30/0.47 => ( notequalI1
% 0.30/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ( A != B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.50/1.36 ---- Embedded in THF ---
% 1.50/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.37 %%% Generated on Tue Feb 24 12:26:56 EST 2026
% 1.50/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.37 %%% Logic specification used:
% 1.50/1.37 %%% thf(spec, logic, $$dhol).
% 1.50/1.37
% 1.50/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NWvZmRhoKK/DTF2DTF11049.p
% See solution above
% 1.50/1.37 ------------------------
% 1.50/1.37 ---- Cleaned THF ---
% 1.50/1.38 thf(in_type,type,
% 1.50/1.38 in: $i > $i > $o ).
% 1.50/1.38
% 1.50/1.38 thf(subset_type,type,
% 1.50/1.38 subset: $i > $i > $o ).
% 1.50/1.38
% 1.50/1.38 thf(notsubsetI_type,type,
% 1.50/1.38 notsubsetI: $o ).
% 1.50/1.38
% 1.50/1.38 thf(notsubsetI,definition,
% 1.50/1.38 ( notsubsetI
% 1.50/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.38 ( ( in @ Xx @ A )
% 1.50/1.38 => ( ~ ( in @ Xx @ B )
% 1.50/1.38 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 1.50/1.38
% 1.50/1.38 thf(notequalI1_type,type,
% 1.50/1.38 notequalI1: $o ).
% 1.50/1.38
% 1.50/1.38 thf(notequalI1,definition,
% 1.50/1.38 ( notequalI1
% 1.50/1.38 = ( ! [A: $i,B: $i] :
% 1.50/1.38 ( ~ ( subset @ A @ B )
% 1.50/1.38 => ( A != B ) ) ) ) ).
% 1.50/1.38
% 1.50/1.38 thf(notequalI2,conjecture,
% 1.50/1.38 ( notsubsetI
% 1.50/1.38 => ( notequalI1
% 1.50/1.38 => ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.38 ( ( in @ Xx @ A )
% 1.50/1.38 => ( ~ ( in @ Xx @ B )
% 1.50/1.38 => ( A != B ) ) ) ) ) ).
% 1.50/1.38 ------------------------
% 1.50/1.40 % (11146)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11049 for (3000ds/183Mi)
% 1.50/1.40 % (11147)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_11049 for (3000ds/4Mi)
% 1.50/1.40 % (11149)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11049 for (3000ds/2Mi)
% 1.50/1.40 % (11148)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_11049 for (3000ds/27Mi)
% 1.50/1.40 % (11150)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_11049 for (3000ds/2Mi)
% 1.50/1.40 % (11151)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_11049 for (3000ds/275Mi)
% 1.50/1.40 % (11152)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11049 for (3000ds/18Mi)
% 1.50/1.40 % (11149)Instruction limit reached!
% 1.50/1.40 % (11149)------------------------------
% 1.50/1.40 % (11149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.40 % (11149)Termination reason: Unknown
% 1.50/1.40 % (11149)Termination phase: Preprocessing 3
% 1.50/1.40
% 1.50/1.40 % (11149)Memory used [KB]: 895
% 1.50/1.40 % (11149)Time elapsed: 0.002 s
% 1.50/1.40 % (11149)Instructions burned: 2 (million)
% 1.50/1.40 % (11149)------------------------------
% 1.50/1.40 % (11149)------------------------------
% 1.50/1.40 % (11150)Instruction limit reached!
% 1.50/1.40 % (11150)------------------------------
% 1.50/1.40 % (11150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.40 % (11150)Termination reason: Unknown
% 1.50/1.40 % (11150)Termination phase: Property scanning
% 1.50/1.40
% 1.50/1.40 % (11150)Memory used [KB]: 895
% 1.50/1.40 % (11150)Time elapsed: 0.002 s
% 1.50/1.40 % (11150)Instructions burned: 2 (million)
% 1.50/1.40 % (11150)------------------------------
% 1.50/1.40 % (11150)------------------------------
% 1.66/1.40 % (11146)First to succeed.
% 1.66/1.40 % (11151)Also succeeded, but the first one will report.
% 1.66/1.40 % (11147)Also succeeded, but the first one will report.
% 1.66/1.40 % (11146)Refutation found. Thanks to Tanya!
% 1.66/1.40 % SZS status Theorem for DTF2THF_11049
% 1.66/1.40 % SZS output start Proof for DTF2THF_11049
% 1.66/1.40 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.40 thf(func_def_1, type, subset: $i > $i > $o).
% 1.66/1.40 thf(f45,plain,(
% 1.66/1.40 $false),
% 1.66/1.40 inference(subsumption_resolution,[status(thm)],[f21,f24])).
% 1.66/1.40 thf(f24,plain,(
% 1.66/1.40 ($true != (in @ sK1 @ sK0))),
% 1.66/1.40 inference(definition_unfolding,[status(thm)],[f23,f22])).
% 1.66/1.40 thf(f22,plain,(
% 1.66/1.40 (sK2 = sK0)),
% 1.66/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.40 thf(f16,plain,(
% 1.66/1.40 (($true != (in @ sK1 @ sK2)) & (sK2 = sK0) & ($true = (in @ sK1 @ sK0))) & (notsubsetI = $true) & (notequalI1 = $true)),
% 1.66/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.66/1.40 thf(f15,plain,(
% 1.66/1.40 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) & (X0 = X2) & ((in @ X1 @ X0) = $true)) => (($true != (in @ sK1 @ sK2)) & (sK2 = sK0) & ($true = (in @ sK1 @ sK0)))),
% 1.66/1.40 introduced(definition,[],[choice_axiom])).
% 1.66/1.40 thf(f14,plain,(
% 1.66/1.40 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) & (X0 = X2) & ((in @ X1 @ X0) = $true)) & (notsubsetI = $true) & (notequalI1 = $true)),
% 1.66/1.40 inference(flattening,[status(thm)],[f13])).
% 1.66/1.40 thf(f13,plain,(
% 1.66/1.40 (? [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X2) & ($true != (in @ X1 @ X2))) & ((in @ X1 @ X0) = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)),
% 1.66/1.40 inference(ennf_transformation,[status(thm)],[f12])).
% 1.66/1.40 thf(f12,plain,(
% 1.66/1.40 ~((notsubsetI = $true) => ((notequalI1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (($true != (in @ X1 @ X2)) => (X0 != X2)))))),
% 1.66/1.40 inference(flattening,[status(thm)],[f11])).
% 1.66/1.40 thf(f11,plain,(
% 1.66/1.40 ~((notsubsetI = $true) => ((notequalI1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) => (~($true = (in @ X1 @ X2)) => (X0 != X2)))))),
% 1.66/1.40 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.40 thf(f10,plain,(
% 1.66/1.40 ~(notsubsetI => (notequalI1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (X0 != X2)))))),
% 1.66/1.40 inference(rectify,[status(thm)],[f4])).
% 1.66/1.40 thf(f4,negated_conjecture,(
% 1.66/1.40 ~(notsubsetI => (notequalI1 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (X0 != X1)))))),
% 1.66/1.40 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.40 thf(f3,conjecture,(
% 1.66/1.40 notsubsetI => (notequalI1 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (X0 != X1))))),
% 1.66/1.40 file('/export/starexec/sandbox/tmp/tmp.NWvZmRhoKK/DTF2THF_11049.p',notequalI2)).
% 1.66/1.40 thf(f23,plain,(
% 1.66/1.40 ($true != (in @ sK1 @ sK2))),
% 1.66/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.40 thf(f21,plain,(
% 1.66/1.40 ($true = (in @ sK1 @ sK0))),
% 1.66/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.66/1.40 % SZS output end Proof for DTF2THF_11049
% 1.66/1.40 % (11146)------------------------------
% 1.66/1.40 % (11146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (11146)Termination reason: Refutation
% 1.66/1.40
% 1.66/1.40 % (11146)Memory used [KB]: 5500
% 1.66/1.40 % (11146)Time elapsed: 0.003 s
% 1.66/1.40 % (11146)Instructions burned: 3 (million)
% 1.66/1.40 % (11146)------------------------------
% 1.66/1.40 % (11146)------------------------------
% 1.66/1.40 % (11145)Success in time 0.017 s
%------------------------------------------------------------------------------