%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU578^2 : 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 : n014.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 09:35:23 AM UTC 2026
% Result : Theorem 1.67s 1.40s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 277 ( 81 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 234 ( 39 ~; 24 |; 17 &; 137 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 33 !; 12 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(f42,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f41,f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f28,f27]) ).
thf(f27,plain,
subsetRefl = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( subsetRefl = $true )
& ( powersetI1 = $true )
& ( $true
!= ( in @ sK0 @ ( powerset @ sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f15]) ).
thf(f15,plain,
( ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true )
=> ( $true
!= ( in @ sK0 @ ( powerset @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( subsetRefl = $true )
& ( powersetI1 = $true )
& ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true )
& ( powersetI1 = $true )
& ( subsetRefl = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( subsetRefl = $true )
=> ( ( powersetI1 = $true )
=> ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( subsetRefl
=> ( powersetI1
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetRefl
=> ( powersetI1
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetRefl
=> ( powersetI1
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',inPowerset) ).
thf(f28,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ X1 ) )
| ( subsetRefl != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( subsetRefl = $true )
| ( ( subset @ sK1 @ sK1 )
!= $true ) )
& ( ! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) )
| ( subsetRefl != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true )
=> ( ( subset @ sK1 @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( subsetRefl = $true )
| ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) )
| ( subsetRefl != $true ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( subsetRefl = $true )
| ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ( subsetRefl != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( subsetRefl = $true )
<=> ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',subsetRefl) ).
thf(f41,plain,
( $true
!= ( subset @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f25,f39]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true != $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f26]) ).
thf(f26,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f32,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( $true
= ( subset @ sK3 @ sK2 ) )
& ( ( in @ sK3 @ ( powerset @ sK2 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f22,f23]) ).
thf(f23,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
=> ( ( $true
= ( subset @ sK3 @ sK2 ) )
& ( ( in @ sK3 @ ( powerset @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',powersetI1) ).
thf(f25,plain,
( $true
!= ( in @ sK0 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU578^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n014.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 12:27:42 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 : SEU578^2 : 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.in A (powerset A))
% 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 : ZFC080l [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 : 8 ( 2 unt; 5 typ; 2 def)
% 0.20/0.46 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.20/0.46 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 10 @)
% 0.20/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 6 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=476
% 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(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 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(subsetRefl_type,type,
% 0.20/0.46 subsetRefl: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl,definition,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1_type,type,
% 0.20/0.46 powersetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1,definition,
% 0.20/0.46 ( powersetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset,conjecture,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 => ( powersetI1
% 0.20/0.46 => ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.37 ---- 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 12:27:43 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.FoLQfrDeaP/DTF2DTF21431.p
% See solution above
% 1.50/1.37 ------------------------
% 1.50/1.38 ---- 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(powerset_type,type,
% 1.50/1.38 powerset: $i > $i ).
% 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(subsetRefl_type,type,
% 1.50/1.38 subsetRefl: $o ).
% 1.50/1.38
% 1.50/1.38 thf(subsetRefl,definition,
% 1.50/1.38 ( subsetRefl
% 1.50/1.38 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 1.50/1.38
% 1.50/1.38 thf(powersetI1_type,type,
% 1.50/1.38 powersetI1: $o ).
% 1.50/1.38
% 1.50/1.38 thf(powersetI1,definition,
% 1.50/1.38 ( powersetI1
% 1.50/1.38 = ( ! [A: $i,B: $i] :
% 1.50/1.38 ( ( subset @ B @ A )
% 1.50/1.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.50/1.38
% 1.50/1.38 thf(inPowerset,conjecture,
% 1.50/1.38 ( subsetRefl
% 1.50/1.38 => ( powersetI1
% 1.50/1.38 => ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 1.50/1.38 ------------------------
% 1.67/1.40 % (21529)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_21431 for (3000ds/4Mi)
% 1.67/1.40 % (21530)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_21431 for (3000ds/27Mi)
% 1.67/1.40 % (21528)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21431 for (3000ds/183Mi)
% 1.67/1.40 % (21531)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21431 for (3000ds/2Mi)
% 1.67/1.40 % (21532)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_21431 for (3000ds/2Mi)
% 1.67/1.40 % (21533)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_21431 for (3000ds/275Mi)
% 1.67/1.40 % (21534)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21431 for (3000ds/18Mi)
% 1.67/1.40 % (21531)Instruction limit reached!
% 1.67/1.40 % (21531)------------------------------
% 1.67/1.40 % (21531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (21531)Termination reason: Unknown
% 1.67/1.40 % (21532)Instruction limit reached!
% 1.67/1.40 % (21532)------------------------------
% 1.67/1.40 % (21532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (21531)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (21531)Memory used [KB]: 5500
% 1.67/1.40 % (21531)Time elapsed: 0.003 s
% 1.67/1.40 % (21531)Instructions burned: 2 (million)
% 1.67/1.40 % (21531)------------------------------
% 1.67/1.40 % (21531)------------------------------
% 1.67/1.40 % (21532)Termination reason: Unknown
% 1.67/1.40 % (21532)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (21532)Memory used [KB]: 5500
% 1.67/1.40 % (21532)Time elapsed: 0.003 s
% 1.67/1.40 % (21532)Instructions burned: 2 (million)
% 1.67/1.40 % (21532)------------------------------
% 1.67/1.40 % (21532)------------------------------
% 1.67/1.40 % (21533)First to succeed.
% 1.67/1.40 % (21528)Also succeeded, but the first one will report.
% 1.67/1.40 % (21533)Refutation found. Thanks to Tanya!
% 1.67/1.40 % SZS status Theorem for DTF2THF_21431
% 1.67/1.40 % SZS output start Proof for DTF2THF_21431
% 1.67/1.40 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.40 thf(func_def_1, type, powerset: $i > $i).
% 1.67/1.40 thf(func_def_2, type, subset: $i > $i > $o).
% 1.67/1.40 thf(f42,plain,(
% 1.67/1.40 $false),
% 1.67/1.40 inference(subsumption_resolution,[status(thm)],[f41,f38])).
% 1.67/1.40 thf(f38,plain,(
% 1.67/1.40 ( ! [X1 : $i] : (($true = (subset @ X1 @ X1))) )),
% 1.67/1.40 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.67/1.40 thf(f34,plain,(
% 1.67/1.40 ( ! [X1 : $i] : (($true = (subset @ X1 @ X1)) | ($true != $true)) )),
% 1.67/1.40 inference(definition_unfolding,[status(thm)],[f28,f27])).
% 1.67/1.40 thf(f27,plain,(
% 1.67/1.40 (subsetRefl = $true)),
% 1.67/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.40 thf(f16,plain,(
% 1.67/1.40 (subsetRefl = $true) & (powersetI1 = $true) & ($true != (in @ sK0 @ (powerset @ sK0)))),
% 1.67/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f15])).
% 1.67/1.40 thf(f15,plain,(
% 1.67/1.40 ? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true) => ($true != (in @ sK0 @ (powerset @ sK0)))),
% 1.67/1.40 introduced(definition,[],[choice_axiom])).
% 1.67/1.40 thf(f13,plain,(
% 1.67/1.40 (subsetRefl = $true) & (powersetI1 = $true) & ? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true)),
% 1.67/1.40 inference(flattening,[status(thm)],[f12])).
% 1.67/1.40 thf(f12,plain,(
% 1.67/1.40 (? [X0 : $i] : ((in @ X0 @ (powerset @ X0)) != $true) & (powersetI1 = $true)) & (subsetRefl = $true)),
% 1.67/1.40 inference(ennf_transformation,[status(thm)],[f11])).
% 1.67/1.40 thf(f11,plain,(
% 1.67/1.40 ~((subsetRefl = $true) => ((powersetI1 = $true) => ! [X0 : $i] : ((in @ X0 @ (powerset @ X0)) = $true)))),
% 1.67/1.40 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.40 thf(f10,plain,(
% 1.67/1.40 ~(subsetRefl => (powersetI1 => ! [X0 : $i] : (in @ X0 @ (powerset @ X0))))),
% 1.67/1.40 inference(rectify,[status(thm)],[f4])).
% 1.67/1.40 thf(f4,negated_conjecture,(
% 1.67/1.40 ~(subsetRefl => (powersetI1 => ! [X0 : $i] : (in @ X0 @ (powerset @ X0))))),
% 1.67/1.40 inference(negated_conjecture,[status(cth)],[f3])).
% 1.67/1.40 thf(f3,conjecture,(
% 1.67/1.40 subsetRefl => (powersetI1 => ! [X0 : $i] : (in @ X0 @ (powerset @ X0)))),
% 1.67/1.40 file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',inPowerset)).
% 1.67/1.40 thf(f28,plain,(
% 1.67/1.40 ( ! [X1 : $i] : (($true = (subset @ X1 @ X1)) | (subsetRefl != $true)) )),
% 1.67/1.40 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.40 thf(f20,plain,(
% 1.67/1.40 ((subsetRefl = $true) | ((subset @ sK1 @ sK1) != $true)) & (! [X1 : $i] : ($true = (subset @ X1 @ X1)) | (subsetRefl != $true))),
% 1.67/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f18,f19])).
% 1.67/1.40 thf(f19,plain,(
% 1.67/1.40 ? [X0 : $i] : ((subset @ X0 @ X0) != $true) => ((subset @ sK1 @ sK1) != $true)),
% 1.67/1.40 introduced(definition,[],[choice_axiom])).
% 1.67/1.40 thf(f18,plain,(
% 1.67/1.40 ((subsetRefl = $true) | ? [X0 : $i] : ((subset @ X0 @ X0) != $true)) & (! [X1 : $i] : ($true = (subset @ X1 @ X1)) | (subsetRefl != $true))),
% 1.67/1.40 inference(rectify,[status(thm)],[f17])).
% 1.67/1.40 thf(f17,plain,(
% 1.67/1.40 ((subsetRefl = $true) | ? [X0 : $i] : ((subset @ X0 @ X0) != $true)) & (! [X0 : $i] : ((subset @ X0 @ X0) = $true) | (subsetRefl != $true))),
% 1.67/1.40 inference(nnf_transformation,[status(thm)],[f9])).
% 1.67/1.40 thf(f9,plain,(
% 1.67/1.40 (subsetRefl = $true) <=> ! [X0 : $i] : ((subset @ X0 @ X0) = $true)),
% 1.67/1.40 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.40 thf(f8,plain,(
% 1.67/1.40 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 1.67/1.40 inference(rectify,[status(thm)],[f1])).
% 1.67/1.40 thf(f1,axiom,(
% 1.67/1.40 (subsetRefl = ! [X0 : $i] : (subset @ X0 @ X0))),
% 1.67/1.40 file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',subsetRefl)).
% 1.67/1.40 thf(f41,plain,(
% 1.67/1.40 ($true != (subset @ sK0 @ sK0))),
% 1.67/1.40 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.67/1.40 thf(f40,plain,(
% 1.67/1.40 ($true != $true) | ($true != (subset @ sK0 @ sK0))),
% 1.67/1.40 inference(superposition,[status(thm)],[f25,f39])).
% 1.67/1.40 thf(f39,plain,(
% 1.67/1.40 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) )),
% 1.67/1.40 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.67/1.40 thf(f35,plain,(
% 1.67/1.40 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true != $true) | ((subset @ X1 @ X0) != $true)) )),
% 1.67/1.40 inference(definition_unfolding,[status(thm)],[f32,f26])).
% 1.67/1.40 thf(f26,plain,(
% 1.67/1.40 (powersetI1 = $true)),
% 1.67/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.40 thf(f32,plain,(
% 1.67/1.40 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true) | (powersetI1 != $true)) )),
% 1.67/1.40 inference(cnf_transformation,[status(thm)],[f24])).
% 1.67/1.40 thf(f24,plain,(
% 1.67/1.40 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | (($true = (subset @ sK3 @ sK2)) & ((in @ sK3 @ (powerset @ sK2)) != $true)))),
% 1.67/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f22,f23])).
% 1.67/1.40 thf(f23,plain,(
% 1.67/1.40 ? [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) & ((in @ X3 @ (powerset @ X2)) != $true)) => (($true = (subset @ sK3 @ sK2)) & ((in @ sK3 @ (powerset @ sK2)) != $true))),
% 1.67/1.40 introduced(definition,[],[choice_axiom])).
% 1.67/1.40 thf(f22,plain,(
% 1.67/1.40 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) & ((in @ X3 @ (powerset @ X2)) != $true)))),
% 1.67/1.40 inference(rectify,[status(thm)],[f21])).
% 1.67/1.40 thf(f21,plain,(
% 1.67/1.40 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X1 @ (powerset @ X0)) != $true)))),
% 1.67/1.40 inference(nnf_transformation,[status(thm)],[f14])).
% 1.67/1.40 thf(f14,plain,(
% 1.67/1.40 ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI1 = $true)),
% 1.67/1.40 inference(ennf_transformation,[status(thm)],[f7])).
% 1.67/1.40 thf(f7,plain,(
% 1.67/1.40 ! [X1 : $i,X0 : $i] : (((subset @ X1 @ X0) = $true) => ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI1 = $true)),
% 1.67/1.40 inference(fool_elimination,[status(thm)],[f6])).
% 1.67/1.40 thf(f6,plain,(
% 1.67/1.40 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 1.67/1.40 inference(rectify,[status(thm)],[f2])).
% 1.67/1.40 thf(f2,axiom,(
% 1.67/1.40 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 1.67/1.40 file('/export/starexec/sandbox/tmp/tmp.FoLQfrDeaP/DTF2THF_21431.p',powersetI1)).
% 1.67/1.40 thf(f25,plain,(
% 1.67/1.40 ($true != (in @ sK0 @ (powerset @ sK0)))),
% 1.67/1.40 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.40 % SZS output end Proof for DTF2THF_21431
% 1.67/1.40 % (21533)------------------------------
% 1.67/1.40 % (21533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (21533)Termination reason: Refutation
% 1.67/1.40
% 1.67/1.40 % (21533)Memory used [KB]: 5500
% 1.67/1.40 % (21533)Time elapsed: 0.004 s
% 1.67/1.40 % (21533)Instructions burned: 2 (million)
% 1.67/1.40 % (21533)------------------------------
% 1.67/1.40 % (21533)------------------------------
% 1.67/1.40 % (21527)Success in time 0.008 s
%------------------------------------------------------------------------------