%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU727^2 : 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 : n007.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 09:36:42 AM UTC 2026
% Result : Theorem 1.30s 1.16s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 434 ( 91 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 611 ( 47 ~; 20 |; 25 &; 431 @)
% ( 2 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 10 con; 0-2 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 110 ( 36 ^; 63 !; 11 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
setminus: $i > $i > $i ).
thf(f98,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f59,f65,f97]) ).
thf(f97,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f70,f23]) ).
thf(f23,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setminusI = $true )
& ( ( in @ sK2 @ sK0 )
= $true )
& ( $true
!= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( setminusER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
& ( ( in @ X2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) )
!= $true )
& ( $true
= ( in @ X2 @ sK1 ) ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ sK0 )
= $true )
& ( ( in @ X2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) )
!= $true )
& ( $true
= ( in @ X2 @ sK1 ) ) )
=> ( ( ( in @ sK2 @ sK0 )
= $true )
& ( $true
!= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) )
& ( ( in @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setminusI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setminusI
=> ( setminusER
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',doubleComplementI1) ).
thf(f70,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f34,f54]) ).
thf(f54,plain,
( ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl3_1
<=> ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( in @ X3 @ X2 ) )
= $true )
| ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ Y0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f17]) ).
thf(f17,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ~ ( in @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) )
= setminusER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',setminusER) ).
thf(f19,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f65,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f21,f58]) ).
thf(f58,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl3_2
<=> ( ( in @ sK2 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f59,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f48,f56,f52]) ).
thf(f48,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( in @ sK2 @ sK1 )
= $false )
| ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f22,f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X2 @ X1 ) )
= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
= $false )
| ( ( ~ ( in @ X3 @ X1 ) )
= $false )
| ( ( in @ X3 @ ( setminus @ X2 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ X1 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
=> ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f24,f18]) ).
thf(f18,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ~ ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setminusI
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',setminusI) ).
thf(f24,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f22,plain,
( $true
!= ( in @ sK2 @ ( setminus @ sK1 @ ( setminus @ sK1 @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU727^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:31:23 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEU727^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.44 % Domain : Set Theory
% 0.16/0.44 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.16/0.44 % Version : Especial > Reduced > Especial.
% 0.16/0.44 % English : (! A:i.! X:i.in X (powerset A) -> (! x:i.in x A -> in x X ->
% 0.16/0.44 % in x (setminus A (setminus A X))))
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.44 % Source : [Bro08]
% 0.16/0.44 % Names : ZFC229l [Bro08]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.16/0.44 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.16/0.44 % Number of atoms : 15 ( 2 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 6 ( 5 avg)
% 0.16/0.44 % Number of connectives : 37 ( 2 ~; 0 |; 0 &; 27 @)
% 0.16/0.44 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 13 ( 5 avg)
% 0.16/0.44 % Number of types : 2 ( 0 usr)
% 0.16/0.44 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.16/0.44 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : http://mathgate.info/detsetitem.php?id=287
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(in_type,type,
% 0.16/0.44 in: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(powerset_type,type,
% 0.16/0.44 powerset: $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setminus_type,type,
% 0.16/0.44 setminus: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setminusI_type,type,
% 0.16/0.44 setminusI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusI,definition,
% 0.16/0.44 ( setminusI
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ~ ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setminusER_type,type,
% 0.16/0.44 setminusER: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setminusER,definition,
% 0.16/0.44 ( setminusER
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.44 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(doubleComplementI1,conjecture,
% 0.16/0.44 ( setminusI
% 0.16/0.44 => ( setminusER
% 0.16/0.44 => ! [A: $i,X: $i] :
% 0.16/0.44 ( ( in @ X @ ( powerset @ A ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( in @ Xx @ X )
% 0.16/0.44 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 1.30/1.13 ---- Embedded in THF ---
% 1.30/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.13 %%% Generated on Tue Feb 24 12:31:24 EST 2026
% 1.30/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.13 %%% Logic specification used:
% 1.30/1.13 %%% thf(spec, logic, $$dhol).
% 1.30/1.13
% 1.30/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2DTF10265.p
% See solution above
% 1.30/1.13 ------------------------
% 1.30/1.14 ---- Cleaned THF ---
% 1.30/1.14 thf(in_type,type,
% 1.30/1.14 in: $i > $i > $o ).
% 1.30/1.14
% 1.30/1.14 thf(powerset_type,type,
% 1.30/1.14 powerset: $i > $i ).
% 1.30/1.14
% 1.30/1.14 thf(setminus_type,type,
% 1.30/1.14 setminus: $i > $i > $i ).
% 1.30/1.14
% 1.30/1.14 thf(setminusI_type,type,
% 1.30/1.14 setminusI: $o ).
% 1.30/1.14
% 1.30/1.14 thf(setminusI,definition,
% 1.30/1.14 ( setminusI
% 1.30/1.14 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.30/1.14 ( ( in @ Xx @ A )
% 1.30/1.14 => ( ~ ( in @ Xx @ B )
% 1.30/1.14 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.30/1.14
% 1.30/1.14 thf(setminusER_type,type,
% 1.30/1.14 setminusER: $o ).
% 1.30/1.14
% 1.30/1.14 thf(setminusER,definition,
% 1.30/1.14 ( setminusER
% 1.30/1.14 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.30/1.14 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.30/1.14 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.30/1.14
% 1.30/1.14 thf(doubleComplementI1,conjecture,
% 1.30/1.14 ( setminusI
% 1.30/1.14 => ( setminusER
% 1.30/1.14 => ! [A: $i,X: $i] :
% 1.30/1.14 ( ( in @ X @ ( powerset @ A ) )
% 1.30/1.14 => ! [Xx: $i] :
% 1.30/1.14 ( ( in @ Xx @ A )
% 1.30/1.14 => ( ( in @ Xx @ X )
% 1.30/1.14 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 1.30/1.14 ------------------------
% 1.30/1.16 % (10364)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10265 for (2999ds/183Mi)
% 1.30/1.16 % (10364)First to succeed.
% 1.30/1.16 % (10364)Refutation found. Thanks to Tanya!
% 1.30/1.16 % SZS status Theorem for DTF2THF_10265
% 1.30/1.16 % SZS output start Proof for DTF2THF_10265
% 1.30/1.16 thf(func_def_0, type, in: $i > $i > $o).
% 1.30/1.16 thf(func_def_1, type, powerset: $i > $i).
% 1.30/1.16 thf(func_def_2, type, setminus: $i > $i > $i).
% 1.30/1.16 thf(f98,plain,(
% 1.30/1.16 $false),
% 1.30/1.16 inference(avatar_sat_refutation,[status(thm)],[f59,f65,f97])).
% 1.30/1.16 thf(f97,plain,(
% 1.30/1.16 ~spl3_1),
% 1.30/1.16 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.30/1.16 thf(f96,plain,(
% 1.30/1.16 $false | ~spl3_1),
% 1.30/1.16 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.30/1.16 thf(f92,plain,(
% 1.30/1.16 ($false = $true) | ~spl3_1),
% 1.30/1.16 inference(superposition,[status(thm)],[f70,f23])).
% 1.30/1.16 thf(f23,plain,(
% 1.30/1.16 ((in @ sK2 @ sK0) = $true)),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f16])).
% 1.30/1.16 thf(f16,plain,(
% 1.30/1.16 (setminusI = $true) & ((((in @ sK2 @ sK0) = $true) & ($true != (in @ sK2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0)))) & ((in @ sK2 @ sK1) = $true)) & ((in @ sK0 @ (powerset @ sK1)) = $true)) & (setminusER = $true)),
% 1.30/1.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15,f14])).
% 1.30/1.16 thf(f14,plain,(
% 1.30/1.16 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) != $true) & ((in @ X2 @ X1) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (((in @ X2 @ sK0) = $true) & ((in @ X2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0))) != $true) & ($true = (in @ X2 @ sK1))) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 1.30/1.16 introduced(definition,[],[choice_axiom])).
% 1.30/1.16 thf(f15,plain,(
% 1.30/1.16 ? [X2 : $i] : (((in @ X2 @ sK0) = $true) & ((in @ X2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0))) != $true) & ($true = (in @ X2 @ sK1))) => (((in @ sK2 @ sK0) = $true) & ($true != (in @ sK2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0)))) & ((in @ sK2 @ sK1) = $true))),
% 1.30/1.16 introduced(definition,[],[choice_axiom])).
% 1.30/1.16 thf(f13,plain,(
% 1.30/1.16 (setminusI = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) != $true) & ((in @ X2 @ X1) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (setminusER = $true)),
% 1.30/1.16 inference(flattening,[status(thm)],[f12])).
% 1.30/1.16 thf(f12,plain,(
% 1.30/1.16 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) != $true) & ((in @ X2 @ X0) = $true)) & ((in @ X2 @ X1) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (setminusER = $true)) & (setminusI = $true)),
% 1.30/1.16 inference(ennf_transformation,[status(thm)],[f7])).
% 1.30/1.16 thf(f7,plain,(
% 1.30/1.16 ~((setminusI = $true) => ((setminusER = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))) = $true))))))),
% 1.30/1.16 inference(fool_elimination,[status(thm)],[f6])).
% 1.30/1.16 thf(f6,plain,(
% 1.30/1.16 ~(setminusI => (setminusER => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ (setminus @ X1 @ X0))))))))),
% 1.30/1.16 inference(rectify,[status(thm)],[f4])).
% 1.30/1.16 thf(f4,negated_conjecture,(
% 1.30/1.16 ~(setminusI => (setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X3))))))))),
% 1.30/1.16 inference(negated_conjecture,[status(cth)],[f3])).
% 1.30/1.16 thf(f3,conjecture,(
% 1.30/1.16 setminusI => (setminusER => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ (setminus @ X0 @ (setminus @ X0 @ X3)))))))),
% 1.30/1.16 file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',doubleComplementI1)).
% 1.30/1.16 thf(f70,plain,(
% 1.30/1.16 ($false = (in @ sK2 @ sK0)) | ~spl3_1),
% 1.30/1.16 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.30/1.16 thf(f68,plain,(
% 1.30/1.16 ($false = (in @ sK2 @ sK0)) | ($false = $true) | ~spl3_1),
% 1.30/1.16 inference(superposition,[status(thm)],[f34,f54])).
% 1.30/1.16 thf(f54,plain,(
% 1.30/1.16 ($true = (in @ sK2 @ (setminus @ sK1 @ sK0))) | ~spl3_1),
% 1.30/1.16 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.30/1.16 thf(f52,definition,(
% 1.30/1.16 spl3_1 <=> ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))),
% 1.30/1.16 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.30/1.16 thf(f34,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (setminus @ X1 @ X2))) | ((in @ X3 @ X2) = $false)) )),
% 1.30/1.16 inference(not_proxy_clausification,[status(thm)],[f33])).
% 1.30/1.16 thf(f33,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (in @ X3 @ X2)) = $true) | ($false = (in @ X3 @ (setminus @ X1 @ X2)))) )),
% 1.30/1.16 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.30/1.16 thf(f32,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (setminus @ X1 @ X2)) => (~ (in @ X3 @ X2))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.30/1.16 thf(f31,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (~ (in @ Y0 @ X2)))) @ X3))) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f30])).
% 1.30/1.16 thf(f30,plain,(
% 1.30/1.16 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (~ (in @ Y0 @ X2))))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.30/1.16 thf(f29,plain,(
% 1.30/1.16 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (~ (in @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f28])).
% 1.30/1.16 thf(f28,plain,(
% 1.30/1.16 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (~ (in @ Y1 @ Y0))))))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.30/1.16 thf(f27,plain,(
% 1.30/1.16 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1)))))))) @ X1) = $true)) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f26])).
% 1.30/1.16 thf(f26,plain,(
% 1.30/1.16 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))) = $true)),
% 1.30/1.16 inference(definition_unfolding,[status(thm)],[f19,f17])).
% 1.30/1.16 thf(f17,plain,(
% 1.30/1.16 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))))),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f11])).
% 1.30/1.16 thf(f11,plain,(
% 1.30/1.16 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (~ (in @ Y2 @ Y1))))))))))),
% 1.30/1.16 inference(fool_elimination,[status(thm)],[f10])).
% 1.30/1.16 thf(f10,plain,(
% 1.30/1.16 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)) = setminusER)),
% 1.30/1.16 inference(rectify,[status(thm)],[f2])).
% 1.30/1.16 thf(f2,axiom,(
% 1.30/1.16 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)) = setminusER)),
% 1.30/1.16 file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',setminusER)).
% 1.30/1.16 thf(f19,plain,(
% 1.30/1.16 (setminusER = $true)),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f16])).
% 1.30/1.16 thf(f65,plain,(
% 1.30/1.16 ~spl3_2),
% 1.30/1.16 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.30/1.16 thf(f64,plain,(
% 1.30/1.16 $false | ~spl3_2),
% 1.30/1.16 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.30/1.16 thf(f61,plain,(
% 1.30/1.16 ($false = $true) | ~spl3_2),
% 1.30/1.16 inference(superposition,[status(thm)],[f21,f58])).
% 1.30/1.16 thf(f58,plain,(
% 1.30/1.16 ((in @ sK2 @ sK1) = $false) | ~spl3_2),
% 1.30/1.16 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.30/1.16 thf(f56,definition,(
% 1.30/1.16 spl3_2 <=> ((in @ sK2 @ sK1) = $false)),
% 1.30/1.16 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.30/1.16 thf(f21,plain,(
% 1.30/1.16 ((in @ sK2 @ sK1) = $true)),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f16])).
% 1.30/1.16 thf(f59,plain,(
% 1.30/1.16 spl3_1 | spl3_2),
% 1.30/1.16 inference(avatar_split_clause,[status(thm)],[f48,f56,f52])).
% 1.30/1.16 thf(f48,plain,(
% 1.30/1.16 ((in @ sK2 @ sK1) = $false) | ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))),
% 1.30/1.16 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.30/1.16 thf(f46,plain,(
% 1.30/1.16 ((in @ sK2 @ sK1) = $false) | ($true = (in @ sK2 @ (setminus @ sK1 @ sK0))) | ($true != $true)),
% 1.30/1.16 inference(superposition,[status(thm)],[f22,f43])).
% 1.30/1.16 thf(f43,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setminus @ X2 @ X1)) = $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ X2) = $false)) )),
% 1.30/1.16 inference(not_proxy_clausification,[status(thm)],[f42])).
% 1.30/1.16 thf(f42,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ X2) = $false) | ((~ (in @ X3 @ X1)) = $false) | ((in @ X3 @ (setminus @ X2 @ X1)) = $true)) )),
% 1.30/1.16 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.30/1.16 thf(f41,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (in @ X3 @ X1)) => (in @ X3 @ (setminus @ X2 @ X1))) = $true) | ((in @ X3 @ X2) = $false)) )),
% 1.30/1.16 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.30/1.16 thf(f40,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X2) => ((~ (in @ X3 @ X1)) => (in @ X3 @ (setminus @ X2 @ X1)))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.30/1.16 thf(f39,plain,(
% 1.30/1.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ X1)) => (in @ Y0 @ (setminus @ X2 @ X1))))) @ X3) = $true)) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f38])).
% 1.30/1.16 thf(f38,plain,(
% 1.30/1.16 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ X1)) => (in @ Y0 @ (setminus @ X2 @ X1)))))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.30/1.16 thf(f37,plain,(
% 1.30/1.16 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ X1)) => (in @ Y1 @ (setminus @ Y0 @ X1))))))) @ X2) = $true)) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f36])).
% 1.30/1.16 thf(f36,plain,(
% 1.30/1.16 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ X1)) => (in @ Y1 @ (setminus @ Y0 @ X1)))))))) = $true)) )),
% 1.30/1.16 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.30/1.16 thf(f35,plain,(
% 1.30/1.16 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0))))))))) @ X1) = $true)) )),
% 1.30/1.16 inference(pi_clausification,[status(thm)],[f25])).
% 1.30/1.16 thf(f25,plain,(
% 1.30/1.16 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) = $true)),
% 1.30/1.16 inference(definition_unfolding,[status(thm)],[f24,f18])).
% 1.30/1.16 thf(f18,plain,(
% 1.30/1.16 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))))),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f9])).
% 1.30/1.16 thf(f9,plain,(
% 1.30/1.16 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))))),
% 1.30/1.16 inference(fool_elimination,[status(thm)],[f8])).
% 1.30/1.16 thf(f8,plain,(
% 1.30/1.16 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))))),
% 1.30/1.16 inference(rectify,[status(thm)],[f1])).
% 1.30/1.16 thf(f1,axiom,(
% 1.30/1.16 (setminusI = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.30/1.16 file('/export/starexec/sandbox/tmp/tmp.zfzdsCG7IL/DTF2THF_10265.p',setminusI)).
% 1.30/1.16 thf(f24,plain,(
% 1.30/1.16 (setminusI = $true)),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f16])).
% 1.30/1.16 thf(f22,plain,(
% 1.30/1.16 ($true != (in @ sK2 @ (setminus @ sK1 @ (setminus @ sK1 @ sK0))))),
% 1.30/1.16 inference(cnf_transformation,[status(thm)],[f16])).
% 1.30/1.16 % SZS output end Proof for DTF2THF_10265
% 1.30/1.16 % (10364)------------------------------
% 1.30/1.16 % (10364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.16 % (10364)Termination reason: Refutation
% 1.30/1.16
% 1.30/1.16 % (10364)Memory used [KB]: 5500
% 1.30/1.16 % (10364)Time elapsed: 0.006 s
% 1.30/1.16 % (10364)Instructions burned: 6 (million)
% 1.30/1.16 % (10364)------------------------------
% 1.30/1.16 % (10364)------------------------------
% 1.30/1.16 % (10363)Success in time 0.015 s
%------------------------------------------------------------------------------