%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU569^2 : 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 : n011.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 1.65s 1.45s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 76 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 248 ( 36 ~; 27 |; 16 &; 154 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 40 !; 12 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i > $i ).
thf(f34,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f33,f22]) ).
thf(f22,plain,
( $true
!= ( subset @ sK3 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( subsetI2 = $true )
& ( $true
!= ( subset @ sK3 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f16]) ).
thf(f16,plain,
( ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true )
=> ( $true
!= ( subset @ sK3 @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( subsetI2 = $true )
& ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( subsetI2 = $true )
=> ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.xQLHD0rn4Z/DTF2THF_4738.p',subsetRefl) ).
thf(f33,plain,
( $true
= ( subset @ sK3 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $true != $true )
| ( $true
= ( subset @ sK3 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f28,f31]) ).
thf(f31,plain,
( $true
= ( in @ ( sK0 @ sK3 @ sK3 ) @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( in @ ( sK0 @ sK3 @ sK3 ) @ sK3 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f22,f29]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK0 @ X1 @ X0 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK0 @ X1 @ X0 ) @ X0 ) )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f21,f23]) ).
thf(f23,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
= ( in @ ( sK0 @ X1 @ X0 ) @ X0 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( $true
= ( in @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( in @ ( sK0 @ X1 @ X0 ) @ X1 ) ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK1 @ sK2 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK1 ) )
| ( $true
= ( in @ X5 @ sK2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( in @ ( sK0 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) ) ) )
=> ( ( $true
!= ( subset @ sK1 @ sK2 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK1 ) )
| ( $true
= ( in @ X5 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ( $true
!= ( subset @ X3 @ X4 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
file('/export/starexec/sandbox/tmp/tmp.xQLHD0rn4Z/DTF2THF_4738.p',subsetI2) ).
thf(f28,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( ( subset @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f20,f23]) ).
thf(f20,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU569^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n011.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:26:47 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEU569^2 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.49 % Domain : Set Theory
% 0.33/0.49 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.33/0.49 % Version : Especial > Reduced > Especial.
% 0.33/0.49 % English : (! A:i.subset A A)
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.33/0.49 % Source : [Bro08]
% 0.33/0.49 % Names : ZFC071l [Bro08]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % 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
% 0.33/0.49 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.33/0.49 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 2 ( 3 avg)
% 0.33/0.49 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.33/0.49 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 5 ( 3 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.33/0.49 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : http://mathgate.info/detsetitem.php?id=475
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(in_type,type,
% 0.33/0.49 in: $i > $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(subset_type,type,
% 0.33/0.49 subset: $i > $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(subsetI2_type,type,
% 0.33/0.49 subsetI2: $o ).
% 0.33/0.49
% 0.33/0.49 thf(subsetI2,definition,
% 0.33/0.49 ( subsetI2
% 0.33/0.49 = ( ! [A: $i,B: $i] :
% 0.33/0.49 ( ! [Xx: $i] :
% 0.33/0.49 ( ( in @ Xx @ A )
% 0.33/0.49 => ( in @ Xx @ B ) )
% 0.33/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(subsetRefl,conjecture,
% 0.33/0.49 ( subsetI2
% 0.33/0.49 => ! [A: $i] : ( subset @ A @ A ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.65/1.41 ---- Embedded in THF ---
% 1.65/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.41 %%% Generated on Tue Feb 24 12:26:48 EST 2026
% 1.65/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.41 %%% Logic specification used:
% 1.65/1.41 %%% thf(spec, logic, $$dhol).
% 1.65/1.41
% 1.65/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xQLHD0rn4Z/DTF2DTF4738.p
% See solution above
% 1.65/1.42 ------------------------
% 1.65/1.42 ---- Cleaned THF ---
% 1.65/1.42 thf(in_type,type,
% 1.65/1.42 in: $i > $i > $o ).
% 1.65/1.42
% 1.65/1.42 thf(subset_type,type,
% 1.65/1.42 subset: $i > $i > $o ).
% 1.65/1.42
% 1.65/1.42 thf(subsetI2_type,type,
% 1.65/1.42 subsetI2: $o ).
% 1.65/1.42
% 1.65/1.42 thf(subsetI2,definition,
% 1.65/1.42 ( subsetI2
% 1.65/1.42 = ( ! [A: $i,B: $i] :
% 1.65/1.42 ( ! [Xx: $i] :
% 1.65/1.42 ( ( in @ Xx @ A )
% 1.65/1.42 => ( in @ Xx @ B ) )
% 1.65/1.42 => ( subset @ A @ B ) ) ) ) ).
% 1.65/1.42
% 1.65/1.42 thf(subsetRefl,conjecture,
% 1.65/1.42 ( subsetI2
% 1.65/1.42 => ! [A: $i] : ( subset @ A @ A ) ) ).
% 1.65/1.42 ------------------------
% 1.65/1.44 % (4841)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4738 for (3000ds/18Mi)
% 1.65/1.44 % (4836)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_4738 for (3000ds/4Mi)
% 1.65/1.44 % (4835)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4738 for (3000ds/183Mi)
% 1.65/1.44 % (4837)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_4738 for (3000ds/27Mi)
% 1.65/1.44 % (4839)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_4738 for (3000ds/2Mi)
% 1.65/1.44 % (4840)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_4738 for (3000ds/275Mi)
% 1.65/1.44 % (4838)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4738 for (3000ds/2Mi)
% 1.65/1.44 % (4840)Refutation not found, incomplete strategy
% 1.65/1.44 % (4840)------------------------------
% 1.65/1.44 % (4840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (4840)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.44
% 1.65/1.44
% 1.65/1.44 % (4840)Memory used [KB]: 5373
% 1.65/1.44 % (4840)Time elapsed: 0.002 s
% 1.65/1.44 % (4840)Instructions burned: 1 (million)
% 1.65/1.44 % (4840)------------------------------
% 1.65/1.44 % (4840)------------------------------
% 1.65/1.44 % (4838)Instruction limit reached!
% 1.65/1.44 % (4838)------------------------------
% 1.65/1.44 % (4838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (4838)Termination reason: Unknown
% 1.65/1.44 % (4838)Termination phase: Saturation
% 1.65/1.44
% 1.65/1.44 % (4838)Memory used [KB]: 5500
% 1.65/1.44 % (4838)Time elapsed: 0.003 s
% 1.65/1.44 % (4838)Instructions burned: 2 (million)
% 1.65/1.44 % (4838)------------------------------
% 1.65/1.44 % (4838)------------------------------
% 1.65/1.44 % (4839)Instruction limit reached!
% 1.65/1.44 % (4839)------------------------------
% 1.65/1.44 % (4839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (4839)Termination reason: Unknown
% 1.65/1.44 % (4839)Termination phase: Saturation
% 1.65/1.44
% 1.65/1.44 % (4839)Memory used [KB]: 5500
% 1.65/1.44 % (4839)Time elapsed: 0.003 s
% 1.65/1.44 % (4839)Instructions burned: 3 (million)
% 1.65/1.44 % (4839)------------------------------
% 1.65/1.44 % (4839)------------------------------
% 1.65/1.45 % (4841)First to succeed.
% 1.65/1.45 % (4836)Instruction limit reached!
% 1.65/1.45 % (4836)------------------------------
% 1.65/1.45 % (4836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (4836)Termination reason: Unknown
% 1.65/1.45 % (4836)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (4836)Memory used [KB]: 5500
% 1.65/1.45 % (4836)Time elapsed: 0.004 s
% 1.65/1.45 % (4836)Instructions burned: 4 (million)
% 1.65/1.45 % (4836)------------------------------
% 1.65/1.45 % (4836)------------------------------
% 1.65/1.45 % (4835)Also succeeded, but the first one will report.
% 1.65/1.45 % (4841)Refutation found. Thanks to Tanya!
% 1.65/1.45 % SZS status Theorem for DTF2THF_4738
% 1.65/1.45 % SZS output start Proof for DTF2THF_4738
% 1.65/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.45 thf(func_def_1, type, subset: $i > $i > $o).
% 1.65/1.45 thf(func_def_6, type, sK0: $i > $i > $i).
% 1.65/1.45 thf(f34,plain,(
% 1.65/1.45 $false),
% 1.65/1.45 inference(subsumption_resolution,[status(thm)],[f33,f22])).
% 1.65/1.45 thf(f22,plain,(
% 1.65/1.45 ($true != (subset @ sK3 @ sK3))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.65/1.45 thf(f17,plain,(
% 1.65/1.45 (subsetI2 = $true) & ($true != (subset @ sK3 @ sK3))),
% 1.65/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f16])).
% 1.65/1.45 thf(f16,plain,(
% 1.65/1.45 ? [X0 : $i] : ((subset @ X0 @ X0) != $true) => ($true != (subset @ sK3 @ sK3))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f9,plain,(
% 1.65/1.45 (subsetI2 = $true) & ? [X0 : $i] : ((subset @ X0 @ X0) != $true)),
% 1.65/1.45 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.45 thf(f6,plain,(
% 1.65/1.45 ~((subsetI2 = $true) => ! [X0 : $i] : ((subset @ X0 @ X0) = $true))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.45 thf(f5,plain,(
% 1.65/1.45 ~(subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0))),
% 1.65/1.45 inference(rectify,[status(thm)],[f3])).
% 1.65/1.45 thf(f3,negated_conjecture,(
% 1.65/1.45 ~(subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0))),
% 1.65/1.45 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.45 thf(f2,conjecture,(
% 1.65/1.45 subsetI2 => ! [X0 : $i] : (subset @ X0 @ X0)),
% 1.65/1.45 file('/export/starexec/sandbox/tmp/tmp.xQLHD0rn4Z/DTF2THF_4738.p',subsetRefl)).
% 1.65/1.45 thf(f33,plain,(
% 1.65/1.45 ($true = (subset @ sK3 @ sK3))),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.65/1.45 thf(f32,plain,(
% 1.65/1.45 ($true != $true) | ($true = (subset @ sK3 @ sK3))),
% 1.65/1.45 inference(superposition,[status(thm)],[f28,f31])).
% 1.65/1.45 thf(f31,plain,(
% 1.65/1.45 ($true = (in @ (sK0 @ sK3 @ sK3) @ sK3))),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.65/1.45 thf(f30,plain,(
% 1.65/1.45 ($true = (in @ (sK0 @ sK3 @ sK3) @ sK3)) | ($true != $true)),
% 1.65/1.45 inference(superposition,[status(thm)],[f22,f29])).
% 1.65/1.45 thf(f29,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK0 @ X1 @ X0) @ X0))) )),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.65/1.45 thf(f24,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ (sK0 @ X1 @ X0) @ X0)) | ((subset @ X0 @ X1) = $true)) )),
% 1.65/1.45 inference(definition_unfolding,[status(thm)],[f21,f23])).
% 1.65/1.45 thf(f23,plain,(
% 1.65/1.45 (subsetI2 = $true)),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f17])).
% 1.65/1.45 thf(f21,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK0 @ X1 @ X0) @ X0)) | (subsetI2 != $true)) )),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 thf(f15,plain,(
% 1.65/1.45 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (($true = (in @ (sK0 @ X1 @ X0) @ X0)) & ($true != (in @ (sK0 @ X1 @ X0) @ X1)))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (($true != (subset @ sK1 @ sK2)) & ! [X5 : $i] : (($true != (in @ X5 @ sK1)) | ($true = (in @ X5 @ sK2)))))),
% 1.65/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13])).
% 1.65/1.45 thf(f13,plain,(
% 1.65/1.45 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (($true = (in @ (sK0 @ X1 @ X0) @ X0)) & ($true != (in @ (sK0 @ X1 @ X0) @ X1))))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f14,plain,(
% 1.65/1.45 ? [X3 : $i,X4 : $i] : (($true != (subset @ X3 @ X4)) & ! [X5 : $i] : (($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4)))) => (($true != (subset @ sK1 @ sK2)) & ! [X5 : $i] : (($true != (in @ X5 @ sK1)) | ($true = (in @ X5 @ sK2))))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f12,plain,(
% 1.65/1.45 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (($true != (subset @ X3 @ X4)) & ! [X5 : $i] : (($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4)))))),
% 1.65/1.45 inference(rectify,[status(thm)],[f11])).
% 1.65/1.45 thf(f11,plain,(
% 1.65/1.45 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))))),
% 1.65/1.45 inference(nnf_transformation,[status(thm)],[f10])).
% 1.65/1.45 thf(f10,plain,(
% 1.65/1.45 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) <=> (subsetI2 = $true)),
% 1.65/1.45 inference(ennf_transformation,[status(thm)],[f8])).
% 1.65/1.45 thf(f8,plain,(
% 1.65/1.45 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.45 thf(f7,plain,(
% 1.65/1.45 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.65/1.45 inference(rectify,[status(thm)],[f1])).
% 1.65/1.45 thf(f1,axiom,(
% 1.65/1.45 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.65/1.45 file('/export/starexec/sandbox/tmp/tmp.xQLHD0rn4Z/DTF2THF_4738.p',subsetI2)).
% 1.65/1.45 thf(f28,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK0 @ X1 @ X0) @ X1)) | ((subset @ X0 @ X1) = $true)) )),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.65/1.45 thf(f25,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true != (in @ (sK0 @ X1 @ X0) @ X1)) | ($true != $true)) )),
% 1.65/1.45 inference(definition_unfolding,[status(thm)],[f20,f23])).
% 1.65/1.45 thf(f20,plain,(
% 1.65/1.45 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true != (in @ (sK0 @ X1 @ X0) @ X1)) | (subsetI2 != $true)) )),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.45 % SZS output end Proof for DTF2THF_4738
% 1.65/1.45 % (4841)------------------------------
% 1.65/1.45 % (4841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (4841)Termination reason: Refutation
% 1.65/1.45
% 1.65/1.45 % (4841)Memory used [KB]: 5500
% 1.65/1.45 % (4841)Time elapsed: 0.004 s
% 1.65/1.45 % (4841)Instructions burned: 3 (million)
% 1.65/1.45 % (4841)------------------------------
% 1.65/1.45 % (4841)------------------------------
% 1.65/1.45 % (4834)Success in time 0.018 s
%------------------------------------------------------------------------------