%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU611^2 : 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 : n029.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 09:35:36 AM UTC 2026
% Result : Theorem 1.58s 1.39s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 1015 ( 272 equ; 0 cnn)
% Maximal formula atoms : 16 ( 10 avg)
% Number of connectives : 1020 ( 147 ~; 138 |; 57 &; 602 @)
% ( 12 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 21 con; 0-2 aty)
% Number of variables : 208 ( 48 ^; 119 !; 41 ?; 208 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_7,type,
symdiff: $i > $i > $i ).
thf(func_def_22,type,
sK6: $i > $o ).
thf(func_def_28,type,
sK12: $i > $o ).
thf(func_def_30,type,
ph14:
!>[X0: $tType] : X0 ).
thf(f128,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f87,f88,f89,f106,f116,f119,f122,f126]) ).
thf(f126,plain,
( spl13_3
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f125]) ).
thf(f125,plain,
( $false
| spl13_3
| ~ spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ( $false = $true )
| spl13_3
| ~ spl13_5 ),
inference(forward_demodulation,[status(thm)],[f123,f105]) ).
thf(f105,plain,
( ( ( in @ sK1 @ sK2 )
= $false )
| ~ spl13_5 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl13_5
<=> ( ( in @ sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition]) ).
thf(f123,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| spl13_3 ),
inference(subsumption_resolution,[status(thm)],[f109,f85]) ).
thf(f85,plain,
( ( $true
!= ( in @ sK1 @ sK0 ) )
| spl13_3 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl13_3
<=> ( $true
= ( in @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition]) ).
thf(f109,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ( $true
= ( in @ sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( $true
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f71,f97]) ).
thf(f97,plain,
( $true
= ( in @ sK1 @ ( binunion @ sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( $true
= ( in @ sK1 @ ( binunion @ sK2 @ sK0 ) ) ) ),
inference(superposition,[status(thm)],[f73,f74]) ).
thf(f74,plain,
( ( in @ sK1
@ ( dsetconstr @ ( binunion @ sK2 @ sK0 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) )
@ sK2
@ sK0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f41,f50]) ).
thf(f50,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) )
= symdiff ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( binunion @ X0 @ X4 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X4 )
| ~ ( in @ X2 @ X0 ) ) ) )
= symdiff ),
file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',symdiff) ).
thf(f41,plain,
( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( dsetconstrEL = $true )
& ( binunionE = $true )
& ( $true != sK3 )
& ( ( $true
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
!= $true )
| ( $true = sK3 ) )
& ( ( $true
!= ( in @ sK1 @ sK0 ) )
| ( $true = sK3 )
| ( ( in @ sK1 @ sK2 )
= $true ) )
& ( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f26,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true = X3 ) )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 )
| ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) )
=> ( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
!= $true )
| ( $true = X3 ) )
& ( ( $true
!= ( in @ sK1 @ sK0 ) )
| ( $true = X3 )
| ( ( in @ sK1 @ sK2 )
= $true ) ) )
& ( $true
= ( in @ sK1 @ ( symdiff @ sK2 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
!= $true )
| ( $true = X3 ) )
& ( ( $true
!= ( in @ sK1 @ sK0 ) )
| ( $true = X3 )
| ( ( in @ sK1 @ sK2 )
= $true ) ) )
=> ( ( $true != sK3 )
& ( ( $true
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
!= $true )
| ( $true = sK3 ) )
& ( ( $true
!= ( in @ sK1 @ sK0 ) )
| ( $true = sK3 )
| ( ( in @ sK1 @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( dsetconstrEL = $true )
& ( binunionE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) )
| ( $true = X3 ) )
& ( ( ( in @ X1 @ X0 )
!= $true )
| ( $true = X3 )
| ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) )
& ( dsetconstrER = $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) )
& ( binunionE = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( binunionE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [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)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X4: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X4 ) )
=> ! [X1: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> X1 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> X1 ) )
=> X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X4: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( symdiff @ X0 @ X4 ) )
=> ! [X1: $o] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X4 )
=> X1 ) )
=> ( ( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> X1 ) )
=> X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',symdiffE) ).
thf(f73,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) ) )
| ( $true
= ( in @ X4 @ X3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X4 @ X3 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f47,f46]) ).
thf(f46,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f47,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( dsetconstrEL = $true )
| ( ( ( in @ sK5 @ sK4 )
!= $true )
& ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK6 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f30]) ).
thf(f30,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
=> ( ( ( in @ sK5 @ sK4 )
!= $true )
& ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK6 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4 @ X3 ) )
| ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( in @ X1 @ X0 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',dsetconstrEL) ).
thf(f71,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( binunion @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X3 )
= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binunion @ X4 @ X3 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f51,f45]) ).
thf(f45,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f51,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binunion @ X4 @ X3 ) ) )
| ( binunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( binunionE = $true )
| ( ( $true
!= ( in @ sK9 @ sK8 ) )
& ( $true
!= ( in @ sK9 @ sK7 ) )
& ( ( in @ sK9 @ ( binunion @ sK8 @ sK7 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binunion @ X4 @ X3 ) ) ) )
| ( binunionE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f33,f34]) ).
thf(f34,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
=> ( ( $true
!= ( in @ sK9 @ sK8 ) )
& ( $true
!= ( in @ sK9 @ sK7 ) )
& ( ( in @ sK9 @ ( binunion @ sK8 @ sK7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( $true
!= ( in @ X5 @ ( binunion @ X4 @ X3 ) ) ) )
| ( binunionE != $true ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
| ( binunionE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( binunionE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) )
= binunionE ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X4 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X0 ) ) )
= binunionE ),
file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',binunionE) ).
thf(f122,plain,
( ~ spl13_2
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f121]) ).
thf(f121,plain,
( $false
| ~ spl13_2
| ~ spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $false = $true )
| ~ spl13_2
| ~ spl13_5 ),
inference(backward_demodulation,[status(thm)],[f81,f105]) ).
thf(f81,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ~ spl13_2 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl13_2
<=> ( ( in @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f119,plain,
( spl13_2
| ~ spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f118,f99,f80]) ).
thf(f99,definition,
( spl13_4
<=> ( $false
= ( in @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition]) ).
thf(f118,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ~ spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ( $false = $true )
| ~ spl13_4 ),
inference(forward_demodulation,[status(thm)],[f109,f101]) ).
thf(f101,plain,
( ( $false
= ( in @ sK1 @ sK0 ) )
| ~ spl13_4 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f116,plain,
( ~ spl13_3
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl13_3
| ~ spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
( ( $false = $true )
| ~ spl13_3
| ~ spl13_4 ),
inference(forward_demodulation,[status(thm)],[f86,f101]) ).
thf(f86,plain,
( ( $true
= ( in @ sK1 @ sK0 ) )
| ~ spl13_3 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f106,plain,
( spl13_4
| spl13_5 ),
inference(avatar_split_clause,[status(thm)],[f96,f103,f99]) ).
thf(f96,plain,
( ( $false
= ( in @ sK1 @ sK0 ) )
| ( ( in @ sK1 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( in @ sK1 @ sK2 )
= $false )
| ( ( ~ ( in @ sK1 @ sK0 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true
= ( ~ ( in @ sK1 @ sK2 ) ) )
| ( ( ~ ( in @ sK1 @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( $true
= ( ~ ( in @ sK1 @ sK2 )
| ~ ( in @ sK1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK0 ) )
@ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK0 ) )
@ sK1 ) ) ),
inference(superposition,[status(thm)],[f70,f74]) ).
thf(f70,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X3 @ ( dsetconstr @ X4 @ X5 ) ) )
| ( ( X5 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( X5 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true != $true )
| ( ( X5 @ X3 )
= $true )
| ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f55,f40]) ).
thf(f40,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f55,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
= $true )
| ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK12 @ sK10 ) )
& ( ( in @ sK10
@ ( dsetconstr @ sK11
@ ^ [Y0: $i] : ( sK12 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
= $true )
| ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f37,f38]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) )
=> ( ( $true
!= ( sK12 @ sK10 ) )
& ( ( in @ sK10
@ ( dsetconstr @ sK11
@ ^ [Y0: $i] : ( sK12 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
= $true )
| ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X0 ) )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( $true
= ( X2 @ X0 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( dsetconstrER
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',dsetconstrER) ).
thf(f89,plain,
~ spl13_1,
inference(avatar_split_clause,[status(thm)],[f44,f76]) ).
thf(f76,definition,
( spl13_1
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f44,plain,
$true != sK3,
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f88,plain,
( spl13_1
| spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[status(thm)],[f42,f84,f80,f76]) ).
thf(f42,plain,
( ( ( in @ sK1 @ sK2 )
= $true )
| ( $true
!= ( in @ sK1 @ sK0 ) )
| ( $true = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f87,plain,
( spl13_1
| ~ spl13_2
| spl13_3 ),
inference(avatar_split_clause,[status(thm)],[f43,f84,f80,f76]) ).
thf(f43,plain,
( ( ( in @ sK1 @ sK2 )
!= $true )
| ( $true = sK3 )
| ( $true
= ( in @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU611^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.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 12:28:59 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
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : SEU611^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.44 % Domain : Set Theory
% 0.20/0.44 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.20/0.44 % Version : Especial > Reduced > Especial.
% 0.20/0.44 % English : (! A:i.! B:i.! x:i.in x (symdiff A B) -> (! phi:o.(in x A ->
% 0.20/0.44 % ~(in x B) -> phi) -> (~(in x A) -> in x B -> phi) -> phi))
% 0.20/0.44
% 0.20/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.44 % Source : [Bro08]
% 0.20/0.44 % Names : ZFC113l [Bro08]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.20/0.44 % Syntax : Number of formulae : 12 ( 4 unt; 7 typ; 4 def)
% 0.20/0.44 % Number of atoms : 23 ( 4 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 8 ( 4 avg)
% 0.20/0.44 % Number of connectives : 60 ( 4 ~; 2 |; 0 &; 41 @)
% 0.20/0.44 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 15 ( 4 avg)
% 0.20/0.44 % Number of types : 2 ( 0 usr)
% 0.20/0.44 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.20/0.44 % Number of variables : 18 ( 5 ^; 13 !; 0 ?; 18 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : http://mathgate.info/detsetitem.php?id=489
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(in_type,type,
% 0.20/0.44 in: $i > $i > $o ).
% 0.20/0.44
% 0.20/0.44 thf(dsetconstr_type,type,
% 0.20/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.44
% 0.20/0.44 thf(dsetconstrEL_type,type,
% 0.20/0.44 dsetconstrEL: $o ).
% 0.20/0.44
% 0.20/0.44 thf(dsetconstrEL,definition,
% 0.20/0.44 ( dsetconstrEL
% 0.20/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.44 ( ( in @ Xx
% 0.20/0.44 @ ( dsetconstr @ A
% 0.20/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(dsetconstrER_type,type,
% 0.20/0.44 dsetconstrER: $o ).
% 0.20/0.44
% 0.20/0.44 thf(dsetconstrER,definition,
% 0.20/0.44 ( dsetconstrER
% 0.20/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.44 ( ( in @ Xx
% 0.20/0.44 @ ( dsetconstr @ A
% 0.20/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(binunion_type,type,
% 0.20/0.44 binunion: $i > $i > $i ).
% 0.20/0.44
% 0.20/0.44 thf(binunionE_type,type,
% 0.20/0.44 binunionE: $o ).
% 0.20/0.44
% 0.20/0.44 thf(binunionE,definition,
% 0.20/0.44 ( binunionE
% 0.20/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.44 => ( ( in @ Xx @ A )
% 0.20/0.44 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(symdiff_type,type,
% 0.20/0.44 symdiff: $i > $i > $i ).
% 0.20/0.44
% 0.20/0.44 thf(symdiff,definition,
% 0.20/0.44 ( symdiff
% 0.20/0.44 = ( ^ [A: $i,B: $i] :
% 0.20/0.44 ( dsetconstr @ ( binunion @ A @ B )
% 0.20/0.44 @ ^ [Xx: $i] :
% 0.20/0.44 ( ~ ( in @ Xx @ A )
% 0.20/0.44 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(symdiffE,conjecture,
% 0.20/0.44 ( dsetconstrEL
% 0.20/0.44 => ( dsetconstrER
% 0.20/0.44 => ( binunionE
% 0.20/0.44 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.44 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.44 => ! [Xphi: $o] :
% 0.20/0.44 ( ( ( in @ Xx @ A )
% 0.20/0.44 => ( ~ ( in @ Xx @ B )
% 0.20/0.44 => Xphi ) )
% 0.20/0.44 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.44 => ( ( in @ Xx @ B )
% 0.20/0.44 => Xphi ) )
% 0.20/0.44 => Xphi ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.58/1.35 ---- Embedded in THF ---
% 1.58/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.35 %%% Generated on Tue Feb 24 12:29:00 EST 2026
% 1.58/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.35 %%% Logic specification used:
% 1.58/1.35 %%% thf(spec, logic, $$dhol).
% 1.58/1.35
% 1.58/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2DTF10084.p
% See solution above
% 1.58/1.35 ------------------------
% 1.58/1.36 ---- Cleaned THF ---
% 1.58/1.36 thf(in_type,type,
% 1.58/1.36 in: $i > $i > $o ).
% 1.58/1.36
% 1.58/1.36 thf(dsetconstr_type,type,
% 1.58/1.36 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.58/1.36
% 1.58/1.36 thf(dsetconstrEL_type,type,
% 1.58/1.36 dsetconstrEL: $o ).
% 1.58/1.36
% 1.58/1.36 thf(dsetconstrEL,definition,
% 1.58/1.36 ( dsetconstrEL
% 1.58/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.58/1.36 ( ( in @ Xx
% 1.58/1.36 @ ( dsetconstr @ A
% 1.58/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.58/1.36 => ( in @ Xx @ A ) ) ) ) ).
% 1.58/1.36
% 1.58/1.36 thf(dsetconstrER_type,type,
% 1.58/1.36 dsetconstrER: $o ).
% 1.58/1.36
% 1.58/1.36 thf(dsetconstrER,definition,
% 1.58/1.36 ( dsetconstrER
% 1.58/1.36 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.58/1.36 ( ( in @ Xx
% 1.58/1.36 @ ( dsetconstr @ A
% 1.58/1.36 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.58/1.36 => ( Xphi @ Xx ) ) ) ) ).
% 1.58/1.36
% 1.58/1.36 thf(binunion_type,type,
% 1.58/1.36 binunion: $i > $i > $i ).
% 1.58/1.36
% 1.58/1.36 thf(binunionE_type,type,
% 1.58/1.36 binunionE: $o ).
% 1.58/1.36
% 1.58/1.36 thf(binunionE,definition,
% 1.58/1.36 ( binunionE
% 1.58/1.36 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.58/1.36 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.58/1.36 => ( ( in @ Xx @ A )
% 1.58/1.36 | ( in @ Xx @ B ) ) ) ) ) ).
% 1.58/1.36
% 1.58/1.36 thf(symdiff_type,type,
% 1.58/1.36 symdiff: $i > $i > $i ).
% 1.58/1.36
% 1.58/1.36 thf(symdiff,definition,
% 1.58/1.36 ( symdiff
% 1.58/1.36 = ( ^ [A: $i,B: $i] :
% 1.58/1.36 ( dsetconstr @ ( binunion @ A @ B )
% 1.58/1.36 @ ^ [Xx: $i] :
% 1.58/1.36 ( ~ ( in @ Xx @ A )
% 1.58/1.36 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 1.58/1.36
% 1.58/1.36 thf(symdiffE,conjecture,
% 1.58/1.36 ( dsetconstrEL
% 1.58/1.36 => ( dsetconstrER
% 1.58/1.36 => ( binunionE
% 1.58/1.36 => ! [A: $i,B: $i,Xx: $i] :
% 1.58/1.36 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 1.58/1.36 => ! [Xphi: $o] :
% 1.58/1.36 ( ( ( in @ Xx @ A )
% 1.58/1.36 => ( ~ ( in @ Xx @ B )
% 1.58/1.36 => Xphi ) )
% 1.58/1.36 => ( ( ~ ( in @ Xx @ A )
% 1.58/1.36 => ( ( in @ Xx @ B )
% 1.58/1.36 => Xphi ) )
% 1.58/1.36 => Xphi ) ) ) ) ) ) ).
% 1.58/1.36 ------------------------
% 1.58/1.38 % (10183)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_10084 for (2999ds/27Mi)
% 1.58/1.38 % (10184)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10084 for (2999ds/2Mi)
% 1.58/1.38 % (10181)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10084 for (2999ds/183Mi)
% 1.58/1.38 % (10185)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_10084 for (2999ds/2Mi)
% 1.58/1.38 % (10182)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_10084 for (2999ds/4Mi)
% 1.58/1.38 % (10186)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_10084 for (2999ds/275Mi)
% 1.58/1.38 % (10187)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10084 for (2999ds/18Mi)
% 1.58/1.38 % (10184)Instruction limit reached!
% 1.58/1.38 % (10184)------------------------------
% 1.58/1.38 % (10184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (10184)Termination reason: Unknown
% 1.58/1.38 % (10184)Termination phase: Property scanning
% 1.58/1.38 % (10185)Instruction limit reached!
% 1.58/1.38 % (10185)------------------------------
% 1.58/1.38 % (10185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (10185)Termination reason: Unknown
% 1.58/1.38 % (10185)Termination phase: Property scanning
% 1.58/1.38
% 1.58/1.38 % (10185)Memory used [KB]: 1023
% 1.58/1.38 % (10185)Time elapsed: 0.003 s
% 1.58/1.38 % (10185)Instructions burned: 3 (million)
% 1.58/1.38 % (10185)------------------------------
% 1.58/1.38 % (10185)------------------------------
% 1.58/1.38
% 1.58/1.38 % (10184)Memory used [KB]: 1023
% 1.58/1.38 % (10184)Time elapsed: 0.003 s
% 1.58/1.38 % (10184)Instructions burned: 3 (million)
% 1.58/1.38 % (10184)------------------------------
% 1.58/1.38 % (10184)------------------------------
% 1.58/1.38 % (10182)Instruction limit reached!
% 1.58/1.38 % (10182)------------------------------
% 1.58/1.38 % (10182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (10182)Termination reason: Unknown
% 1.58/1.38 % (10182)Termination phase: Saturation
% 1.58/1.38
% 1.58/1.38 % (10182)Memory used [KB]: 5500
% 1.58/1.38 % (10182)Time elapsed: 0.004 s
% 1.58/1.38 % (10182)Instructions burned: 4 (million)
% 1.58/1.38 % (10182)------------------------------
% 1.58/1.38 % (10182)------------------------------
% 1.58/1.38 % (10186)Refutation not found, incomplete strategy
% 1.58/1.38 % (10186)------------------------------
% 1.58/1.38 % (10186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (10186)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.38
% 1.58/1.38
% 1.58/1.38 % (10186)Memory used [KB]: 5500
% 1.58/1.38 % (10186)Time elapsed: 0.004 s
% 1.58/1.38 % (10186)Instructions burned: 4 (million)
% 1.58/1.38 % (10186)------------------------------
% 1.58/1.38 % (10186)------------------------------
% 1.58/1.38 % (10187)First to succeed.
% 1.58/1.39 % (10181)Also succeeded, but the first one will report.
% 1.58/1.39 % (10187)Refutation found. Thanks to Tanya!
% 1.58/1.39 % SZS status Theorem for DTF2THF_10084
% 1.58/1.39 % SZS output start Proof for DTF2THF_10084
% 1.58/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.58/1.39 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.58/1.39 thf(func_def_5, type, binunion: $i > $i > $i).
% 1.58/1.39 thf(func_def_7, type, symdiff: $i > $i > $i).
% 1.58/1.39 thf(func_def_22, type, sK6: $i > $o).
% 1.58/1.39 thf(func_def_28, type, sK12: $i > $o).
% 1.58/1.39 thf(func_def_30, type, ph14: !>[X0: $tType]:(X0)).
% 1.58/1.39 thf(f128,plain,(
% 1.58/1.39 $false),
% 1.58/1.39 inference(avatar_sat_refutation,[status(thm)],[f87,f88,f89,f106,f116,f119,f122,f126])).
% 1.58/1.39 thf(f126,plain,(
% 1.58/1.39 spl13_3 | ~spl13_5),
% 1.58/1.39 inference(avatar_contradiction_clause,[status(thm)],[f125])).
% 1.58/1.39 thf(f125,plain,(
% 1.58/1.39 $false | (spl13_3 | ~spl13_5)),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.58/1.39 thf(f124,plain,(
% 1.58/1.39 ($false = $true) | (spl13_3 | ~spl13_5)),
% 1.58/1.39 inference(forward_demodulation,[status(thm)],[f123,f105])).
% 1.58/1.39 thf(f105,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $false) | ~spl13_5),
% 1.58/1.39 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.58/1.39 thf(f103,definition,(
% 1.58/1.39 spl13_5 <=> ((in @ sK1 @ sK2) = $false)),
% 1.58/1.39 introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition])).
% 1.58/1.39 thf(f123,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | spl13_3),
% 1.58/1.39 inference(subsumption_resolution,[status(thm)],[f109,f85])).
% 1.58/1.39 thf(f85,plain,(
% 1.58/1.39 ($true != (in @ sK1 @ sK0)) | spl13_3),
% 1.58/1.39 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.58/1.39 thf(f84,definition,(
% 1.58/1.39 spl13_3 <=> ($true = (in @ sK1 @ sK0))),
% 1.58/1.39 introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition])).
% 1.58/1.39 thf(f109,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | ($true = (in @ sK1 @ sK0))),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.58/1.39 thf(f108,plain,(
% 1.58/1.39 ($true = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) = $true) | ($true != $true)),
% 1.58/1.39 inference(superposition,[status(thm)],[f71,f97])).
% 1.58/1.39 thf(f97,plain,(
% 1.58/1.39 ($true = (in @ sK1 @ (binunion @ sK2 @ sK0)))),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.58/1.39 thf(f90,plain,(
% 1.58/1.39 ($true != $true) | ($true = (in @ sK1 @ (binunion @ sK2 @ sK0)))),
% 1.58/1.39 inference(superposition,[status(thm)],[f73,f74])).
% 1.58/1.39 thf(f74,plain,(
% 1.58/1.39 ((in @ sK1 @ (dsetconstr @ (binunion @ sK2 @ sK0) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK0)))))) = $true)),
% 1.58/1.39 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.58/1.39 thf(f58,plain,(
% 1.58/1.39 ((in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))) @ sK2 @ sK0)) = $true)),
% 1.58/1.39 inference(definition_unfolding,[status(thm)],[f41,f50])).
% 1.58/1.39 thf(f50,plain,(
% 1.58/1.39 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.39 thf(f13,plain,(
% 1.58/1.39 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 1.58/1.39 inference(fool_elimination,[status(thm)],[f12])).
% 1.58/1.39 thf(f12,plain,(
% 1.58/1.39 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X1) | ~(in @ X2 @ X0))))) = symdiff)),
% 1.58/1.39 inference(rectify,[status(thm)],[f4])).
% 1.58/1.39 thf(f4,axiom,(
% 1.58/1.39 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (binunion @ X0 @ X4) @ (^[X2 : $i] : (~(in @ X2 @ X4) | ~(in @ X2 @ X0))))) = symdiff)),
% 1.58/1.39 file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',symdiff)).
% 1.58/1.39 thf(f41,plain,(
% 1.58/1.39 ($true = (in @ sK1 @ (symdiff @ sK2 @ sK0)))),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f27,plain,(
% 1.58/1.39 (dsetconstrEL = $true) & (binunionE = $true) & ((($true != sK3) & (($true = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) != $true) | ($true = sK3)) & (($true != (in @ sK1 @ sK0)) | ($true = sK3) | ((in @ sK1 @ sK2) = $true))) & ($true = (in @ sK1 @ (symdiff @ sK2 @ sK0)))) & (dsetconstrER = $true)),
% 1.58/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f26,f25])).
% 1.58/1.39 thf(f25,plain,(
% 1.58/1.39 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ X2)) | ($true = X3)) & (((in @ X1 @ X0) != $true) | ($true = X3) | ($true = (in @ X1 @ X2)))) & ($true = (in @ X1 @ (symdiff @ X2 @ X0)))) => (? [X3 : $o] : (($true != X3) & (($true = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) != $true) | ($true = X3)) & (($true != (in @ sK1 @ sK0)) | ($true = X3) | ((in @ sK1 @ sK2) = $true))) & ($true = (in @ sK1 @ (symdiff @ sK2 @ sK0))))),
% 1.58/1.39 introduced(definition,[],[choice_axiom])).
% 1.58/1.39 thf(f26,plain,(
% 1.58/1.39 ? [X3 : $o] : (($true != X3) & (($true = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) != $true) | ($true = X3)) & (($true != (in @ sK1 @ sK0)) | ($true = X3) | ((in @ sK1 @ sK2) = $true))) => (($true != sK3) & (($true = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) != $true) | ($true = sK3)) & (($true != (in @ sK1 @ sK0)) | ($true = sK3) | ((in @ sK1 @ sK2) = $true)))),
% 1.58/1.39 introduced(definition,[],[choice_axiom])).
% 1.58/1.39 thf(f20,plain,(
% 1.58/1.39 (dsetconstrEL = $true) & (binunionE = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ X2)) | ($true = X3)) & (((in @ X1 @ X0) != $true) | ($true = X3) | ($true = (in @ X1 @ X2)))) & ($true = (in @ X1 @ (symdiff @ X2 @ X0)))) & (dsetconstrER = $true)),
% 1.58/1.39 inference(flattening,[status(thm)],[f19])).
% 1.58/1.39 thf(f19,plain,(
% 1.58/1.39 ((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : ((($true != X3) & ((($true = X3) | ((in @ X1 @ X0) != $true)) | ($true = (in @ X1 @ X2)))) & ((($true = X3) | ((in @ X1 @ X0) = $true)) | ($true != (in @ X1 @ X2)))) & ($true = (in @ X1 @ (symdiff @ X2 @ X0)))) & (binunionE = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)),
% 1.58/1.39 inference(ennf_transformation,[status(thm)],[f18])).
% 1.58/1.39 thf(f18,plain,(
% 1.58/1.39 ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((binunionE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X2 @ X0))) => ! [X3 : $o] : ((($true = (in @ X1 @ X2)) => (((in @ X1 @ X0) != $true) => ($true = X3))) => ((($true != (in @ X1 @ X2)) => (((in @ X1 @ X0) = $true) => ($true = X3))) => ($true = X3)))))))),
% 1.58/1.39 inference(flattening,[status(thm)],[f15])).
% 1.58/1.39 thf(f15,plain,(
% 1.58/1.39 ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((binunionE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X2 @ X0))) => ! [X3 : $o] : ((($true = (in @ X1 @ X2)) => (~((in @ X1 @ X0) = $true) => ($true = X3))) => ((~($true = (in @ X1 @ X2)) => (((in @ X1 @ X0) = $true) => ($true = X3))) => ($true = X3)))))))),
% 1.58/1.39 inference(fool_elimination,[status(thm)],[f14])).
% 1.58/1.39 thf(f14,plain,(
% 1.58/1.39 ~(dsetconstrEL => (dsetconstrER => (binunionE => ! [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))))))),
% 1.58/1.39 inference(rectify,[status(thm)],[f6])).
% 1.58/1.39 thf(f6,negated_conjecture,(
% 1.58/1.39 ~(dsetconstrEL => (dsetconstrER => (binunionE => ! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (symdiff @ X0 @ X4)) => ! [X1 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X4) => X1)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X4) => X1)) => X1))))))),
% 1.58/1.39 inference(negated_conjecture,[status(cth)],[f5])).
% 1.58/1.39 thf(f5,conjecture,(
% 1.58/1.39 dsetconstrEL => (dsetconstrER => (binunionE => ! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (symdiff @ X0 @ X4)) => ! [X1 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X4) => X1)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X4) => X1)) => X1)))))),
% 1.58/1.39 file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',symdiffE)).
% 1.58/1.39 thf(f73,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X4 @ (dsetconstr @ X3 @ X5))) | ($true = (in @ X4 @ X3))) )),
% 1.58/1.39 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.58/1.39 thf(f72,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) )),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.58/1.39 thf(f61,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | ($true = (in @ X4 @ X3)) | ($true != $true)) )),
% 1.58/1.39 inference(definition_unfolding,[status(thm)],[f47,f46])).
% 1.58/1.39 thf(f46,plain,(
% 1.58/1.39 (dsetconstrEL = $true)),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f47,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) | (dsetconstrEL != $true)) )),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f31])).
% 1.58/1.39 thf(f31,plain,(
% 1.58/1.39 ((dsetconstrEL = $true) | (((in @ sK5 @ sK4) != $true) & ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK6 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 1.58/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f30])).
% 1.58/1.39 thf(f30,plain,(
% 1.58/1.39 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (((in @ sK5 @ sK4) != $true) & ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK6 @ Y0))))))),
% 1.58/1.39 introduced(definition,[],[choice_axiom])).
% 1.58/1.39 thf(f29,plain,(
% 1.58/1.39 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 1.58/1.39 inference(rectify,[status(thm)],[f28])).
% 1.58/1.39 thf(f28,plain,(
% 1.58/1.39 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrEL != $true))),
% 1.58/1.39 inference(nnf_transformation,[status(thm)],[f24])).
% 1.58/1.39 thf(f24,plain,(
% 1.58/1.39 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))),
% 1.58/1.39 inference(ennf_transformation,[status(thm)],[f9])).
% 1.58/1.39 thf(f9,plain,(
% 1.58/1.39 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ((in @ X1 @ X0) = $true)) <=> (dsetconstrEL = $true)),
% 1.58/1.39 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.39 thf(f8,plain,(
% 1.58/1.39 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)) = dsetconstrEL)),
% 1.58/1.39 inference(rectify,[status(thm)],[f1])).
% 1.58/1.39 thf(f1,axiom,(
% 1.58/1.39 (! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.58/1.39 file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',dsetconstrEL)).
% 1.58/1.39 thf(f71,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (binunion @ X4 @ X3))) | ((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) = $true)) )),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.58/1.39 thf(f65,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) = $true) | ($true != (in @ X5 @ (binunion @ X4 @ X3)))) )),
% 1.58/1.39 inference(definition_unfolding,[status(thm)],[f51,f45])).
% 1.58/1.39 thf(f45,plain,(
% 1.58/1.39 (binunionE = $true)),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f51,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) = $true) | ($true != (in @ X5 @ (binunion @ X4 @ X3))) | (binunionE != $true)) )),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f35])).
% 1.58/1.39 thf(f35,plain,(
% 1.58/1.39 ((binunionE = $true) | (($true != (in @ sK9 @ sK8)) & ($true != (in @ sK9 @ sK7)) & ((in @ sK9 @ (binunion @ sK8 @ sK7)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) = $true) | ($true != (in @ X5 @ (binunion @ X4 @ X3)))) | (binunionE != $true))),
% 1.58/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f33,f34])).
% 1.58/1.39 thf(f34,plain,(
% 1.58/1.39 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0)))) => (($true != (in @ sK9 @ sK8)) & ($true != (in @ sK9 @ sK7)) & ((in @ sK9 @ (binunion @ sK8 @ sK7)) = $true))),
% 1.58/1.39 introduced(definition,[],[choice_axiom])).
% 1.58/1.39 thf(f33,plain,(
% 1.58/1.39 ((binunionE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) = $true) | ($true != (in @ X5 @ (binunion @ X4 @ X3)))) | (binunionE != $true))),
% 1.58/1.39 inference(rectify,[status(thm)],[f32])).
% 1.58/1.39 thf(f32,plain,(
% 1.58/1.39 ((binunionE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ (binunion @ X1 @ X0)))) | (binunionE != $true))),
% 1.58/1.39 inference(nnf_transformation,[status(thm)],[f22])).
% 1.58/1.39 thf(f22,plain,(
% 1.58/1.39 (binunionE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) = $true) | ($true != (in @ X2 @ (binunion @ X1 @ X0))))),
% 1.58/1.39 inference(flattening,[status(thm)],[f21])).
% 1.58/1.39 thf(f21,plain,(
% 1.58/1.39 (binunionE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)) | ($true != (in @ X2 @ (binunion @ X1 @ X0))))),
% 1.58/1.39 inference(ennf_transformation,[status(thm)],[f11])).
% 1.58/1.39 thf(f11,plain,(
% 1.58/1.39 (binunionE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (binunion @ X1 @ X0))) => (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)))),
% 1.58/1.39 inference(fool_elimination,[status(thm)],[f10])).
% 1.58/1.39 thf(f10,plain,(
% 1.58/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X1 @ X0)) => ((in @ X2 @ X0) | (in @ X2 @ X1))) = binunionE)),
% 1.58/1.39 inference(rectify,[status(thm)],[f3])).
% 1.58/1.39 thf(f3,axiom,(
% 1.58/1.39 (! [X4 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binunion @ X0 @ X4)) => ((in @ X2 @ X4) | (in @ X2 @ X0))) = binunionE)),
% 1.58/1.39 file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',binunionE)).
% 1.58/1.39 thf(f122,plain,(
% 1.58/1.39 ~spl13_2 | ~spl13_5),
% 1.58/1.39 inference(avatar_contradiction_clause,[status(thm)],[f121])).
% 1.58/1.39 thf(f121,plain,(
% 1.58/1.39 $false | (~spl13_2 | ~spl13_5)),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.58/1.39 thf(f120,plain,(
% 1.58/1.39 ($false = $true) | (~spl13_2 | ~spl13_5)),
% 1.58/1.39 inference(backward_demodulation,[status(thm)],[f81,f105])).
% 1.58/1.39 thf(f81,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | ~spl13_2),
% 1.58/1.39 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.58/1.39 thf(f80,definition,(
% 1.58/1.39 spl13_2 <=> ((in @ sK1 @ sK2) = $true)),
% 1.58/1.39 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.58/1.39 thf(f119,plain,(
% 1.58/1.39 spl13_2 | ~spl13_4),
% 1.58/1.39 inference(avatar_split_clause,[status(thm)],[f118,f99,f80])).
% 1.58/1.39 thf(f99,definition,(
% 1.58/1.39 spl13_4 <=> ($false = (in @ sK1 @ sK0))),
% 1.58/1.39 introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition])).
% 1.58/1.39 thf(f118,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | ~spl13_4),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.58/1.39 thf(f117,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | ($false = $true) | ~spl13_4),
% 1.58/1.39 inference(forward_demodulation,[status(thm)],[f109,f101])).
% 1.58/1.39 thf(f101,plain,(
% 1.58/1.39 ($false = (in @ sK1 @ sK0)) | ~spl13_4),
% 1.58/1.39 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.58/1.39 thf(f116,plain,(
% 1.58/1.39 ~spl13_3 | ~spl13_4),
% 1.58/1.39 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.58/1.39 thf(f115,plain,(
% 1.58/1.39 $false | (~spl13_3 | ~spl13_4)),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.58/1.39 thf(f114,plain,(
% 1.58/1.39 ($false = $true) | (~spl13_3 | ~spl13_4)),
% 1.58/1.39 inference(forward_demodulation,[status(thm)],[f86,f101])).
% 1.58/1.39 thf(f86,plain,(
% 1.58/1.39 ($true = (in @ sK1 @ sK0)) | ~spl13_3),
% 1.58/1.39 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.58/1.39 thf(f106,plain,(
% 1.58/1.39 spl13_4 | spl13_5),
% 1.58/1.39 inference(avatar_split_clause,[status(thm)],[f96,f103,f99])).
% 1.58/1.39 thf(f96,plain,(
% 1.58/1.39 ($false = (in @ sK1 @ sK0)) | ((in @ sK1 @ sK2) = $false)),
% 1.58/1.39 inference(not_proxy_clausification,[status(thm)],[f95])).
% 1.58/1.39 thf(f95,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $false) | ((~ (in @ sK1 @ sK0)) = $true)),
% 1.58/1.39 inference(not_proxy_clausification,[status(thm)],[f94])).
% 1.58/1.39 thf(f94,plain,(
% 1.58/1.39 ($true = (~ (in @ sK1 @ sK2))) | ((~ (in @ sK1 @ sK0)) = $true)),
% 1.58/1.39 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.58/1.39 thf(f93,plain,(
% 1.58/1.39 ($true = ((~ (in @ sK1 @ sK2)) | (~ (in @ sK1 @ sK0))))),
% 1.58/1.39 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.58/1.39 thf(f92,plain,(
% 1.58/1.39 ($true = ((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK0)))) @ sK1))),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.58/1.39 thf(f91,plain,(
% 1.58/1.39 ($true != $true) | ($true = ((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK0)))) @ sK1))),
% 1.58/1.39 inference(superposition,[status(thm)],[f70,f74])).
% 1.58/1.39 thf(f70,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X3 @ (dsetconstr @ X4 @ X5))) | ((X5 @ X3) = $true)) )),
% 1.58/1.39 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.58/1.39 thf(f69,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((X5 @ X3) = $true)) )),
% 1.58/1.39 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.58/1.39 thf(f68,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != $true) | ((X5 @ X3) = $true) | ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))))) )),
% 1.58/1.39 inference(definition_unfolding,[status(thm)],[f55,f40])).
% 1.58/1.39 thf(f40,plain,(
% 1.58/1.39 (dsetconstrER = $true)),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f55,plain,(
% 1.58/1.39 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X3) = $true) | ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) | (dsetconstrER != $true)) )),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f39])).
% 1.58/1.39 thf(f39,plain,(
% 1.58/1.39 ((dsetconstrER = $true) | (($true != (sK12 @ sK10)) & ((in @ sK10 @ (dsetconstr @ sK11 @ (^[Y0 : $i]: (sK12 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X3) = $true) | ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrER != $true))),
% 1.58/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f37,f38])).
% 1.58/1.39 thf(f38,plain,(
% 1.58/1.39 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (X2 @ X0)) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)) => (($true != (sK12 @ sK10)) & ((in @ sK10 @ (dsetconstr @ sK11 @ (^[Y0 : $i]: (sK12 @ Y0)))) = $true))),
% 1.58/1.39 introduced(definition,[],[choice_axiom])).
% 1.58/1.39 thf(f37,plain,(
% 1.58/1.39 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (X2 @ X0)) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X3) = $true) | ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrER != $true))),
% 1.58/1.39 inference(rectify,[status(thm)],[f36])).
% 1.58/1.39 thf(f36,plain,(
% 1.58/1.39 ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (X2 @ X0)) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 1.58/1.39 inference(nnf_transformation,[status(thm)],[f23])).
% 1.58/1.39 thf(f23,plain,(
% 1.58/1.39 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true))),
% 1.58/1.39 inference(ennf_transformation,[status(thm)],[f17])).
% 1.58/1.39 thf(f17,plain,(
% 1.58/1.39 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ($true = (X2 @ X0))) <=> (dsetconstrER = $true)),
% 1.58/1.39 inference(fool_elimination,[status(thm)],[f16])).
% 1.58/1.39 thf(f16,plain,(
% 1.58/1.39 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)))),
% 1.58/1.39 inference(rectify,[status(thm)],[f2])).
% 1.58/1.39 thf(f2,axiom,(
% 1.58/1.39 (dsetconstrER = ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.58/1.39 file('/export/starexec/sandbox/tmp/tmp.Xc5ErJGZtb/DTF2THF_10084.p',dsetconstrER)).
% 1.58/1.39 thf(f89,plain,(
% 1.58/1.39 ~spl13_1),
% 1.58/1.39 inference(avatar_split_clause,[status(thm)],[f44,f76])).
% 1.58/1.39 thf(f76,definition,(
% 1.58/1.39 spl13_1 <=> ($true = sK3)),
% 1.58/1.39 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.58/1.39 thf(f44,plain,(
% 1.58/1.39 ($true != sK3)),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f88,plain,(
% 1.58/1.39 spl13_1 | spl13_2 | ~spl13_3),
% 1.58/1.39 inference(avatar_split_clause,[status(thm)],[f42,f84,f80,f76])).
% 1.58/1.39 thf(f42,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) = $true) | ($true != (in @ sK1 @ sK0)) | ($true = sK3)),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 thf(f87,plain,(
% 1.58/1.39 spl13_1 | ~spl13_2 | spl13_3),
% 1.58/1.39 inference(avatar_split_clause,[status(thm)],[f43,f84,f80,f76])).
% 1.58/1.39 thf(f43,plain,(
% 1.58/1.39 ((in @ sK1 @ sK2) != $true) | ($true = sK3) | ($true = (in @ sK1 @ sK0))),
% 1.58/1.39 inference(cnf_transformation,[status(thm)],[f27])).
% 1.58/1.39 % SZS output end Proof for DTF2THF_10084
% 1.58/1.39 % (10187)------------------------------
% 1.58/1.39 % (10187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (10187)Termination reason: Refutation
% 1.58/1.39
% 1.58/1.39 % (10187)Memory used [KB]: 5628
% 1.58/1.39 % (10187)Time elapsed: 0.009 s
% 1.58/1.39 % (10187)Instructions burned: 8 (million)
% 1.58/1.39 % (10187)------------------------------
% 1.58/1.39 % (10187)------------------------------
% 1.58/1.39 % (10180)Success in time 0.023 s
%------------------------------------------------------------------------------