%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU613^2 : 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 : n002.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 1.72s 1.44s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 407 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 604 ( 43 ~; 20 |; 16 &; 435 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 8 con; 0-2 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 131 ( 62 ^; 60 !; 9 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
binunion: $i > $i > $i ).
thf(func_def_6,type,
symdiff: $i > $i > $i ).
thf(func_def_21,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
$true = $false,
inference(superposition,[status(thm)],[f61,f25]) ).
thf(f25,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( binunionIR = $true )
& ( dsetconstrI = $true )
& ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
=> ( ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( binunionIR = $true )
& ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( binunionIR = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( dsetconstrI = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( dsetconstrI
=> ( binunionIR
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dsetconstrI
=> ( binunionIR
=> ! [X2: $i,X0: $i,X4: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( symdiff @ X0 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dsetconstrI
=> ( binunionIR
=> ! [X2: $i,X0: $i,X4: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( symdiff @ X0 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',symdiffI2) ).
thf(f61,plain,
( ( in @ sK0 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f37,f57]) ).
thf(f57,plain,
( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false ),
inference(subsumption_resolution,[status(thm)],[f56,f24]) ).
thf(f24,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f56,plain,
( ( ( in @ sK0 @ sK1 )
= $true )
| ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false )
| ( ( ~ ( in @ sK0 @ sK1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false )
| ( ( ~ ( in @ sK0 @ sK2 )
| ~ ( in @ sK0 @ sK1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK0 )
= $false )
| ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true != $true )
| ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f47,f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f21]) ).
thf(f21,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',dsetconstrI) ).
thf(f26,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f47,plain,
( $true
!= ( in @ sK0
@ ( dsetconstr @ ( binunion @ sK1 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
!= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f22]) ).
thf(f22,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( symdiff
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( binunion @ X0 @ X4 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',symdiff) ).
thf(f23,plain,
( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binunion @ X1 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f27,f20]) ).
thf(f20,plain,
( binunionIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( binunionIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( binunionIR
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binunionIR
= ( ! [X4: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',binunionIR) ).
thf(f27,plain,
binunionIR = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU613^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:18 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEU613^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.47 % Domain : Set Theory
% 0.21/0.47 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.21/0.47 % Version : Especial > Reduced > Especial.
% 0.21/0.47 % English : (! A:i.! B:i.! x:i.~(in x A) -> in x B -> in x (symdiff A B))
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.47 % Source : [Bro08]
% 0.21/0.47 % Names : ZFC115l [Bro08]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.21/0.47 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.21/0.47 % Number of atoms : 16 ( 3 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 5 ( 4 avg)
% 0.21/0.47 % Number of connectives : 41 ( 3 ~; 1 |; 0 &; 30 @)
% 0.21/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 11 ( 4 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.21/0.47 % Number of variables : 13 ( 4 ^; 9 !; 0 ?; 13 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : http://mathgate.info/detsetitem.php?id=491
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(in_type,type,
% 0.21/0.47 in: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(dsetconstr_type,type,
% 0.21/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(dsetconstrI_type,type,
% 0.21/0.47 dsetconstrI: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dsetconstrI,definition,
% 0.21/0.47 ( dsetconstrI
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 => ( in @ Xx
% 0.21/0.47 @ ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunion_type,type,
% 0.21/0.47 binunion: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIR_type,type,
% 0.21/0.47 binunionIR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIR,definition,
% 0.21/0.47 ( binunionIR
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiff_type,type,
% 0.21/0.47 symdiff: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(symdiff,definition,
% 0.21/0.47 ( symdiff
% 0.21/0.47 = ( ^ [A: $i,B: $i] :
% 0.21/0.47 ( dsetconstr @ ( binunion @ A @ B )
% 0.21/0.47 @ ^ [Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ A )
% 0.21/0.47 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffI2,conjecture,
% 0.21/0.47 ( dsetconstrI
% 0.21/0.47 => ( binunionIR
% 0.21/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ A )
% 0.21/0.47 => ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.51/1.40 ---- Embedded in THF ---
% 1.72/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.40 %%% Generated on Tue Feb 24 12:29:19 EST 2026
% 1.72/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.40 %%% Logic specification used:
% 1.72/1.40 %%% thf(spec, logic, $$dhol).
% 1.72/1.40
% 1.72/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2DTF32155.p
% See solution above
% 1.72/1.40 ------------------------
% 1.72/1.41 ---- Cleaned THF ---
% 1.72/1.41 thf(in_type,type,
% 1.72/1.41 in: $i > $i > $o ).
% 1.72/1.41
% 1.72/1.41 thf(dsetconstr_type,type,
% 1.72/1.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.72/1.41
% 1.72/1.41 thf(dsetconstrI_type,type,
% 1.72/1.41 dsetconstrI: $o ).
% 1.72/1.41
% 1.72/1.41 thf(dsetconstrI,definition,
% 1.72/1.41 ( dsetconstrI
% 1.72/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.41 ( ( in @ Xx @ A )
% 1.72/1.41 => ( ( Xphi @ Xx )
% 1.72/1.41 => ( in @ Xx
% 1.72/1.41 @ ( dsetconstr @ A
% 1.72/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.72/1.41
% 1.72/1.41 thf(binunion_type,type,
% 1.72/1.41 binunion: $i > $i > $i ).
% 1.72/1.41
% 1.72/1.41 thf(binunionIR_type,type,
% 1.72/1.41 binunionIR: $o ).
% 1.72/1.41
% 1.72/1.41 thf(binunionIR,definition,
% 1.72/1.41 ( binunionIR
% 1.72/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.72/1.41 ( ( in @ Xx @ B )
% 1.72/1.41 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.72/1.41
% 1.72/1.41 thf(symdiff_type,type,
% 1.72/1.41 symdiff: $i > $i > $i ).
% 1.72/1.41
% 1.72/1.41 thf(symdiff,definition,
% 1.72/1.41 ( symdiff
% 1.72/1.41 = ( ^ [A: $i,B: $i] :
% 1.72/1.41 ( dsetconstr @ ( binunion @ A @ B )
% 1.72/1.41 @ ^ [Xx: $i] :
% 1.72/1.41 ( ~ ( in @ Xx @ A )
% 1.72/1.41 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 1.72/1.41
% 1.72/1.41 thf(symdiffI2,conjecture,
% 1.72/1.41 ( dsetconstrI
% 1.72/1.41 => ( binunionIR
% 1.72/1.41 => ! [A: $i,B: $i,Xx: $i] :
% 1.72/1.41 ( ~ ( in @ Xx @ A )
% 1.72/1.41 => ( ( in @ Xx @ B )
% 1.72/1.41 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 1.72/1.41 ------------------------
% 1.72/1.43 % (32256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32155 for (2999ds/2Mi)
% 1.72/1.43 % (32257)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_32155 for (2999ds/2Mi)
% 1.72/1.43 % (32255)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_32155 for (2999ds/27Mi)
% 1.72/1.43 % (32253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32155 for (2999ds/183Mi)
% 1.72/1.43 % (32259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32155 for (2999ds/18Mi)
% 1.72/1.43 % (32254)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_32155 for (2999ds/4Mi)
% 1.72/1.43 % (32258)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_32155 for (2999ds/275Mi)
% 1.72/1.43 % (32256)Instruction limit reached!
% 1.72/1.43 % (32256)------------------------------
% 1.72/1.43 % (32256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (32256)Termination reason: Unknown
% 1.72/1.43 % (32256)Termination phase: Property scanning
% 1.72/1.43
% 1.72/1.43 % (32256)Memory used [KB]: 1023
% 1.72/1.43 % (32256)Time elapsed: 0.003 s
% 1.72/1.43 % (32256)Instructions burned: 3 (million)
% 1.72/1.43 % (32256)------------------------------
% 1.72/1.43 % (32256)------------------------------
% 1.72/1.43 % (32254)Instruction limit reached!
% 1.72/1.43 % (32254)------------------------------
% 1.72/1.43 % (32254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (32254)Termination reason: Unknown
% 1.72/1.43 % (32254)Termination phase: Saturation
% 1.72/1.43
% 1.72/1.43 % (32254)Memory used [KB]: 5500
% 1.72/1.43 % (32254)Time elapsed: 0.004 s
% 1.72/1.43 % (32254)Instructions burned: 4 (million)
% 1.72/1.43 % (32254)------------------------------
% 1.72/1.43 % (32254)------------------------------
% 1.72/1.43 % (32257)Instruction limit reached!
% 1.72/1.43 % (32257)------------------------------
% 1.72/1.43 % (32257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (32257)Termination reason: Unknown
% 1.72/1.43 % (32257)Termination phase: Property scanning
% 1.72/1.43
% 1.72/1.43 % (32257)Memory used [KB]: 895
% 1.72/1.43 % (32257)Time elapsed: 0.003 s
% 1.72/1.43 % (32257)Instructions burned: 2 (million)
% 1.72/1.43 % (32257)------------------------------
% 1.72/1.43 % (32257)------------------------------
% 1.72/1.43 % (32258)Refutation not found, incomplete strategy
% 1.72/1.43 % (32258)------------------------------
% 1.72/1.43 % (32258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (32258)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.43
% 1.72/1.43
% 1.72/1.43 % (32258)Memory used [KB]: 5500
% 1.72/1.43 % (32258)Time elapsed: 0.004 s
% 1.72/1.43 % (32258)Instructions burned: 4 (million)
% 1.72/1.43 % (32258)------------------------------
% 1.72/1.43 % (32258)------------------------------
% 1.72/1.43 % (32253)First to succeed.
% 1.72/1.44 % (32255)Also succeeded, but the first one will report.
% 1.72/1.44 % (32253)Refutation found. Thanks to Tanya!
% 1.72/1.44 % SZS status Theorem for DTF2THF_32155
% 1.72/1.44 % SZS output start Proof for DTF2THF_32155
% 1.72/1.44 thf(func_def_0, type, in: $i > $i > $o).
% 1.72/1.44 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.72/1.44 thf(func_def_4, type, binunion: $i > $i > $i).
% 1.72/1.44 thf(func_def_6, type, symdiff: $i > $i > $i).
% 1.72/1.44 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 1.72/1.44 thf(f64,plain,(
% 1.72/1.44 $false),
% 1.72/1.44 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.72/1.44 thf(f62,plain,(
% 1.72/1.44 ($true = $false)),
% 1.72/1.44 inference(superposition,[status(thm)],[f61,f25])).
% 1.72/1.44 thf(f25,plain,(
% 1.72/1.44 ((in @ sK0 @ sK2) = $true)),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.44 thf(f19,plain,(
% 1.72/1.44 (binunionIR = $true) & (dsetconstrI = $true) & (((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true))),
% 1.72/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18])).
% 1.72/1.44 thf(f18,plain,(
% 1.72/1.44 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) => (((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ sK1) != $true) & ((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true))),
% 1.72/1.44 introduced(definition,[],[choice_axiom])).
% 1.72/1.44 thf(f17,plain,(
% 1.72/1.44 (binunionIR = $true) & (dsetconstrI = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ (symdiff @ X1 @ X2)) != $true))),
% 1.72/1.44 inference(flattening,[status(thm)],[f16])).
% 1.72/1.44 thf(f16,plain,(
% 1.72/1.44 (? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (symdiff @ X1 @ X2)) != $true) & ((in @ X0 @ X2) = $true)) & ((in @ X0 @ X1) != $true)) & (binunionIR = $true)) & (dsetconstrI = $true)),
% 1.72/1.44 inference(ennf_transformation,[status(thm)],[f15])).
% 1.72/1.44 thf(f15,plain,(
% 1.72/1.44 ~((dsetconstrI = $true) => ((binunionIR = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) => (((in @ X0 @ X2) = $true) => ((in @ X0 @ (symdiff @ X1 @ X2)) = $true)))))),
% 1.72/1.44 inference(flattening,[status(thm)],[f8])).
% 1.72/1.44 thf(f8,plain,(
% 1.72/1.44 ~((dsetconstrI = $true) => ((binunionIR = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (~((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) = $true) => ((in @ X0 @ (symdiff @ X1 @ X2)) = $true)))))),
% 1.72/1.44 inference(fool_elimination,[status(thm)],[f7])).
% 1.72/1.44 thf(f7,plain,(
% 1.72/1.44 ~(dsetconstrI => (binunionIR => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2))))))),
% 1.72/1.44 inference(rectify,[status(thm)],[f5])).
% 1.72/1.44 thf(f5,negated_conjecture,(
% 1.72/1.44 ~(dsetconstrI => (binunionIR => ! [X2 : $i,X0 : $i,X4 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (symdiff @ X0 @ X4))))))),
% 1.72/1.44 inference(negated_conjecture,[status(cth)],[f4])).
% 1.72/1.44 thf(f4,conjecture,(
% 1.72/1.44 dsetconstrI => (binunionIR => ! [X2 : $i,X0 : $i,X4 : $i] : (~(in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (symdiff @ X0 @ X4)))))),
% 1.72/1.44 file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',symdiffI2)).
% 1.72/1.44 thf(f61,plain,(
% 1.72/1.44 ((in @ sK0 @ sK2) = $false)),
% 1.72/1.44 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.72/1.44 thf(f59,plain,(
% 1.72/1.44 ((in @ sK0 @ sK2) = $false) | ($true = $false)),
% 1.72/1.44 inference(superposition,[status(thm)],[f37,f57])).
% 1.72/1.44 thf(f57,plain,(
% 1.72/1.44 ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false)),
% 1.72/1.44 inference(subsumption_resolution,[status(thm)],[f56,f24])).
% 1.72/1.44 thf(f24,plain,(
% 1.72/1.44 ((in @ sK0 @ sK1) != $true)),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.44 thf(f56,plain,(
% 1.72/1.44 ((in @ sK0 @ sK1) = $true) | ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false)),
% 1.72/1.44 inference(not_proxy_clausification,[status(thm)],[f53])).
% 1.72/1.44 thf(f53,plain,(
% 1.72/1.44 ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false) | ((~ (in @ sK0 @ sK1)) = $false)),
% 1.72/1.44 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.72/1.44 thf(f52,plain,(
% 1.72/1.44 ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false) | (((~ (in @ sK0 @ sK2)) | (~ (in @ sK0 @ sK1))) = $false)),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.72/1.44 thf(f51,plain,(
% 1.72/1.44 (((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))) @ sK0) = $false) | ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false)),
% 1.72/1.44 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.72/1.44 thf(f50,plain,(
% 1.72/1.44 ($true != $true) | ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $false) | (((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))) @ sK0) = $false)),
% 1.72/1.44 inference(superposition,[status(thm)],[f47,f46])).
% 1.72/1.44 thf(f46,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X3)) = $true) | ((in @ X2 @ X1) = $false) | ((X3 @ X2) = $false)) )),
% 1.72/1.44 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.72/1.44 thf(f45,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ X1) = $false) | (((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3))) = $true)) )),
% 1.72/1.44 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.72/1.44 thf(f44,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))))) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.72/1.44 thf(f43,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f42])).
% 1.72/1.44 thf(f42,plain,(
% 1.72/1.44 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))) = $true)) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.72/1.44 thf(f41,plain,(
% 1.72/1.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f40])).
% 1.72/1.44 thf(f40,plain,(
% 1.72/1.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))) = $true)) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.72/1.44 thf(f39,plain,(
% 1.72/1.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f38])).
% 1.72/1.44 thf(f38,plain,(
% 1.72/1.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) = $true)),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.72/1.44 thf(f29,plain,(
% 1.72/1.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 1.72/1.44 inference(definition_unfolding,[status(thm)],[f26,f21])).
% 1.72/1.44 thf(f21,plain,(
% 1.72/1.44 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f14])).
% 1.72/1.44 thf(f14,plain,(
% 1.72/1.44 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.72/1.44 inference(fool_elimination,[status(thm)],[f13])).
% 1.72/1.44 thf(f13,plain,(
% 1.72/1.44 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 1.72/1.44 inference(rectify,[status(thm)],[f1])).
% 1.72/1.44 thf(f1,axiom,(
% 1.72/1.44 (dsetconstrI = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.72/1.44 file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',dsetconstrI)).
% 1.72/1.44 thf(f26,plain,(
% 1.72/1.44 (dsetconstrI = $true)),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.44 thf(f47,plain,(
% 1.72/1.44 ($true != (in @ sK0 @ (dsetconstr @ (binunion @ sK1 @ sK2) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))))))),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.72/1.44 thf(f30,plain,(
% 1.72/1.44 ($true != (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))) @ sK1 @ sK2)))),
% 1.72/1.44 inference(definition_unfolding,[status(thm)],[f23,f22])).
% 1.72/1.44 thf(f22,plain,(
% 1.72/1.44 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.72/1.44 thf(f10,plain,(
% 1.72/1.44 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 1.72/1.44 inference(fool_elimination,[status(thm)],[f9])).
% 1.72/1.44 thf(f9,plain,(
% 1.72/1.44 (symdiff = (^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X0) | ~(in @ X2 @ X1))))))),
% 1.72/1.44 inference(rectify,[status(thm)],[f3])).
% 1.72/1.44 thf(f3,axiom,(
% 1.72/1.44 (symdiff = (^[X0 : $i, X4 : $i] : (dsetconstr @ (binunion @ X0 @ X4) @ (^[X2 : $i] : (~(in @ X2 @ X0) | ~(in @ X2 @ X4))))))),
% 1.72/1.44 file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',symdiff)).
% 1.72/1.44 thf(f23,plain,(
% 1.72/1.44 ((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true)),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.44 thf(f37,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (binunion @ X1 @ X3)) = $true) | ((in @ X2 @ X3) = $false)) )),
% 1.72/1.44 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.72/1.44 thf(f36,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X3) => (in @ X2 @ (binunion @ X1 @ X3))) = $true)) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.72/1.44 thf(f35,plain,(
% 1.72/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ X1 @ Y0)))) @ X3))) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f34])).
% 1.72/1.44 thf(f34,plain,(
% 1.72/1.44 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ X1 @ Y0))))) = $true)) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.72/1.44 thf(f33,plain,(
% 1.72/1.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ X1 @ Y1)))))) @ X2) = $true)) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f32])).
% 1.72/1.44 thf(f32,plain,(
% 1.72/1.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ X1 @ Y1))))))) = $true)) )),
% 1.72/1.44 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.72/1.44 thf(f31,plain,(
% 1.72/1.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2)))))))) @ X1) = $true)) )),
% 1.72/1.44 inference(pi_clausification,[status(thm)],[f28])).
% 1.72/1.44 thf(f28,plain,(
% 1.72/1.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) = $true)),
% 1.72/1.44 inference(definition_unfolding,[status(thm)],[f27,f20])).
% 1.72/1.44 thf(f20,plain,(
% 1.72/1.44 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f12])).
% 1.72/1.44 thf(f12,plain,(
% 1.72/1.44 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 1.72/1.44 inference(fool_elimination,[status(thm)],[f11])).
% 1.72/1.44 thf(f11,plain,(
% 1.72/1.44 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 1.72/1.44 inference(rectify,[status(thm)],[f2])).
% 1.72/1.44 thf(f2,axiom,(
% 1.72/1.44 (binunionIR = ! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X4) => (in @ X2 @ (binunion @ X0 @ X4))))),
% 1.72/1.44 file('/export/starexec/sandbox/tmp/tmp.3vs43EWtUE/DTF2THF_32155.p',binunionIR)).
% 1.72/1.44 thf(f27,plain,(
% 1.72/1.44 (binunionIR = $true)),
% 1.72/1.44 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.44 % SZS output end Proof for DTF2THF_32155
% 1.72/1.44 % (32253)------------------------------
% 1.72/1.44 % (32253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (32253)Termination reason: Refutation
% 1.72/1.44
% 1.72/1.44 % (32253)Memory used [KB]: 5500
% 1.72/1.44 % (32253)Time elapsed: 0.007 s
% 1.72/1.44 % (32253)Instructions burned: 5 (million)
% 1.72/1.44 % (32253)------------------------------
% 1.72/1.44 % (32253)------------------------------
% 1.72/1.44 % (32252)Success in time 0.021 s
%------------------------------------------------------------------------------