%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU566^2 : 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 : n027.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 09:35:18 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 97 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 318 ( 55 ~; 28 |; 29 &; 180 @)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 50 !; 21 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f38,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f37,f21]) ).
thf(f21,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subsetE = $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( subset @ sK2 @ sK1 )
= $true )
& ( ( in @ sK0 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
=> ( ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( subset @ sK2 @ sK1 )
= $true )
& ( ( in @ sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( subsetE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( subsetE = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( subsetE = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( subset @ X1 @ X2 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( subsetE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( subset @ X1 @ X2 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( subsetE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ~ ( subset @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( subsetE
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( subsetE
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( subset @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1YBNno61RV/DTF2THF_351.p',notsubsetI) ).
thf(f37,plain,
( ( in @ sK0 @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( in @ sK0 @ sK2 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f35,f22]) ).
thf(f22,plain,
( ( subset @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f35,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK1 )
!= $true )
| ( ( in @ sK0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i] :
( ( ( in @ sK0 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f23,f33]) ).
thf(f33,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f25,f24]) ).
thf(f24,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f25,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( subsetE = $true )
| ( ( ( in @ sK4 @ sK3 )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true ) )
=> ( ( ( in @ sK4 @ sK3 )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true )
& ( ( subset @ sK3 @ sK5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( subset @ X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( subsetE = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetE
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1YBNno61RV/DTF2THF_351.p',subsetE) ).
thf(f23,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU566^2 : 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
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:27:22 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU566^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> ~(subset A B))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC068l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % 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
% 0.20/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.46 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.46 % Number of connectives : 19 ( 2 ~; 0 |; 0 &; 12 @)
% 0.20/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 6 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=438
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI,conjecture,
% 0.20/0.46 ( subsetE
% 0.20/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 12:27:23 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1YBNno61RV/DTF2DTF351.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(in_type,type,
% 1.46/1.29 in: $i > $i > $o ).
% 1.46/1.29
% 1.46/1.29 thf(subset_type,type,
% 1.46/1.29 subset: $i > $i > $o ).
% 1.46/1.29
% 1.46/1.29 thf(subsetE_type,type,
% 1.46/1.29 subsetE: $o ).
% 1.46/1.29
% 1.46/1.29 thf(subsetE,definition,
% 1.46/1.29 ( subsetE
% 1.46/1.29 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.46/1.29 ( ( subset @ A @ B )
% 1.46/1.29 => ( ( in @ Xx @ A )
% 1.46/1.29 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.46/1.29
% 1.46/1.29 thf(notsubsetI,conjecture,
% 1.46/1.29 ( subsetE
% 1.46/1.29 => ! [A: $i,B: $i,Xx: $i] :
% 1.46/1.29 ( ( in @ Xx @ A )
% 1.46/1.29 => ( ~ ( in @ Xx @ B )
% 1.46/1.29 => ~ ( subset @ A @ B ) ) ) ) ).
% 1.46/1.29 ------------------------
% 1.61/1.31 % (730)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_351 for (2999ds/275Mi)
% 1.61/1.31 % (731)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/18Mi)
% 1.61/1.31 % (730)First to succeed.
% 1.61/1.31 % (731)Also succeeded, but the first one will report.
% 1.61/1.31 % (730)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_351
% 1.61/1.31 % SZS output start Proof for DTF2THF_351
% 1.61/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.61/1.31 thf(func_def_1, type, subset: $i > $i > $o).
% 1.61/1.31 thf(f38,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(subsumption_resolution,[status(thm)],[f37,f21])).
% 1.61/1.31 thf(f21,plain,(
% 1.61/1.31 ((in @ sK0 @ sK2) = $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.31 thf(f16,plain,(
% 1.61/1.31 (subsetE = $true) & (((in @ sK0 @ sK1) != $true) & ((subset @ sK2 @ sK1) = $true) & ((in @ sK0 @ sK2) = $true))),
% 1.61/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.61/1.31 thf(f15,plain,(
% 1.61/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ((subset @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true)) => (((in @ sK0 @ sK1) != $true) & ((subset @ sK2 @ sK1) = $true) & ((in @ sK0 @ sK2) = $true))),
% 1.61/1.31 introduced(definition,[],[choice_axiom])).
% 1.61/1.31 thf(f14,plain,(
% 1.61/1.31 (subsetE = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) & ((subset @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true))),
% 1.61/1.31 inference(rectify,[status(thm)],[f11])).
% 1.61/1.31 thf(f11,plain,(
% 1.61/1.31 (subsetE = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) & ((subset @ X1 @ X2) = $true) & ((in @ X0 @ X1) = $true))),
% 1.61/1.31 inference(flattening,[status(thm)],[f10])).
% 1.61/1.31 thf(f10,plain,(
% 1.61/1.31 ? [X1 : $i,X2 : $i,X0 : $i] : ((((subset @ X1 @ X2) = $true) & ((in @ X0 @ X2) != $true)) & ((in @ X0 @ X1) = $true)) & (subsetE = $true)),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 ~((subsetE = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ((subset @ X1 @ X2) != $true))))),
% 1.61/1.31 inference(flattening,[status(thm)],[f6])).
% 1.61/1.31 thf(f6,plain,(
% 1.61/1.31 ~((subsetE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ~((subset @ X1 @ X2) = $true))))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.61/1.31 thf(f5,plain,(
% 1.61/1.31 ~(subsetE => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => ~(subset @ X1 @ X2))))),
% 1.61/1.31 inference(rectify,[status(thm)],[f3])).
% 1.61/1.31 thf(f3,negated_conjecture,(
% 1.61/1.31 ~(subsetE => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.61/1.31 thf(f2,conjecture,(
% 1.61/1.31 subsetE => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1)))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.1YBNno61RV/DTF2THF_351.p',notsubsetI)).
% 1.61/1.31 thf(f37,plain,(
% 1.61/1.31 ((in @ sK0 @ sK2) != $true)),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.61/1.31 thf(f36,plain,(
% 1.61/1.31 ((in @ sK0 @ sK2) != $true) | ($true != $true)),
% 1.61/1.31 inference(superposition,[status(thm)],[f35,f22])).
% 1.61/1.31 thf(f22,plain,(
% 1.61/1.31 ((subset @ sK2 @ sK1) = $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.31 thf(f35,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((subset @ X0 @ sK1) != $true) | ((in @ sK0 @ X0) != $true)) )),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.61/1.31 thf(f34,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((in @ sK0 @ X0) != $true) | ((subset @ X0 @ sK1) != $true) | ($true != $true)) )),
% 1.61/1.31 inference(superposition,[status(thm)],[f23,f33])).
% 1.61/1.31 thf(f33,plain,(
% 1.61/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true) | ((in @ X4 @ X3) != $true)) )),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.61/1.31 thf(f32,plain,(
% 1.61/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ((subset @ X3 @ X5) != $true) | ((in @ X4 @ X5) = $true) | ($true != $true)) )),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f25,f24])).
% 1.61/1.31 thf(f24,plain,(
% 1.61/1.31 (subsetE = $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.31 thf(f25,plain,(
% 1.61/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true) | (subsetE != $true)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.31 thf(f20,plain,(
% 1.61/1.31 ((subsetE = $true) | (((in @ sK4 @ sK3) = $true) & ((in @ sK4 @ sK5) != $true) & ((subset @ sK3 @ sK5) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true)) | (subsetE != $true))),
% 1.61/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f18,f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ X2) != $true) & ((subset @ X0 @ X2) = $true)) => (((in @ sK4 @ sK3) = $true) & ((in @ sK4 @ sK5) != $true) & ((subset @ sK3 @ sK5) = $true))),
% 1.61/1.31 introduced(definition,[],[choice_axiom])).
% 1.61/1.31 thf(f18,plain,(
% 1.61/1.31 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ X2) != $true) & ((subset @ X0 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ((in @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true)) | (subsetE != $true))),
% 1.61/1.31 inference(rectify,[status(thm)],[f17])).
% 1.61/1.31 thf(f17,plain,(
% 1.61/1.31 ((subsetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true) & ((subset @ X1 @ X2) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true)) | (subsetE != $true))),
% 1.61/1.31 inference(nnf_transformation,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 (subsetE = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true))),
% 1.61/1.31 inference(flattening,[status(thm)],[f12])).
% 1.61/1.31 thf(f12,plain,(
% 1.61/1.31 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ((subset @ X1 @ X2) != $true))),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true)))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.61/1.31 thf(f7,plain,(
% 1.61/1.31 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 1.61/1.31 inference(rectify,[status(thm)],[f1])).
% 1.61/1.31 thf(f1,axiom,(
% 1.61/1.31 (subsetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.1YBNno61RV/DTF2THF_351.p',subsetE)).
% 1.61/1.31 thf(f23,plain,(
% 1.61/1.31 ((in @ sK0 @ sK1) != $true)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.31 % SZS output end Proof for DTF2THF_351
% 1.61/1.31 % (730)------------------------------
% 1.61/1.31 % (730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (730)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (730)Memory used [KB]: 5500
% 1.61/1.31 % (730)Time elapsed: 0.003 s
% 1.61/1.31 % (730)Instructions burned: 2 (million)
% 1.61/1.31 % (730)------------------------------
% 1.61/1.31 % (730)------------------------------
% 1.61/1.31 % (722)Success in time 0.013 s
%------------------------------------------------------------------------------