%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU615^2 : 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 : n018.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 09:35:38 AM UTC 2026
% Result : Theorem 1.50s 1.28s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 390 ( 83 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 662 ( 76 ~; 33 |; 13 &; 388 @)
% ( 4 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 11 con; 0-2 aty)
% ( 25 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 113 ( 29 ^; 75 !; 9 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
symdiff: $i > $i > $i ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f163,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f91,f101,f159,f161,f162]) ).
thf(f162,plain,
~ spl3_13,
inference(avatar_split_clause,[status(thm)],[f17,f146]) ).
thf(f146,definition,
( spl3_13
<=> ( ( in @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_13])],[avatar_definition]) ).
thf(f17,plain,
( ( in @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) )
& ( ( in @ sK1 @ sK0 )
!= $true )
& ( $true
!= ( in @ sK1 @ sK2 ) )
& ( symdiffE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) ) )
=> ( ( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) )
& ( ( in @ sK1 @ sK0 )
!= $true )
& ( $true
!= ( in @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) ) )
& ( symdiffE = $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
& ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) ) )
& ( symdiffE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( $true
!= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( $true
!= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( symdiffE
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( symdiffE
=> ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( symdiffE
=> ! [X1: $i,X2: $i,X0: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JmWU9g9kXA/DTF2THF_25558.p',symdiffIneg2) ).
thf(f161,plain,
~ spl3_12,
inference(avatar_split_clause,[status(thm)],[f16,f142]) ).
thf(f142,definition,
( spl3_12
<=> ( $true
= ( in @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_12])],[avatar_definition]) ).
thf(f16,plain,
( $true
!= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f159,plain,
( spl3_12
| spl3_13
| ~ spl3_10 ),
inference(avatar_split_clause,[status(thm)],[f129,f89,f146,f142]) ).
thf(f89,definition,
( spl3_10
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_10])],[avatar_definition]) ).
thf(f129,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
| ( $true
= ( in @ sK1 @ sK2 ) )
| ~ spl3_10 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true
= ( in @ sK1 @ sK2 ) )
| ( ( in @ sK1 @ sK0 )
= $true )
| ( $true = $false )
| ~ spl3_10 ),
inference(superposition,[status(thm)],[f90,f18]) ).
thf(f18,plain,
( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f90,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
= ( in @ X2 @ X3 ) ) )
| ~ spl3_10 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f101,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
| ~ spl3_7 ),
inference(equality_resolution,[status(thm)],[f97]) ).
thf(f97,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f4,f78]) ).
thf(f78,plain,
( ! [X4: $o] : ( $true = X4 )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl3_7
<=> ! [X4: $o] : ( $true = X4 ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f4,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f91,plain,
( spl3_10
| spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f37,f77,f89]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true = X4 )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( ( ( in @ X2 @ X3 )
=> X4 )
= $false )
| ( $true = X4 )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true = X4 )
| ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> X4 ) )
= $false )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true = X4 )
| ( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> X4 ) )
= $false )
| ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> X4 ) )
= $false )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true
= ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> X4 ) )
=> X4 ) )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> X4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( $true
= ( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> X4 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> X4 ) )
=> X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true
= ( ^ [Y0: $o] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> Y0 ) )
=> Y0 ) )
@ X4 ) )
| ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
= $false )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( symdiff @ X1 @ X3 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X3 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X3 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( symdiff @ X1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ Y0 )
=> Y1 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> Y1 ) )
=> Y1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( symdiff @ X1 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ Y0 )
=> Y1 ) )
=> ( ( ~ ( in @ X2 @ X1 )
=> ( ( in @ X2 @ Y0 )
=> Y1 ) )
=> Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( symdiff @ X1 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y2 ) )
=> ( ( ~ ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> Y2 ) )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( symdiff @ X1 @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ Y0 @ X1 )
=> ( ~ ( in @ Y0 @ Y1 )
=> Y2 ) )
=> ( ( ~ ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ Y1 )
=> Y2 ) )
=> Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y0 @ Y2 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> Y3 ) )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y0 @ Y2 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f14]) ).
thf(f14,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y0 @ Y2 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y0 @ Y2 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y0 )
=> ( ~ ( in @ Y1 @ Y2 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X2 )
=> ( ( in @ X1 @ X0 )
=> X3 ) )
=> X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( symdiffE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> X3 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> X3 ) )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JmWU9g9kXA/DTF2THF_25558.p',symdiffE) ).
thf(f15,plain,
symdiffE = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU615^2 : 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
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:29:01 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU615^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.20/0.45 % Version : Especial > Reduced > Especial.
% 0.20/0.45 % English : (! A:i.! B:i.! x:i.~(in x A) -> ~(in x B) -> ~(in x
% 0.20/0.45 % (symdiff A B)))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC117l [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % 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
% 0.20/0.45 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.20/0.45 % Number of atoms : 11 ( 1 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 4 ( 5 avg)
% 0.20/0.45 % Number of connectives : 35 ( 5 ~; 0 |; 0 &; 20 @)
% 0.20/0.45 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 11 ( 6 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=493
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(symdiff_type,type,
% 0.20/0.45 symdiff: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(symdiffE_type,type,
% 0.20/0.45 symdiffE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(symdiffE,definition,
% 0.20/0.45 ( symdiffE
% 0.20/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.45 => ! [Xphi: $o] :
% 0.20/0.45 ( ( ( in @ Xx @ A )
% 0.20/0.45 => ( ~ ( in @ Xx @ B )
% 0.20/0.45 => Xphi ) )
% 0.20/0.45 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.45 => ( ( in @ Xx @ B )
% 0.20/0.45 => Xphi ) )
% 0.20/0.45 => Xphi ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(symdiffIneg2,conjecture,
% 0.20/0.45 ( symdiffE
% 0.20/0.45 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.45 ( ~ ( in @ Xx @ A )
% 0.20/0.45 => ( ~ ( in @ Xx @ B )
% 0.20/0.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 12:29:01 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JmWU9g9kXA/DTF2DTF25558.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(in_type,type,
% 1.50/1.26 in: $i > $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(symdiff_type,type,
% 1.50/1.26 symdiff: $i > $i > $i ).
% 1.50/1.26
% 1.50/1.26 thf(symdiffE_type,type,
% 1.50/1.26 symdiffE: $o ).
% 1.50/1.26
% 1.50/1.26 thf(symdiffE,definition,
% 1.50/1.26 ( symdiffE
% 1.50/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.26 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 1.50/1.26 => ! [Xphi: $o] :
% 1.50/1.26 ( ( ( in @ Xx @ A )
% 1.50/1.26 => ( ~ ( in @ Xx @ B )
% 1.50/1.26 => Xphi ) )
% 1.50/1.26 => ( ( ~ ( in @ Xx @ A )
% 1.50/1.26 => ( ( in @ Xx @ B )
% 1.50/1.26 => Xphi ) )
% 1.50/1.26 => Xphi ) ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(symdiffIneg2,conjecture,
% 1.50/1.26 ( symdiffE
% 1.50/1.26 => ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.26 ( ~ ( in @ Xx @ A )
% 1.50/1.26 => ( ~ ( in @ Xx @ B )
% 1.50/1.26 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (25842)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_25558 for (2999ds/27Mi)
% 1.50/1.27 % (25840)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25558 for (2999ds/183Mi)
% 1.50/1.28 % (25842)First to succeed.
% 1.50/1.28 % (25840)Also succeeded, but the first one will report.
% 1.50/1.28 % (25842)Refutation found. Thanks to Tanya!
% 1.50/1.28 % SZS status Theorem for DTF2THF_25558
% 1.50/1.28 % SZS output start Proof for DTF2THF_25558
% 1.50/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.50/1.28 thf(func_def_1, type, symdiff: $i > $i > $i).
% 1.50/1.28 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.28 thf(f163,plain,(
% 1.50/1.28 $false),
% 1.50/1.28 inference(avatar_sat_refutation,[status(thm)],[f91,f101,f159,f161,f162])).
% 1.50/1.28 thf(f162,plain,(
% 1.50/1.28 ~spl3_13),
% 1.50/1.28 inference(avatar_split_clause,[status(thm)],[f17,f146])).
% 1.50/1.28 thf(f146,definition,(
% 1.50/1.28 spl3_13 <=> ((in @ sK1 @ sK0) = $true)),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl3_13])],[avatar_definition])).
% 1.50/1.28 thf(f17,plain,(
% 1.50/1.28 ((in @ sK1 @ sK0) != $true)),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.28 thf(f13,plain,(
% 1.50/1.28 (($true = (in @ sK1 @ (symdiff @ sK2 @ sK0))) & ((in @ sK1 @ sK0) != $true) & ($true != (in @ sK1 @ sK2))) & (symdiffE = $true)),
% 1.50/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12])).
% 1.50/1.28 thf(f12,plain,(
% 1.50/1.28 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X2 @ X0))) & ($true != (in @ X1 @ X0)) & ($true != (in @ X1 @ X2))) => (($true = (in @ sK1 @ (symdiff @ sK2 @ sK0))) & ((in @ sK1 @ sK0) != $true) & ($true != (in @ sK1 @ sK2)))),
% 1.50/1.28 introduced(definition,[],[choice_axiom])).
% 1.50/1.28 thf(f11,plain,(
% 1.50/1.28 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X2 @ X0))) & ($true != (in @ X1 @ X0)) & ($true != (in @ X1 @ X2))) & (symdiffE = $true)),
% 1.50/1.28 inference(flattening,[status(thm)],[f10])).
% 1.50/1.28 thf(f10,plain,(
% 1.50/1.28 ? [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (symdiff @ X2 @ X0))) & ($true != (in @ X1 @ X0))) & ($true != (in @ X1 @ X2))) & (symdiffE = $true)),
% 1.50/1.28 inference(ennf_transformation,[status(thm)],[f9])).
% 1.50/1.28 thf(f9,plain,(
% 1.50/1.28 ~((symdiffE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) => (($true != (in @ X1 @ X0)) => ($true != (in @ X1 @ (symdiff @ X2 @ X0))))))),
% 1.50/1.28 inference(flattening,[status(thm)],[f6])).
% 1.50/1.28 thf(f6,plain,(
% 1.50/1.28 ~((symdiffE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (~($true = (in @ X1 @ X2)) => (~($true = (in @ X1 @ X0)) => ~($true = (in @ X1 @ (symdiff @ X2 @ X0))))))),
% 1.50/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.28 thf(f5,plain,(
% 1.50/1.28 ~(symdiffE => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ X2) => (~(in @ X1 @ X0) => ~(in @ X1 @ (symdiff @ X2 @ X0)))))),
% 1.50/1.28 inference(rectify,[status(thm)],[f3])).
% 1.50/1.28 thf(f3,negated_conjecture,(
% 1.50/1.28 ~(symdiffE => ! [X1 : $i,X2 : $i,X0 : $i] : (~(in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))))),
% 1.50/1.28 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.28 thf(f2,conjecture,(
% 1.50/1.28 symdiffE => ! [X1 : $i,X2 : $i,X0 : $i] : (~(in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1))))),
% 1.50/1.28 file('/export/starexec/sandbox/tmp/tmp.JmWU9g9kXA/DTF2THF_25558.p',symdiffIneg2)).
% 1.50/1.28 thf(f161,plain,(
% 1.50/1.28 ~spl3_12),
% 1.50/1.28 inference(avatar_split_clause,[status(thm)],[f16,f142])).
% 1.50/1.28 thf(f142,definition,(
% 1.50/1.28 spl3_12 <=> ($true = (in @ sK1 @ sK2))),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl3_12])],[avatar_definition])).
% 1.50/1.28 thf(f16,plain,(
% 1.50/1.28 ($true != (in @ sK1 @ sK2))),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.28 thf(f159,plain,(
% 1.50/1.28 spl3_12 | spl3_13 | ~spl3_10),
% 1.50/1.28 inference(avatar_split_clause,[status(thm)],[f129,f89,f146,f142])).
% 1.50/1.28 thf(f89,definition,(
% 1.50/1.28 spl3_10 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (($true = (in @ X2 @ X3)) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | ((in @ X2 @ X1) = $true))),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl3_10])],[avatar_definition])).
% 1.50/1.28 thf(f129,plain,(
% 1.50/1.28 ((in @ sK1 @ sK0) = $true) | ($true = (in @ sK1 @ sK2)) | ~spl3_10),
% 1.50/1.28 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.50/1.28 thf(f125,plain,(
% 1.50/1.28 ($true = (in @ sK1 @ sK2)) | ((in @ sK1 @ sK0) = $true) | ($true = $false) | ~spl3_10),
% 1.50/1.28 inference(superposition,[status(thm)],[f90,f18])).
% 1.50/1.28 thf(f18,plain,(
% 1.50/1.28 ($true = (in @ sK1 @ (symdiff @ sK2 @ sK0)))),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.28 thf(f90,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | ((in @ X2 @ X1) = $true) | ($true = (in @ X2 @ X3))) ) | ~spl3_10),
% 1.50/1.28 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.50/1.28 thf(f101,plain,(
% 1.50/1.28 ~spl3_7),
% 1.50/1.28 inference(avatar_contradiction_clause,[status(thm)],[f100])).
% 1.50/1.28 thf(f100,plain,(
% 1.50/1.28 $false | ~spl3_7),
% 1.50/1.28 inference(equality_resolution,[status(thm)],[f97])).
% 1.50/1.28 thf(f97,plain,(
% 1.50/1.28 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_7),
% 1.50/1.28 inference(superposition,[status(thm)],[f4,f78])).
% 1.50/1.28 thf(f78,plain,(
% 1.50/1.28 ( ! [X4 : $o] : (($true = X4)) ) | ~spl3_7),
% 1.50/1.28 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.50/1.28 thf(f77,definition,(
% 1.50/1.28 spl3_7 <=> ! [X4 : $o] : ($true = X4)),
% 1.50/1.28 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.50/1.28 thf(f4,plain,(
% 1.50/1.28 ($true != $false)),
% 1.50/1.28 introduced(definition,[],[fool_axiom])).
% 1.50/1.28 thf(f91,plain,(
% 1.50/1.28 spl3_10 | spl3_7),
% 1.50/1.28 inference(avatar_split_clause,[status(thm)],[f37,f77,f89])).
% 1.50/1.28 thf(f37,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $true) | ($true = X4) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false)) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.50/1.28 thf(f33,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | (((in @ X2 @ X3) => X4) = $false) | ($true = X4) | ((in @ X2 @ X1) = $true)) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.50/1.28 thf(f32,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = X4) | (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => X4)) = $false) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | ((in @ X2 @ X1) = $true)) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.50/1.28 thf(f30,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = X4) | (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => X4)) = $false) | (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => X4)) = $false) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false)) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.50/1.28 thf(f29,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => X4)) => X4)) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => X4)) = $false)) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.50/1.28 thf(f28,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | ($true = (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => X4)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => X4)) => X4)))) )),
% 1.50/1.28 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.50/1.28 thf(f27,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = ((^[Y0 : $o]: (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => Y0)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => Y0)) => Y0))) @ X4)) | ((in @ X2 @ (symdiff @ X1 @ X3)) = $false)) )),
% 1.50/1.28 inference(pi_clausification,[status(thm)],[f26])).
% 1.50/1.28 thf(f26,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (symdiff @ X1 @ X3)) = $false) | ($true = (!! @ $o @ (^[Y0 : $o]: (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => Y0)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => Y0)) => Y0)))))) )),
% 1.50/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.50/1.28 thf(f25,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ (symdiff @ X1 @ X3)) => (!! @ $o @ (^[Y0 : $o]: (((in @ X2 @ X1) => ((~ (in @ X2 @ X3)) => Y0)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ X3) => Y0)) => Y0))))))) )),
% 1.50/1.28 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.50/1.28 thf(f24,plain,(
% 1.50/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ (symdiff @ X1 @ Y0)) => (!! @ $o @ (^[Y1 : $o]: (((in @ X2 @ X1) => ((~ (in @ X2 @ Y0)) => Y1)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ Y0) => Y1)) => Y1)))))) @ X3))) )),
% 1.50/1.28 inference(pi_clausification,[status(thm)],[f23])).
% 1.50/1.28 thf(f23,plain,(
% 1.50/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (symdiff @ X1 @ Y0)) => (!! @ $o @ (^[Y1 : $o]: (((in @ X2 @ X1) => ((~ (in @ X2 @ Y0)) => Y1)) => (((~ (in @ X2 @ X1)) => ((in @ X2 @ Y0) => Y1)) => Y1))))))))) )),
% 1.50/1.28 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.50/1.28 thf(f22,plain,(
% 1.50/1.28 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (symdiff @ X1 @ Y1)) => (!! @ $o @ (^[Y2 : $o]: (((in @ Y0 @ X1) => ((~ (in @ Y0 @ Y1)) => Y2)) => (((~ (in @ Y0 @ X1)) => ((in @ Y0 @ Y1) => Y2)) => Y2)))))))) @ X2))) )),
% 1.50/1.28 inference(pi_clausification,[status(thm)],[f21])).
% 1.50/1.28 thf(f21,plain,(
% 1.50/1.28 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (symdiff @ X1 @ Y1)) => (!! @ $o @ (^[Y2 : $o]: (((in @ Y0 @ X1) => ((~ (in @ Y0 @ Y1)) => Y2)) => (((~ (in @ Y0 @ X1)) => ((in @ Y0 @ Y1) => Y2)) => Y2))))))))))) )),
% 1.50/1.28 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.50/1.28 thf(f20,plain,(
% 1.50/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => Y3)) => (((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => Y3)) => Y3)))))))))) @ X1))) )),
% 1.50/1.28 inference(pi_clausification,[status(thm)],[f19])).
% 1.50/1.28 thf(f19,plain,(
% 1.50/1.28 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => Y3)) => (((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => Y3)) => Y3))))))))))))),
% 1.50/1.28 inference(definition_unfolding,[status(thm)],[f15,f14])).
% 1.50/1.28 thf(f14,plain,(
% 1.50/1.28 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => Y3)) => (((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => Y3)) => Y3))))))))))))),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.28 thf(f8,plain,(
% 1.50/1.28 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => Y3)) => (((~ (in @ Y1 @ Y0)) => ((in @ Y1 @ Y2) => Y3)) => Y3))))))))))))),
% 1.50/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.28 thf(f7,plain,(
% 1.50/1.28 (symdiffE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (symdiff @ X2 @ X0)) => ! [X3 : $o] : (((in @ X1 @ X2) => (~(in @ X1 @ X0) => X3)) => ((~(in @ X1 @ X2) => ((in @ X1 @ X0) => X3)) => X3))))),
% 1.50/1.28 inference(rectify,[status(thm)],[f1])).
% 1.50/1.28 thf(f1,axiom,(
% 1.50/1.28 (symdiffE = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (symdiff @ X0 @ X1)) => ! [X3 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X1) => X3)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X1) => X3)) => X3))))),
% 1.50/1.28 file('/export/starexec/sandbox/tmp/tmp.JmWU9g9kXA/DTF2THF_25558.p',symdiffE)).
% 1.50/1.28 thf(f15,plain,(
% 1.50/1.28 (symdiffE = $true)),
% 1.50/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.28 % SZS output end Proof for DTF2THF_25558
% 1.50/1.28 % (25842)------------------------------
% 1.50/1.28 % (25842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (25842)Termination reason: Refutation
% 1.50/1.28
% 1.50/1.28 % (25842)Memory used [KB]: 5628
% 1.50/1.28 % (25842)Time elapsed: 0.006 s
% 1.50/1.28 % (25842)Instructions burned: 10 (million)
% 1.50/1.28 % (25842)------------------------------
% 1.50/1.28 % (25842)------------------------------
% 1.50/1.28 % (25839)Success in time 0.016 s
%------------------------------------------------------------------------------