%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU521^2 : 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 : n009.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 09:35:03 AM UTC 2026
% Result : Theorem 1.64s 1.33s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 294 ( 10 ~; 9 |; 13 &; 217 @)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 7 con; 0-2 aty)
% ( 17 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 68 ( 20 ^; 39 !; 9 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK4: $i > $i > $i ).
thf(f42,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f16,f40]) ).
thf(f40,plain,
( $false
= ( in @ sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( $false
= ( in @ sK0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f14,f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f15,f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f17,f13]) ).
thf(f13,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( powersetAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
=> ( ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( powersetAx = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( powersetAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( powersetAx = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( powersetAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( powersetAx
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( powersetAx
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.487NeeJufe/DTF2THF_4574.p',powersetE) ).
thf(f17,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
<=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( powersetAx
= ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
<=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.487NeeJufe/DTF2THF_4574.p',powersetAx) ).
thf(f15,plain,
( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f16,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU521^2 : 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
% 0.17/0.34 % Computer : n009.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 12:25:25 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU521^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Power Sets and Unions
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! B:i.! x:i.in B (powerset A) -> in x B -> in x A)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC023l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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
% 0.30/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.30/0.46 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.46 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 14 @)
% 0.30/0.46 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=86
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE,conjecture,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 12:25:25 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.487NeeJufe/DTF2DTF4574.p
% See solution above
% 1.47/1.29 ------------------------
% 1.47/1.30 ---- Cleaned THF ---
% 1.64/1.30 thf(in_type,type,
% 1.64/1.30 in: $i > $i > $o ).
% 1.64/1.30
% 1.64/1.30 thf(powerset_type,type,
% 1.64/1.30 powerset: $i > $i ).
% 1.64/1.30
% 1.64/1.30 thf(powersetAx_type,type,
% 1.64/1.30 powersetAx: $o ).
% 1.64/1.30
% 1.64/1.30 thf(powersetAx,definition,
% 1.64/1.30 ( powersetAx
% 1.64/1.30 = ( ! [A: $i,B: $i] :
% 1.64/1.30 ( ( in @ B @ ( powerset @ A ) )
% 1.64/1.30 <=> ! [Xx: $i] :
% 1.64/1.30 ( ( in @ Xx @ B )
% 1.64/1.30 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.64/1.30
% 1.64/1.30 thf(powersetE,conjecture,
% 1.64/1.30 ( powersetAx
% 1.64/1.30 => ! [A: $i,B: $i,Xx: $i] :
% 1.64/1.30 ( ( in @ B @ ( powerset @ A ) )
% 1.64/1.30 => ( ( in @ Xx @ B )
% 1.64/1.30 => ( in @ Xx @ A ) ) ) ) ).
% 1.64/1.30 ------------------------
% 1.64/1.31 % (4692)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_4574 for (2999ds/2Mi)
% 1.64/1.31 % (4692)Instruction limit reached!
% 1.64/1.31 % (4692)------------------------------
% 1.64/1.31 % (4692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (4692)Termination reason: Unknown
% 1.64/1.31 % (4692)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (4692)Memory used [KB]: 895
% 1.64/1.31 % (4692)Time elapsed: 0.002 s
% 1.64/1.31 % (4692)Instructions burned: 2 (million)
% 1.64/1.31 % (4692)------------------------------
% 1.64/1.31 % (4692)------------------------------
% 1.64/1.32 % (4688)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4574 for (2999ds/183Mi)
% 1.64/1.32 % (4689)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_4574 for (2999ds/4Mi)
% 1.64/1.32 % (4691)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4574 for (2999ds/2Mi)
% 1.64/1.32 % (4690)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_4574 for (2999ds/27Mi)
% 1.64/1.32 % (4693)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_4574 for (2999ds/275Mi)
% 1.64/1.32 % (4694)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4574 for (2999ds/18Mi)
% 1.64/1.32 % (4691)Instruction limit reached!
% 1.64/1.32 % (4691)------------------------------
% 1.64/1.32 % (4691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (4691)Termination reason: Unknown
% 1.64/1.32 % (4691)Termination phase: Function definition elimination
% 1.64/1.32
% 1.64/1.32 % (4691)Memory used [KB]: 895
% 1.64/1.32 % (4691)Time elapsed: 0.003 s
% 1.64/1.32 % (4691)Instructions burned: 2 (million)
% 1.64/1.32 % (4691)------------------------------
% 1.64/1.32 % (4691)------------------------------
% 1.64/1.32 % (4695)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4574 for (2999ds/3Mi)
% 1.64/1.32 % (4689)Instruction limit reached!
% 1.64/1.32 % (4689)------------------------------
% 1.64/1.32 % (4689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (4689)Termination reason: Unknown
% 1.64/1.32 % (4689)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (4689)Memory used [KB]: 5500
% 1.64/1.32 % (4689)Time elapsed: 0.005 s
% 1.64/1.32 % (4689)Instructions burned: 4 (million)
% 1.64/1.32 % (4689)------------------------------
% 1.64/1.32 % (4689)------------------------------
% 1.64/1.32 % (4695)Refutation not found, incomplete strategy
% 1.64/1.32 % (4695)------------------------------
% 1.64/1.32 % (4695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (4695)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.32
% 1.64/1.32
% 1.64/1.32 % (4695)Memory used [KB]: 5500
% 1.64/1.32 % (4695)Time elapsed: 0.002 s
% 1.64/1.32 % (4695)Instructions burned: 1 (million)
% 1.64/1.32 % (4695)------------------------------
% 1.64/1.32 % (4695)------------------------------
% 1.64/1.32 % (4690)First to succeed.
% 1.64/1.32 % (4693)Also succeeded, but the first one will report.
% 1.64/1.33 % (4690)Refutation found. Thanks to Tanya!
% 1.64/1.33 % SZS status Theorem for DTF2THF_4574
% 1.64/1.33 % SZS output start Proof for DTF2THF_4574
% 1.64/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.33 thf(func_def_1, type, powerset: $i > $i).
% 1.64/1.33 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.33 thf(func_def_18, type, sK4: $i > $i > $i).
% 1.64/1.33 thf(f42,plain,(
% 1.64/1.33 $false),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.64/1.33 thf(f41,plain,(
% 1.64/1.33 ($false = $true)),
% 1.64/1.33 inference(backward_demodulation,[status(thm)],[f16,f40])).
% 1.64/1.33 thf(f40,plain,(
% 1.64/1.33 ($false = (in @ sK0 @ sK2))),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.64/1.33 thf(f39,plain,(
% 1.64/1.33 ($true != $true) | ($false = (in @ sK0 @ sK2))),
% 1.64/1.33 inference(superposition,[status(thm)],[f14,f36])).
% 1.64/1.33 thf(f36,plain,(
% 1.64/1.33 ( ! [X0 : $i] : (($true = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK2))) )),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.64/1.33 thf(f34,plain,(
% 1.64/1.33 ( ! [X0 : $i] : (($false = (in @ X0 @ sK2)) | ($true = (in @ X0 @ sK1)) | ($false = $true)) )),
% 1.64/1.33 inference(superposition,[status(thm)],[f15,f28])).
% 1.64/1.33 thf(f28,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ X2)) | ((in @ X3 @ X1) = $true)) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.64/1.33 thf(f27,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((in @ X3 @ X2) => (in @ X3 @ X1)) = $true)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.64/1.33 thf(f26,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ X3) = $true)) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f25])).
% 1.64/1.33 thf(f25,plain,(
% 1.64/1.33 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))))) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.64/1.33 thf(f23,plain,(
% 1.64/1.33 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.33 thf(f22,plain,(
% 1.64/1.33 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.33 thf(f21,plain,(
% 1.64/1.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1)))) @ X2) = $true)) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f20])).
% 1.64/1.33 thf(f20,plain,(
% 1.64/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1))))) = $true)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.64/1.33 thf(f19,plain,(
% 1.64/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f18])).
% 1.64/1.33 thf(f18,plain,(
% 1.64/1.33 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) = $true)),
% 1.64/1.33 inference(definition_unfolding,[status(thm)],[f17,f13])).
% 1.64/1.33 thf(f13,plain,(
% 1.64/1.33 (powersetAx = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.33 thf(f12,plain,(
% 1.64/1.33 (((in @ sK0 @ sK2) = $true) & ((in @ sK2 @ (powerset @ sK1)) = $true) & ((in @ sK0 @ sK1) != $true)) & (powersetAx = $true)),
% 1.64/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.64/1.33 thf(f11,plain,(
% 1.64/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ((in @ X2 @ (powerset @ X1)) = $true) & ((in @ X0 @ X1) != $true)) => (((in @ sK0 @ sK2) = $true) & ((in @ sK2 @ (powerset @ sK1)) = $true) & ((in @ sK0 @ sK1) != $true))),
% 1.64/1.33 introduced(definition,[],[choice_axiom])).
% 1.64/1.33 thf(f10,plain,(
% 1.64/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ((in @ X2 @ (powerset @ X1)) = $true) & ((in @ X0 @ X1) != $true)) & (powersetAx = $true)),
% 1.64/1.33 inference(flattening,[status(thm)],[f9])).
% 1.64/1.33 thf(f9,plain,(
% 1.64/1.33 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1) != $true) & ($true = (in @ X0 @ X2))) & ((in @ X2 @ (powerset @ X1)) = $true)) & (powersetAx = $true)),
% 1.64/1.33 inference(ennf_transformation,[status(thm)],[f8])).
% 1.64/1.33 thf(f8,plain,(
% 1.64/1.33 ~((powersetAx = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (($true = (in @ X0 @ X2)) => ((in @ X0 @ X1) = $true))))),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.33 thf(f7,plain,(
% 1.64/1.33 ~(powersetAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 1.64/1.33 inference(rectify,[status(thm)],[f3])).
% 1.64/1.33 thf(f3,negated_conjecture,(
% 1.64/1.33 ~(powersetAx => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 1.64/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.33 thf(f2,conjecture,(
% 1.64/1.33 powersetAx => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0)))),
% 1.64/1.33 file('/export/starexec/sandbox/tmp/tmp.487NeeJufe/DTF2THF_4574.p',powersetE)).
% 1.64/1.33 thf(f17,plain,(
% 1.64/1.33 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 1.64/1.33 thf(f6,plain,(
% 1.64/1.33 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.33 thf(f5,plain,(
% 1.64/1.33 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))))),
% 1.64/1.33 inference(rectify,[status(thm)],[f1])).
% 1.64/1.33 thf(f1,axiom,(
% 1.64/1.33 (powersetAx = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))))),
% 1.64/1.33 file('/export/starexec/sandbox/tmp/tmp.487NeeJufe/DTF2THF_4574.p',powersetAx)).
% 1.64/1.33 thf(f15,plain,(
% 1.64/1.33 ((in @ sK2 @ (powerset @ sK1)) = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.33 thf(f14,plain,(
% 1.64/1.33 ((in @ sK0 @ sK1) != $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.33 thf(f16,plain,(
% 1.64/1.33 ((in @ sK0 @ sK2) = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.33 % SZS output end Proof for DTF2THF_4574
% 1.64/1.33 % (4690)------------------------------
% 1.64/1.33 % (4690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (4690)Termination reason: Refutation
% 1.64/1.33
% 1.64/1.33 % (4690)Memory used [KB]: 5500
% 1.64/1.33 % (4690)Time elapsed: 0.007 s
% 1.64/1.33 % (4690)Instructions burned: 4 (million)
% 1.64/1.33 % (4690)------------------------------
% 1.64/1.33 % (4690)------------------------------
% 1.64/1.33 % (4687)Success in time 0.013 s
%------------------------------------------------------------------------------