%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU614^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:35:37 AM UTC 2026
% Result : Theorem 1.61s 1.36s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 412 ( 90 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 673 ( 60 ~; 39 |; 13 &; 406 @)
% ( 2 <=>; 128 =>; 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 : 13 ( 9 usr; 9 con; 0-2 aty)
% ( 25 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 121 ( 29 ^; 83 !; 9 ?; 121 :)
% 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(f124,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f83,f101,f123]) ).
thf(f123,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true = $false )
| ~ spl3_8 ),
inference(backward_demodulation,[status(thm)],[f15,f116]) ).
thf(f116,plain,
( ( ( in @ sK1 @ sK2 )
= $false )
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sK2 )
= $false )
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f113,f17]) ).
thf(f17,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( symdiffE = $true )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) )
= $true )
& ( $true
= ( in @ sK1 @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) )
= $true )
& ( $true
= ( in @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( symdiffE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( $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 ) )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( symdiffE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,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/sandbox2/tmp/tmp.gK8q6H94QX/DTF2THF_15416.p',symdiffIneg1) ).
thf(f113,plain,
( ( ( in @ sK1 @ sK2 )
= $false )
| ( ( in @ sK1 @ sK0 )
= $false )
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sK2 )
= $false )
| ( ( in @ sK1 @ sK0 )
= $false )
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f82,f16]) ).
thf(f16,plain,
( ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f82,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $false ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl3_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f15,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
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(f83,plain,
( spl3_8
| spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f44,f77,f81]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true = X4 )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ~ ( in @ X2 @ X3 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true = X4 )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( ( in @ X2 @ X1 )
= $false )
| ( $true = X4 )
| ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true
= ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
=> X4 ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ~ ( in @ X2 @ X1 ) )
= $true )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( $true
= ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
=> X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ~ ( in @ X2 @ X1 )
=> X4 )
= $false )
| ( $true
= ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
=> X4 ) )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X1 )
=> X4 ) )
= $false )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( $true
= ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
=> X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ( ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X1 )
=> X4 ) )
=> ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> X4 ) )
=> X4 ) )
= $true )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false )
| ( ( ^ [Y0: $o] :
( ( ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X1 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> Y0 ) )
=> Y0 ) )
@ X4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X1 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> Y0 ) )
=> Y0 ) ) ) )
| ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( symdiff @ X3 @ X1 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( ( in @ X2 @ X3 )
=> ( ~ ( in @ X2 @ X1 )
=> Y0 ) )
=> ( ( ~ ( in @ X2 @ X3 )
=> ( ( in @ X2 @ X1 )
=> Y0 ) )
=> Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( symdiff @ Y0 @ X1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X2 @ Y0 )
=> ( ~ ( in @ X2 @ X1 )
=> Y1 ) )
=> ( ( ~ ( in @ X2 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> Y1 ) )
=> Y1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( symdiff @ Y0 @ X1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( ( in @ X2 @ Y0 )
=> ( ~ ( in @ X2 @ X1 )
=> Y1 ) )
=> ( ( ~ ( in @ X2 @ Y0 )
=> ( ( in @ X2 @ X1 )
=> Y1 ) )
=> Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( symdiff @ Y1 @ X1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ Y0 @ Y1 )
=> ( ~ ( in @ Y0 @ X1 )
=> Y2 ) )
=> ( ( ~ ( in @ Y0 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> Y2 ) )
=> Y2 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( symdiff @ Y1 @ X1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( ( in @ Y0 @ Y1 )
=> ( ~ ( in @ Y0 @ X1 )
=> Y2 ) )
=> ( ( ~ ( in @ Y0 @ Y1 )
=> ( ( in @ Y0 @ X1 )
=> Y2 ) )
=> Y2 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y2 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> Y3 ) )
=> Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y2 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f18,f14]) ).
thf(f14,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y2 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( symdiffE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( symdiff @ Y2 @ Y0 ) )
=> ( !! @ $o
@ ^ [Y3: $o] :
( ( ( in @ Y1 @ Y2 )
=> ( ~ ( in @ Y1 @ Y0 )
=> Y3 ) )
=> ( ( ~ ( in @ Y1 @ Y2 )
=> ( ( in @ Y1 @ Y0 )
=> Y3 ) )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> X3 ) )
=> X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( symdiffE
= ( ! [X0: $i,X2: $i,X1: $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/sandbox2/tmp/tmp.gK8q6H94QX/DTF2THF_15416.p',symdiffE) ).
thf(f18,plain,
symdiffE = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU614^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.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 12:30:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU614^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.27/0.46 % Version : Especial > Reduced > Especial.
% 0.27/0.46 % English : (! A:i.! B:i.! x:i.in x A -> in x B -> ~(in x (symdiff A B)))
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC116l [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 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
% 0.27/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.27/0.46 % Number of atoms : 11 ( 1 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 4 ( 5 avg)
% 0.27/0.46 % Number of connectives : 33 ( 3 ~; 0 |; 0 &; 20 @)
% 0.27/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 11 ( 6 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.27/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=492
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(symdiff_type,type,
% 0.27/0.46 symdiff: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(symdiffE_type,type,
% 0.27/0.46 symdiffE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(symdiffE,definition,
% 0.27/0.46 ( symdiffE
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.27/0.46 => ! [Xphi: $o] :
% 0.27/0.46 ( ( ( in @ Xx @ A )
% 0.27/0.46 => ( ~ ( in @ Xx @ B )
% 0.27/0.46 => Xphi ) )
% 0.27/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx @ B )
% 0.27/0.46 => Xphi ) )
% 0.27/0.46 => Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(symdiffIneg1,conjecture,
% 0.27/0.46 ( symdiffE
% 0.27/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx @ B )
% 0.27/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.61/1.32 ---- Embedded in THF ---
% 1.61/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.32 %%% Generated on Tue Feb 24 12:30:04 EST 2026
% 1.61/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.32 %%% Logic specification used:
% 1.61/1.32 %%% thf(spec, logic, $$dhol).
% 1.61/1.32
% 1.61/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gK8q6H94QX/DTF2DTF15416.p
% See solution above
% 1.61/1.32 ------------------------
% 1.61/1.33 ---- Cleaned THF ---
% 1.61/1.33 thf(in_type,type,
% 1.61/1.33 in: $i > $i > $o ).
% 1.61/1.33
% 1.61/1.33 thf(symdiff_type,type,
% 1.61/1.33 symdiff: $i > $i > $i ).
% 1.61/1.33
% 1.61/1.33 thf(symdiffE_type,type,
% 1.61/1.33 symdiffE: $o ).
% 1.61/1.33
% 1.61/1.33 thf(symdiffE,definition,
% 1.61/1.33 ( symdiffE
% 1.61/1.33 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.61/1.33 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 1.61/1.33 => ! [Xphi: $o] :
% 1.61/1.33 ( ( ( in @ Xx @ A )
% 1.61/1.33 => ( ~ ( in @ Xx @ B )
% 1.61/1.33 => Xphi ) )
% 1.61/1.33 => ( ( ~ ( in @ Xx @ A )
% 1.61/1.33 => ( ( in @ Xx @ B )
% 1.61/1.33 => Xphi ) )
% 1.61/1.33 => Xphi ) ) ) ) ) ).
% 1.61/1.33
% 1.61/1.33 thf(symdiffIneg1,conjecture,
% 1.61/1.33 ( symdiffE
% 1.61/1.33 => ! [A: $i,B: $i,Xx: $i] :
% 1.61/1.33 ( ( in @ Xx @ A )
% 1.61/1.33 => ( ( in @ Xx @ B )
% 1.61/1.33 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ).
% 1.61/1.33 ------------------------
% 1.61/1.34 % (15687)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15416 for (3000ds/18Mi)
% 1.61/1.35 % (15687)Instruction limit reached!
% 1.61/1.35 % (15687)------------------------------
% 1.61/1.35 % (15687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (15687)Termination reason: Unknown
% 1.61/1.35 % (15687)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (15687)Memory used [KB]: 5628
% 1.61/1.35 % (15687)Time elapsed: 0.008 s
% 1.61/1.35 % (15687)Instructions burned: 19 (million)
% 1.61/1.35 % (15687)------------------------------
% 1.61/1.35 % (15687)------------------------------
% 1.61/1.35 % (15681)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15416 for (3000ds/183Mi)
% 1.61/1.35 % (15682)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_15416 for (3000ds/4Mi)
% 1.61/1.35 % (15683)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_15416 for (3000ds/27Mi)
% 1.61/1.35 % (15684)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15416 for (3000ds/2Mi)
% 1.61/1.35 % (15685)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_15416 for (3000ds/2Mi)
% 1.61/1.35 % (15686)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_15416 for (3000ds/275Mi)
% 1.61/1.35 % (15684)Instruction limit reached!
% 1.61/1.35 % (15684)------------------------------
% 1.61/1.35 % (15684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (15684)Termination reason: Unknown
% 1.61/1.35 % (15684)Termination phase: Property scanning
% 1.61/1.35
% 1.61/1.35 % (15684)Memory used [KB]: 895
% 1.61/1.35 % (15684)Time elapsed: 0.003 s
% 1.61/1.35 % (15684)Instructions burned: 2 (million)
% 1.61/1.35 % (15684)------------------------------
% 1.61/1.35 % (15684)------------------------------
% 1.61/1.35 % (15685)Instruction limit reached!
% 1.61/1.35 % (15685)------------------------------
% 1.61/1.35 % (15685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (15685)Termination reason: Unknown
% 1.61/1.35 % (15685)Termination phase: Property scanning
% 1.61/1.35
% 1.61/1.35 % (15685)Memory used [KB]: 895
% 1.61/1.35 % (15685)Time elapsed: 0.003 s
% 1.61/1.35 % (15685)Instructions burned: 2 (million)
% 1.61/1.35 % (15685)------------------------------
% 1.61/1.35 % (15685)------------------------------
% 1.61/1.36 % (15682)Instruction limit reached!
% 1.61/1.36 % (15682)------------------------------
% 1.61/1.36 % (15682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15682)Termination reason: Unknown
% 1.61/1.36 % (15682)Termination phase: Saturation
% 1.61/1.36
% 1.61/1.36 % (15682)Memory used [KB]: 5500
% 1.61/1.36 % (15682)Time elapsed: 0.005 s
% 1.61/1.36 % (15682)Instructions burned: 4 (million)
% 1.61/1.36 % (15682)------------------------------
% 1.61/1.36 % (15682)------------------------------
% 1.61/1.36 % (15683)First to succeed.
% 1.61/1.36 % (15686)Also succeeded, but the first one will report.
% 1.61/1.36 % (15688)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15416 for (2999ds/3Mi)
% 1.61/1.36 % (15683)Refutation found. Thanks to Tanya!
% 1.61/1.36 % SZS status Theorem for DTF2THF_15416
% 1.61/1.36 % SZS output start Proof for DTF2THF_15416
% 1.61/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 1.61/1.36 thf(func_def_1, type, symdiff: $i > $i > $i).
% 1.61/1.36 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.36 thf(f124,plain,(
% 1.61/1.36 $false),
% 1.61/1.36 inference(avatar_sat_refutation,[status(thm)],[f83,f101,f123])).
% 1.61/1.36 thf(f123,plain,(
% 1.61/1.36 ~spl3_8),
% 1.61/1.36 inference(avatar_contradiction_clause,[status(thm)],[f122])).
% 1.61/1.36 thf(f122,plain,(
% 1.61/1.36 $false | ~spl3_8),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.61/1.36 thf(f119,plain,(
% 1.61/1.36 ($true = $false) | ~spl3_8),
% 1.61/1.36 inference(backward_demodulation,[status(thm)],[f15,f116])).
% 1.61/1.36 thf(f116,plain,(
% 1.61/1.36 ((in @ sK1 @ sK2) = $false) | ~spl3_8),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.61/1.36 thf(f115,plain,(
% 1.61/1.36 ($true = $false) | ((in @ sK1 @ sK2) = $false) | ~spl3_8),
% 1.61/1.36 inference(forward_demodulation,[status(thm)],[f113,f17])).
% 1.61/1.36 thf(f17,plain,(
% 1.61/1.36 ((in @ sK1 @ sK0) = $true)),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.36 thf(f13,plain,(
% 1.61/1.36 (symdiffE = $true) & (((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ (symdiff @ sK2 @ sK0)) = $true) & ($true = (in @ sK1 @ sK2)))),
% 1.61/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12])).
% 1.61/1.36 thf(f12,plain,(
% 1.61/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ($true = (in @ X1 @ X2))) => (((in @ sK1 @ sK0) = $true) & ((in @ sK1 @ (symdiff @ sK2 @ sK0)) = $true) & ($true = (in @ sK1 @ sK2)))),
% 1.61/1.36 introduced(definition,[],[choice_axiom])).
% 1.61/1.36 thf(f11,plain,(
% 1.61/1.36 (symdiffE = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ($true = (in @ X1 @ X2)))),
% 1.61/1.36 inference(flattening,[status(thm)],[f10])).
% 1.61/1.36 thf(f10,plain,(
% 1.61/1.36 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ($true = (in @ X1 @ X0))) & ($true = (in @ X1 @ X2))) & (symdiffE = $true)),
% 1.61/1.36 inference(ennf_transformation,[status(thm)],[f9])).
% 1.61/1.36 thf(f9,plain,(
% 1.61/1.36 ~((symdiffE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => (($true = (in @ X1 @ X0)) => ((in @ X1 @ (symdiff @ X2 @ X0)) != $true))))),
% 1.61/1.36 inference(flattening,[status(thm)],[f8])).
% 1.61/1.36 thf(f8,plain,(
% 1.61/1.36 ~((symdiffE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => (($true = (in @ X1 @ X0)) => ~((in @ X1 @ (symdiff @ X2 @ X0)) = $true))))),
% 1.61/1.36 inference(fool_elimination,[status(thm)],[f7])).
% 1.61/1.36 thf(f7,plain,(
% 1.61/1.36 ~(symdiffE => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => ~(in @ X1 @ (symdiff @ X2 @ X0)))))),
% 1.61/1.36 inference(rectify,[status(thm)],[f3])).
% 1.61/1.36 thf(f3,negated_conjecture,(
% 1.61/1.36 ~(symdiffE => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1)))))),
% 1.61/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 1.61/1.36 thf(f2,conjecture,(
% 1.61/1.36 symdiffE => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => ~(in @ X2 @ (symdiff @ X0 @ X1))))),
% 1.61/1.36 file('/export/starexec/sandbox2/tmp/tmp.gK8q6H94QX/DTF2THF_15416.p',symdiffIneg1)).
% 1.61/1.36 thf(f113,plain,(
% 1.61/1.36 ((in @ sK1 @ sK2) = $false) | ((in @ sK1 @ sK0) = $false) | ~spl3_8),
% 1.61/1.36 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.61/1.36 thf(f109,plain,(
% 1.61/1.36 ($true = $false) | ((in @ sK1 @ sK2) = $false) | ((in @ sK1 @ sK0) = $false) | ~spl3_8),
% 1.61/1.36 inference(superposition,[status(thm)],[f82,f16])).
% 1.61/1.36 thf(f16,plain,(
% 1.61/1.36 ((in @ sK1 @ (symdiff @ sK2 @ sK0)) = $true)),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.36 thf(f82,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ($false = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $false)) ) | ~spl3_8),
% 1.61/1.36 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.61/1.36 thf(f81,definition,(
% 1.61/1.36 spl3_8 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ((in @ X2 @ X1) = $false) | ($false = (in @ X2 @ X3)))),
% 1.61/1.36 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.61/1.36 thf(f15,plain,(
% 1.61/1.36 ($true = (in @ sK1 @ sK2))),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.36 thf(f101,plain,(
% 1.61/1.36 ~spl3_7),
% 1.61/1.36 inference(avatar_contradiction_clause,[status(thm)],[f100])).
% 1.61/1.36 thf(f100,plain,(
% 1.61/1.36 $false | ~spl3_7),
% 1.61/1.36 inference(equality_resolution,[status(thm)],[f97])).
% 1.61/1.36 thf(f97,plain,(
% 1.61/1.36 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_7),
% 1.61/1.36 inference(superposition,[status(thm)],[f4,f78])).
% 1.61/1.36 thf(f78,plain,(
% 1.61/1.36 ( ! [X4 : $o] : (($true = X4)) ) | ~spl3_7),
% 1.61/1.36 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.61/1.36 thf(f77,definition,(
% 1.61/1.36 spl3_7 <=> ! [X4 : $o] : ($true = X4)),
% 1.61/1.36 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.61/1.36 thf(f4,plain,(
% 1.61/1.36 ($true != $false)),
% 1.61/1.36 introduced(definition,[],[fool_axiom])).
% 1.61/1.36 thf(f83,plain,(
% 1.61/1.36 spl3_8 | spl3_7),
% 1.61/1.36 inference(avatar_split_clause,[status(thm)],[f44,f77,f81])).
% 1.61/1.36 thf(f44,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = X4) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ($false = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $false)) )),
% 1.61/1.36 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.61/1.36 thf(f43,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((~ (in @ X2 @ X3)) = $true) | ((in @ X2 @ X1) = $false) | ($true = X4) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false)) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.61/1.36 thf(f41,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ((in @ X2 @ X1) = $false) | ($true = X4) | (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) = $false)) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.61/1.36 thf(f40,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) => X4)) | ((in @ X2 @ X1) = $false) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false)) )),
% 1.61/1.36 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.61/1.36 thf(f39,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((~ (in @ X2 @ X1)) = $true) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ($true = (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) => X4))) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.61/1.36 thf(f30,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((~ (in @ X2 @ X1)) => X4) = $false) | ($true = (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) => X4)) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false)) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.61/1.36 thf(f29,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((in @ X2 @ X3) => ((~ (in @ X2 @ X1)) => X4)) = $false) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | ($true = (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) => X4))) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.61/1.36 thf(f28,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((((in @ X2 @ X3) => ((~ (in @ X2 @ X1)) => X4)) => (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => X4)) => X4)) = $true) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false)) )),
% 1.61/1.36 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.61/1.36 thf(f27,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X2 @ (symdiff @ X3 @ X1)) = $false) | (((^[Y0 : $o]: (((in @ X2 @ X3) => ((~ (in @ X2 @ X1)) => Y0)) => (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => Y0)) => Y0))) @ X4) = $true)) )),
% 1.61/1.36 inference(pi_clausification,[status(thm)],[f26])).
% 1.61/1.36 thf(f26,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (((in @ X2 @ X3) => ((~ (in @ X2 @ X1)) => Y0)) => (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => Y0)) => Y0))))) | ((in @ X2 @ (symdiff @ X3 @ X1)) = $false)) )),
% 1.61/1.36 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.61/1.36 thf(f25,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ (symdiff @ X3 @ X1)) => (!! @ $o @ (^[Y0 : $o]: (((in @ X2 @ X3) => ((~ (in @ X2 @ X1)) => Y0)) => (((~ (in @ X2 @ X3)) => ((in @ X2 @ X1) => Y0)) => Y0))))))) )),
% 1.61/1.36 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.61/1.36 thf(f24,plain,(
% 1.61/1.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ (symdiff @ Y0 @ X1)) => (!! @ $o @ (^[Y1 : $o]: (((in @ X2 @ Y0) => ((~ (in @ X2 @ X1)) => Y1)) => (((~ (in @ X2 @ Y0)) => ((in @ X2 @ X1) => Y1)) => Y1)))))) @ X3) = $true)) )),
% 1.61/1.36 inference(pi_clausification,[status(thm)],[f23])).
% 1.61/1.36 thf(f23,plain,(
% 1.61/1.36 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (symdiff @ Y0 @ X1)) => (!! @ $o @ (^[Y1 : $o]: (((in @ X2 @ Y0) => ((~ (in @ X2 @ X1)) => Y1)) => (((~ (in @ X2 @ Y0)) => ((in @ X2 @ X1) => Y1)) => Y1))))))) = $true)) )),
% 1.61/1.36 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.61/1.36 thf(f22,plain,(
% 1.61/1.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (symdiff @ Y1 @ X1)) => (!! @ $o @ (^[Y2 : $o]: (((in @ Y0 @ Y1) => ((~ (in @ Y0 @ X1)) => Y2)) => (((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ X1) => Y2)) => Y2)))))))) @ X2))) )),
% 1.61/1.36 inference(pi_clausification,[status(thm)],[f21])).
% 1.61/1.36 thf(f21,plain,(
% 1.61/1.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (symdiff @ Y1 @ X1)) => (!! @ $o @ (^[Y2 : $o]: (((in @ Y0 @ Y1) => ((~ (in @ Y0 @ X1)) => Y2)) => (((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ X1) => Y2)) => Y2))))))))) = $true)) )),
% 1.61/1.36 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.61/1.36 thf(f20,plain,(
% 1.61/1.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3)))))))))) @ X1))) )),
% 1.61/1.36 inference(pi_clausification,[status(thm)],[f19])).
% 1.61/1.36 thf(f19,plain,(
% 1.61/1.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) = $true)),
% 1.61/1.36 inference(definition_unfolding,[status(thm)],[f18,f14])).
% 1.61/1.36 thf(f14,plain,(
% 1.61/1.36 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))))),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f6])).
% 1.61/1.36 thf(f6,plain,(
% 1.61/1.36 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))))),
% 1.61/1.36 inference(fool_elimination,[status(thm)],[f5])).
% 1.61/1.36 thf(f5,plain,(
% 1.61/1.36 (symdiffE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (symdiff @ X0 @ X2)) => ! [X3 : $o] : (((in @ X1 @ X0) => (~(in @ X1 @ X2) => X3)) => ((~(in @ X1 @ X0) => ((in @ X1 @ X2) => X3)) => X3))))),
% 1.61/1.36 inference(rectify,[status(thm)],[f1])).
% 1.61/1.36 thf(f1,axiom,(
% 1.61/1.36 (symdiffE = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (symdiff @ X0 @ X1)) => ! [X3 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X1) => X3)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X1) => X3)) => X3))))),
% 1.61/1.36 file('/export/starexec/sandbox2/tmp/tmp.gK8q6H94QX/DTF2THF_15416.p',symdiffE)).
% 1.61/1.36 thf(f18,plain,(
% 1.61/1.36 (symdiffE = $true)),
% 1.61/1.36 inference(cnf_transformation,[status(thm)],[f13])).
% 1.61/1.36 % SZS output end Proof for DTF2THF_15416
% 1.61/1.36 % (15683)------------------------------
% 1.61/1.36 % (15683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (15683)Termination reason: Refutation
% 1.61/1.36
% 1.61/1.36 % (15683)Memory used [KB]: 5628
% 1.61/1.36 % (15683)Time elapsed: 0.009 s
% 1.61/1.36 % (15683)Instructions burned: 7 (million)
% 1.61/1.36 % (15683)------------------------------
% 1.61/1.36 % (15683)------------------------------
% 1.61/1.36 % (15680)Success in time 0.023 s
%------------------------------------------------------------------------------