%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU606^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:34 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 250 ( 56 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 363 ( 45 ~; 8 |; 13 &; 243 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 69 ( 18 ^; 42 !; 9 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setminus: $i > $i > $i ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
$false = $true,
inference(superposition,[status(thm)],[f17,f31]) ).
thf(f31,plain,
( $false
= ( in @ sK2 @ sK0 ) ),
inference(subsumption_resolution,[status(thm)],[f30,f16]) ).
thf(f16,plain,
( ( in @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
!= $true )
& ( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
!= $true )
& ( setminusERneg = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
!= $true )
& ( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( setminusERneg = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( setminusERneg = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( setminusERneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setminusERneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ X0 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setminusERneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setminusERneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setminusERneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbAOrO1wDh/DTF2THF_6220.p',setminusELneg) ).
thf(f30,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ( ( in @ sK2 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ( $true != $true )
| ( ( in @ sK2 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f15,f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X3 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) )
= $true )
| ( ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ~ ( in @ X1 @ ( setminus @ X3 @ X2 ) )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
=> ( in @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f18,f14]) ).
thf(f14,plain,
setminusERneg = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,plain,
( setminusERneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( setminusERneg
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= setminusERneg ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= setminusERneg ),
file('/export/starexec/sandbox/tmp/tmp.JbAOrO1wDh/DTF2THF_6220.p',setminusERneg) ).
thf(f15,plain,
( ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f17,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU606^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:28:37 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU606^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.31/0.47 % Version : Especial > Reduced > Especial.
% 0.31/0.47 % English : (! A:i.! B:i.! x:i.~(in x (setminus A B)) -> ~(in x B) ->
% 0.31/0.47 % ~(in x A))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC108l [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.31/0.47 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.47 % Number of connectives : 25 ( 4 ~; 0 |; 0 &; 16 @)
% 0.31/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 10 ( 6 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=461
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setminus_type,type,
% 0.31/0.47 setminus: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setminusERneg_type,type,
% 0.31/0.47 setminusERneg: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setminusERneg,definition,
% 0.31/0.47 ( setminusERneg
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setminusELneg,conjecture,
% 0.31/0.47 ( setminusERneg
% 0.31/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.44/1.29 ---- Embedded in THF ---
% 1.44/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.29 %%% Generated on Tue Feb 24 12:28:38 EST 2026
% 1.44/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.29 %%% Logic specification used:
% 1.44/1.29 %%% thf(spec, logic, $$dhol).
% 1.44/1.29
% 1.44/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JbAOrO1wDh/DTF2DTF6220.p
% See solution above
% 1.44/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(in_type,type,
% 1.65/1.30 in: $i > $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(setminus_type,type,
% 1.65/1.30 setminus: $i > $i > $i ).
% 1.65/1.30
% 1.65/1.30 thf(setminusERneg_type,type,
% 1.65/1.30 setminusERneg: $o ).
% 1.65/1.30
% 1.65/1.30 thf(setminusERneg,definition,
% 1.65/1.30 ( setminusERneg
% 1.65/1.30 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.65/1.30 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 1.65/1.30 => ( ( in @ Xx @ A )
% 1.65/1.30 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(setminusELneg,conjecture,
% 1.65/1.30 ( setminusERneg
% 1.65/1.30 => ! [A: $i,B: $i,Xx: $i] :
% 1.65/1.30 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 1.65/1.30 => ( ~ ( in @ Xx @ B )
% 1.65/1.30 => ~ ( in @ Xx @ A ) ) ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.32 % (6547)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6220 for (3000ds/183Mi)
% 1.65/1.32 % (6547)First to succeed.
% 1.65/1.32 % (6547)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_6220
% 1.65/1.32 % SZS output start Proof for DTF2THF_6220
% 1.65/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.32 thf(func_def_1, type, setminus: $i > $i > $i).
% 1.65/1.32 thf(f34,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.65/1.32 thf(f33,plain,(
% 1.65/1.32 ($false = $true)),
% 1.65/1.32 inference(superposition,[status(thm)],[f17,f31])).
% 1.65/1.32 thf(f31,plain,(
% 1.65/1.32 ($false = (in @ sK2 @ sK0))),
% 1.65/1.32 inference(subsumption_resolution,[status(thm)],[f30,f16])).
% 1.65/1.32 thf(f16,plain,(
% 1.65/1.32 ((in @ sK2 @ sK1) != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 (($true = (in @ sK2 @ sK0)) & ((in @ sK2 @ sK1) != $true) & ((in @ sK2 @ (setminus @ sK0 @ sK1)) != $true)) & (setminusERneg = $true)),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) => (($true = (in @ sK2 @ sK0)) & ((in @ sK2 @ sK1) != $true) & ((in @ sK2 @ (setminus @ sK0 @ sK1)) != $true))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) & (setminusERneg = $true)),
% 1.65/1.32 inference(flattening,[status(thm)],[f10])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) & ((in @ X2 @ (setminus @ X0 @ X1)) != $true)) & (setminusERneg = $true)),
% 1.65/1.32 inference(ennf_transformation,[status(thm)],[f9])).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 ~((setminusERneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X0 @ X1)) != $true) => (((in @ X2 @ X1) != $true) => ((in @ X2 @ X0) != $true))))),
% 1.65/1.32 inference(flattening,[status(thm)],[f8])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 ~((setminusERneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (~((in @ X2 @ (setminus @ X0 @ X1)) = $true) => (~((in @ X2 @ X1) = $true) => ~((in @ X2 @ X0) = $true))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 ~(setminusERneg => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 1.65/1.32 inference(rectify,[status(thm)],[f3])).
% 1.65/1.32 thf(f3,negated_conjecture,(
% 1.65/1.32 ~(setminusERneg => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.32 thf(f2,conjecture,(
% 1.65/1.32 setminusERneg => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0)))),
% 1.65/1.32 file('/export/starexec/sandbox/tmp/tmp.JbAOrO1wDh/DTF2THF_6220.p',setminusELneg)).
% 1.65/1.32 thf(f30,plain,(
% 1.65/1.32 ($false = (in @ sK2 @ sK0)) | ((in @ sK2 @ sK1) = $true)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.65/1.32 thf(f29,plain,(
% 1.65/1.32 ($false = (in @ sK2 @ sK0)) | ($true != $true) | ((in @ sK2 @ sK1) = $true)),
% 1.65/1.32 inference(superposition,[status(thm)],[f15,f28])).
% 1.65/1.32 thf(f28,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X3 @ X2)) = $true) | ((in @ X1 @ X2) = $true) | ($false = (in @ X1 @ X3))) )),
% 1.65/1.32 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.65/1.32 thf(f27,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ X3)) | ((in @ X1 @ X2) = $true) | ((~ (in @ X1 @ (setminus @ X3 @ X2))) = $false)) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.65/1.32 thf(f26,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X3) => (in @ X1 @ X2)) = $true) | ((~ (in @ X1 @ (setminus @ X3 @ X2))) = $false)) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.65/1.32 thf(f25,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (in @ X1 @ (setminus @ X3 @ X2))) => ((in @ X1 @ X3) => (in @ X1 @ X2))) = $true)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.65/1.32 thf(f24,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (in @ X1 @ (setminus @ Y0 @ X2))) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))) @ X3) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f23])).
% 1.65/1.32 thf(f23,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (in @ X1 @ (setminus @ Y0 @ X2))) => ((in @ X1 @ Y0) => (in @ X1 @ X2))))) = $true)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.65/1.32 thf(f22,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (in @ X1 @ (setminus @ Y1 @ Y0))) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))) @ X2) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f21])).
% 1.65/1.32 thf(f21,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (in @ X1 @ (setminus @ Y1 @ Y0))) => ((in @ X1 @ Y1) => (in @ X1 @ Y0))))))) = $true)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.65/1.32 thf(f20,plain,(
% 1.65/1.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))) @ X1) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f19])).
% 1.65/1.32 thf(f19,plain,(
% 1.65/1.32 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) = $true)),
% 1.65/1.32 inference(definition_unfolding,[status(thm)],[f18,f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 (setminusERneg = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.65/1.32 thf(f18,plain,(
% 1.65/1.32 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.32 thf(f6,plain,(
% 1.65/1.32 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,plain,(
% 1.65/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = setminusERneg)),
% 1.65/1.32 inference(rectify,[status(thm)],[f1])).
% 1.65/1.32 thf(f1,axiom,(
% 1.65/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X0 @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = setminusERneg)),
% 1.65/1.32 file('/export/starexec/sandbox/tmp/tmp.JbAOrO1wDh/DTF2THF_6220.p',setminusERneg)).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 ((in @ sK2 @ (setminus @ sK0 @ sK1)) != $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.65/1.32 thf(f17,plain,(
% 1.65/1.32 ($true = (in @ sK2 @ sK0))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.65/1.32 % SZS output end Proof for DTF2THF_6220
% 1.65/1.32 % (6547)------------------------------
% 1.65/1.32 % (6547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (6547)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (6547)Memory used [KB]: 5500
% 1.65/1.32 % (6547)Time elapsed: 0.004 s
% 1.65/1.32 % (6547)Instructions burned: 3 (million)
% 1.65/1.32 % (6547)------------------------------
% 1.65/1.32 % (6547)------------------------------
% 1.65/1.32 % (6546)Success in time 0.015 s
%------------------------------------------------------------------------------