%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU700^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:36:30 AM UTC 2026
% Result : Theorem 1.36s 1.30s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 468 ( 151 equ; 0 cnn)
% Maximal formula atoms : 8 ( 13 avg)
% Number of connectives : 491 ( 86 ~; 52 |; 70 &; 251 @)
% ( 3 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 110 ( 31 ^; 56 !; 23 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_12,type,
sK0: $i > $o ).
thf(func_def_20,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f57,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f56,f27]) ).
thf(f27,plain,
( ( in @ sK6 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( in @ sK3 @ sK5 ) )
& ( ( in @ sK6
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK6 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true != sK4 )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f13,f19,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( X1
& ( X0 = Y0 ) ) ) ) ) )
& ( $true
= ( in @ X3 @ X2 ) )
& ( $true != X1 ) ) )
=> ( ( $true
= ( in @ sK3 @ sK5 ) )
& ? [X3: $i] :
( ( ( in @ X3
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ~ sK4
& ( X3 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK5 ) )
& ( $true != sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ( ( in @ X3
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ~ sK4
& ( X3 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK5 ) )
& ( $true != sK4 ) )
=> ( ( ( in @ sK6
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK6 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ sK6 @ sK5 )
= $true )
& ( $true != sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( X1
& ( X0 = Y0 ) ) ) ) ) )
& ( $true
= ( in @ X3 @ X2 ) )
& ( $true != X1 ) ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( X1
& ( X0 = Y0 ) ) ) ) ) )
& ( $true != X1 )
& ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $o,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true != X1 )
=> ( $true
= ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( X1
& ( X0 = Y0 ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $o,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true != X1 )
=> ( $true
= ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( X1
& ( X0 = Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X0 = X4 )
& X1 )
| ( ( X3 = X4 )
& ~ X1 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( dsetconstrI
=> ! [X2: $i,X1: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X2 = X4 )
& X1 )
| ( ( X3 = X4 )
& ~ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( dsetconstrI
=> ! [X2: $i,X1: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X2 = X4 )
& X1 )
| ( ( X3 = X4 )
& ~ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QDIGYCiPtE/DTF2THF_19384.p',iffalseProp1) ).
thf(f56,plain,
( ( in @ sK6 @ sK5 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f43,f26]) ).
thf(f26,plain,
$true != sK4,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f43,plain,
( ( $true = sK4 )
| ( ( in @ sK6 @ sK5 )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ~ sK4 ) = $false )
| ( ( in @ sK6 @ sK5 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( in @ sK6 @ sK5 )
!= $true )
| ( ( ~ sK4
| ( sK4
& ( sK3 = sK6 ) ) )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( in @ sK6 @ sK5 )
!= $true )
| ( ( ( ~ sK4
& $true )
| ( sK4
& ( sK3 = sK6 ) ) )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( in @ sK6 @ sK5 )
!= $true )
| ( $true
!= ( ( ~ sK4
& ( sK6 = sK6 ) )
| ( sK4
& ( sK3 = sK6 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( in @ sK6 @ sK5 )
!= $true )
| ( ( ^ [Y0: $i] :
( ( ~ sK4
& ( sK6 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) )
@ sK6 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ^ [Y0: $i] :
( ( ~ sK4
& ( sK6 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) )
@ sK6 )
!= $true )
| ( ( in @ sK6 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28,f35]) ).
thf(f35,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( dsetconstr @ X5 @ X3 ) )
= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( ( X3 @ X4 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
!= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
!= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f21,f25]) ).
thf(f25,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f21,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
!= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( dsetconstrI = $true )
| ( ( $true
= ( sK0 @ sK1 ) )
& ( ( in @ sK1 @ sK2 )
= $true )
& ( ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
!= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
=> ( ( $true
= ( sK0 @ sK1 ) )
& ( ( in @ sK1 @ sK2 )
= $true )
& ( ( in @ sK1
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X4 )
!= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
& ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( X0 @ X1 )
= $true )
=> ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) )
<=> ( dsetconstrI = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.QDIGYCiPtE/DTF2THF_19384.p',dsetconstrI) ).
thf(f28,plain,
( ( in @ sK6
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ~ sK4
& ( sK6 = Y0 ) )
| ( sK4
& ( sK3 = Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU700^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n019.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:31:24 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU700^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : Conditionals
% 0.17/0.38 % Version : Especial > Reduced > Especial.
% 0.17/0.38 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> ~phi ->
% 0.17/0.38 % in y (dsetconstr A (^ z:i.phi & z = x | ~phi & z = y))))
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC202l [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.43 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.17/0.38 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.17/0.38 % Number of atoms : 10 ( 3 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 6 ( 5 avg)
% 0.17/0.38 % Number of connectives : 27 ( 2 ~; 1 |; 2 &; 16 @)
% 0.17/0.38 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 15 ( 8 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.17/0.38 % Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=252
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(in_type,type,
% 0.17/0.38 in: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstr_type,type,
% 0.17/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI_type,type,
% 0.17/0.38 dsetconstrI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI,definition,
% 0.17/0.38 ( dsetconstrI
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 => ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(iffalseProp1,conjecture,
% 0.17/0.38 ( dsetconstrI
% 0.17/0.38 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ! [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ A )
% 0.17/0.38 => ( ~ Xphi
% 0.17/0.38 => ( in @ Xy
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xz: $i] :
% 0.17/0.38 ( ( Xphi
% 0.17/0.38 & ( Xz = Xx ) )
% 0.17/0.38 | ( ~ Xphi
% 0.17/0.38 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.36/1.26 ---- Embedded in THF ---
% 1.36/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.26 %%% Generated on Tue Feb 24 12:31:25 EST 2026
% 1.36/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.26 %%% Logic specification used:
% 1.36/1.26 %%% thf(spec, logic, $$dhol).
% 1.36/1.26
% 1.36/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.QDIGYCiPtE/DTF2DTF19384.p
% See solution above
% 1.36/1.26 ------------------------
% 1.36/1.27 ---- Cleaned THF ---
% 1.36/1.27 thf(in_type,type,
% 1.36/1.27 in: $i > $i > $o ).
% 1.36/1.27
% 1.36/1.27 thf(dsetconstr_type,type,
% 1.36/1.27 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.36/1.27
% 1.36/1.27 thf(dsetconstrI_type,type,
% 1.36/1.27 dsetconstrI: $o ).
% 1.36/1.27
% 1.36/1.27 thf(dsetconstrI,definition,
% 1.36/1.27 ( dsetconstrI
% 1.36/1.27 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.36/1.27 ( ( in @ Xx @ A )
% 1.36/1.27 => ( ( Xphi @ Xx )
% 1.36/1.27 => ( in @ Xx
% 1.36/1.27 @ ( dsetconstr @ A
% 1.36/1.27 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.36/1.27
% 1.36/1.27 thf(iffalseProp1,conjecture,
% 1.36/1.27 ( dsetconstrI
% 1.36/1.27 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.36/1.27 ( ( in @ Xx @ A )
% 1.36/1.27 => ! [Xy: $i] :
% 1.36/1.27 ( ( in @ Xy @ A )
% 1.36/1.27 => ( ~ Xphi
% 1.36/1.27 => ( in @ Xy
% 1.36/1.27 @ ( dsetconstr @ A
% 1.36/1.27 @ ^ [Xz: $i] :
% 1.36/1.27 ( ( Xphi
% 1.36/1.27 & ( Xz = Xx ) )
% 1.36/1.27 | ( ~ Xphi
% 1.36/1.27 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 1.36/1.27 ------------------------
% 1.36/1.29 % (19483)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_19384 for (2999ds/27Mi)
% 1.36/1.29 % (19484)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19384 for (2999ds/2Mi)
% 1.36/1.29 % (19482)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_19384 for (2999ds/4Mi)
% 1.36/1.29 % (19481)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19384 for (2999ds/183Mi)
% 1.36/1.29 % (19485)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_19384 for (2999ds/2Mi)
% 1.36/1.29 % (19487)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19384 for (2999ds/18Mi)
% 1.36/1.29 % (19486)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_19384 for (2999ds/275Mi)
% 1.36/1.29 % (19484)Instruction limit reached!
% 1.36/1.29 % (19484)------------------------------
% 1.36/1.29 % (19484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.29 % (19484)Termination reason: Unknown
% 1.36/1.29 % (19485)Instruction limit reached!
% 1.36/1.29 % (19485)------------------------------
% 1.36/1.29 % (19485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.29 % (19484)Termination phase: Saturation
% 1.36/1.29
% 1.36/1.29 % (19485)Termination reason: Unknown
% 1.36/1.29 % (19485)Termination phase: Saturation
% 1.36/1.29 % (19484)Memory used [KB]: 5500
% 1.36/1.29
% 1.36/1.29 % (19484)Time elapsed: 0.003 s
% 1.36/1.29 % (19485)Memory used [KB]: 5500
% 1.36/1.29 % (19484)Instructions burned: 3 (million)
% 1.36/1.29 % (19485)Time elapsed: 0.003 s
% 1.36/1.29 % (19484)------------------------------
% 1.36/1.29 % (19484)------------------------------
% 1.36/1.29 % (19485)Instructions burned: 3 (million)
% 1.36/1.29 % (19485)------------------------------
% 1.36/1.29 % (19485)------------------------------
% 1.36/1.29 % (19482)Instruction limit reached!
% 1.36/1.29 % (19482)------------------------------
% 1.36/1.29 % (19482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.29 % (19482)Termination reason: Unknown
% 1.36/1.29 % (19482)Termination phase: Saturation
% 1.36/1.29
% 1.36/1.29 % (19482)Memory used [KB]: 5500
% 1.36/1.29 % (19482)Time elapsed: 0.004 s
% 1.36/1.29 % (19482)Instructions burned: 4 (million)
% 1.36/1.29 % (19482)------------------------------
% 1.36/1.29 % (19482)------------------------------
% 1.36/1.29 % (19486)First to succeed.
% 1.36/1.29 % (19481)Also succeeded, but the first one will report.
% 1.36/1.29 % (19483)Also succeeded, but the first one will report.
% 1.36/1.30 % (19486)Refutation found. Thanks to Tanya!
% 1.36/1.30 % SZS status Theorem for DTF2THF_19384
% 1.36/1.30 % SZS output start Proof for DTF2THF_19384
% 1.36/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.36/1.30 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.36/1.30 thf(func_def_12, type, sK0: $i > $o).
% 1.36/1.30 thf(func_def_20, type, ph8: !>[X0: $tType]:(X0)).
% 1.36/1.30 thf(f57,plain,(
% 1.36/1.30 $false),
% 1.36/1.30 inference(subsumption_resolution,[status(thm)],[f56,f27])).
% 1.36/1.30 thf(f27,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) = $true)),
% 1.36/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.30 thf(f20,plain,(
% 1.36/1.30 (($true = (in @ sK3 @ sK5)) & (((in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((~ sK4) & (sK6 = Y0)) | (sK4 & (sK3 = Y0)))))) != $true) & ((in @ sK6 @ sK5) = $true) & ($true != sK4))) & (dsetconstrI = $true)),
% 1.36/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f13,f19,f18])).
% 1.36/1.30 thf(f18,plain,(
% 1.36/1.30 ? [X0 : $i,X1 : $o,X2 : $i] : (($true = (in @ X0 @ X2)) & ? [X3 : $i] : (($true != (in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | (X1 & (X0 = Y0))))))) & ($true = (in @ X3 @ X2)) & ($true != X1))) => (($true = (in @ sK3 @ sK5)) & ? [X3 : $i] : (((in @ X3 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((~ sK4) & (X3 = Y0)) | (sK4 & (sK3 = Y0)))))) != $true) & ($true = (in @ X3 @ sK5)) & ($true != sK4)))),
% 1.36/1.30 introduced(definition,[],[choice_axiom])).
% 1.36/1.30 thf(f19,plain,(
% 1.36/1.30 ? [X3 : $i] : (((in @ X3 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((~ sK4) & (X3 = Y0)) | (sK4 & (sK3 = Y0)))))) != $true) & ($true = (in @ X3 @ sK5)) & ($true != sK4)) => (((in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((~ sK4) & (sK6 = Y0)) | (sK4 & (sK3 = Y0)))))) != $true) & ((in @ sK6 @ sK5) = $true) & ($true != sK4))),
% 1.36/1.30 introduced(definition,[],[choice_axiom])).
% 1.36/1.30 thf(f13,plain,(
% 1.36/1.30 ? [X0 : $i,X1 : $o,X2 : $i] : (($true = (in @ X0 @ X2)) & ? [X3 : $i] : (($true != (in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | (X1 & (X0 = Y0))))))) & ($true = (in @ X3 @ X2)) & ($true != X1))) & (dsetconstrI = $true)),
% 1.36/1.30 inference(flattening,[status(thm)],[f12])).
% 1.36/1.30 thf(f12,plain,(
% 1.36/1.30 ? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : ((($true != (in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | (X1 & (X0 = Y0))))))) & ($true != X1)) & ($true = (in @ X3 @ X2))) & ($true = (in @ X0 @ X2))) & (dsetconstrI = $true)),
% 1.36/1.30 inference(ennf_transformation,[status(thm)],[f9])).
% 1.36/1.30 thf(f9,plain,(
% 1.36/1.30 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $o,X2 : $i] : (($true = (in @ X0 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => (($true != X1) => ($true = (in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | (X1 & (X0 = Y0)))))))))))),
% 1.36/1.30 inference(flattening,[status(thm)],[f8])).
% 1.36/1.30 thf(f8,plain,(
% 1.36/1.30 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $o,X2 : $i] : (($true = (in @ X0 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => (~($true = X1) => ($true = (in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | (X1 & (X0 = Y0)))))))))))),
% 1.36/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.36/1.30 thf(f7,plain,(
% 1.36/1.30 ~(dsetconstrI => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (~X1 => (in @ X3 @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X0 = X4) & X1) | ((X3 = X4) & ~X1)))))))))),
% 1.36/1.30 inference(rectify,[status(thm)],[f3])).
% 1.36/1.30 thf(f3,negated_conjecture,(
% 1.36/1.30 ~(dsetconstrI => ! [X2 : $i,X1 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X2 = X4) & X1) | ((X3 = X4) & ~X1)))))))))),
% 1.36/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.36/1.30 thf(f2,conjecture,(
% 1.36/1.30 dsetconstrI => ! [X2 : $i,X1 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X2 = X4) & X1) | ((X3 = X4) & ~X1))))))))),
% 1.36/1.30 file('/export/starexec/sandbox2/tmp/tmp.QDIGYCiPtE/DTF2THF_19384.p',iffalseProp1)).
% 1.36/1.30 thf(f56,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) != $true)),
% 1.36/1.30 inference(subsumption_resolution,[status(thm)],[f43,f26])).
% 1.36/1.30 thf(f26,plain,(
% 1.36/1.30 ($true != sK4)),
% 1.36/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.30 thf(f43,plain,(
% 1.36/1.30 ($true = sK4) | ((in @ sK6 @ sK5) != $true)),
% 1.36/1.30 inference(not_proxy_clausification,[status(thm)],[f42])).
% 1.36/1.30 thf(f42,plain,(
% 1.36/1.30 ((~ sK4) = $false) | ((in @ sK6 @ sK5) != $true)),
% 1.36/1.30 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.36/1.30 thf(f40,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) != $true) | (((~ sK4) | (sK4 & (sK3 = sK6))) != $true)),
% 1.36/1.30 inference(boolean_simplification,[status(thm)],[f39])).
% 1.36/1.30 thf(f39,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) != $true) | ((((~ sK4) & $true) | (sK4 & (sK3 = sK6))) != $true)),
% 1.36/1.30 inference(boolean_simplification,[status(thm)],[f38])).
% 1.36/1.30 thf(f38,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) != $true) | ($true != (((~ sK4) & (sK6 = sK6)) | (sK4 & (sK3 = sK6))))),
% 1.36/1.30 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.36/1.30 thf(f37,plain,(
% 1.36/1.30 ((in @ sK6 @ sK5) != $true) | (((^[Y0 : $i]: (((~ sK4) & (sK6 = Y0)) | (sK4 & (sK3 = Y0)))) @ sK6) != $true)),
% 1.36/1.30 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.36/1.30 thf(f36,plain,(
% 1.36/1.30 (((^[Y0 : $i]: (((~ sK4) & (sK6 = Y0)) | (sK4 & (sK3 = Y0)))) @ sK6) != $true) | ((in @ sK6 @ sK5) != $true) | ($true != $true)),
% 1.36/1.30 inference(superposition,[status(thm)],[f28,f35])).
% 1.36/1.30 thf(f35,plain,(
% 1.36/1.30 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X4 @ (dsetconstr @ X5 @ X3)) = $true) | ($true != (in @ X4 @ X5)) | ((X3 @ X4) != $true)) )),
% 1.36/1.30 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.36/1.30 thf(f34,plain,(
% 1.36/1.30 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X4) != $true) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))))) )),
% 1.36/1.30 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.36/1.30 thf(f33,plain,(
% 1.36/1.30 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X4) != $true) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0))))) | ($true != $true)) )),
% 1.36/1.30 inference(definition_unfolding,[status(thm)],[f21,f25])).
% 1.36/1.30 thf(f25,plain,(
% 1.36/1.30 (dsetconstrI = $true)),
% 1.36/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.30 thf(f21,plain,(
% 1.36/1.30 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X4) != $true) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0))))) | (dsetconstrI != $true)) )),
% 1.36/1.30 inference(cnf_transformation,[status(thm)],[f17])).
% 1.36/1.30 thf(f17,plain,(
% 1.36/1.30 ((dsetconstrI = $true) | (($true = (sK0 @ sK1)) & ((in @ sK1 @ sK2) = $true) & ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))) != $true))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X4) != $true) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrI != $true))),
% 1.36/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16])).
% 1.36/1.30 thf(f16,plain,(
% 1.36/1.30 ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) => (($true = (sK0 @ sK1)) & ((in @ sK1 @ sK2) = $true) & ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))) != $true))),
% 1.36/1.30 introduced(definition,[],[choice_axiom])).
% 1.36/1.30 thf(f15,plain,(
% 1.36/1.30 ((dsetconstrI = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X4) != $true) | ($true != (in @ X4 @ X5)) | ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrI != $true))),
% 1.36/1.30 inference(rectify,[status(thm)],[f14])).
% 1.36/1.30 thf(f14,plain,(
% 1.36/1.30 ((dsetconstrI = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) != $true) | ((in @ X1 @ X2) != $true) | ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrI != $true))),
% 1.36/1.30 inference(nnf_transformation,[status(thm)],[f11])).
% 1.36/1.30 thf(f11,plain,(
% 1.36/1.30 (dsetconstrI = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) != $true) | ((in @ X1 @ X2) != $true) | ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))),
% 1.36/1.30 inference(flattening,[status(thm)],[f10])).
% 1.36/1.30 thf(f10,plain,(
% 1.36/1.30 ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) | ((X0 @ X1) != $true)) | ((in @ X1 @ X2) != $true)) <=> (dsetconstrI = $true)),
% 1.36/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.36/1.30 thf(f6,plain,(
% 1.36/1.30 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) => (((X0 @ X1) = $true) => ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) <=> (dsetconstrI = $true)),
% 1.36/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.36/1.30 thf(f5,plain,(
% 1.36/1.30 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
% 1.36/1.30 inference(rectify,[status(thm)],[f1])).
% 1.36/1.30 thf(f1,axiom,(
% 1.36/1.30 (! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.36/1.30 file('/export/starexec/sandbox2/tmp/tmp.QDIGYCiPtE/DTF2THF_19384.p',dsetconstrI)).
% 1.36/1.30 thf(f28,plain,(
% 1.36/1.30 ((in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((~ sK4) & (sK6 = Y0)) | (sK4 & (sK3 = Y0)))))) != $true)),
% 1.36/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.36/1.30 % SZS output end Proof for DTF2THF_19384
% 1.36/1.30 % (19486)------------------------------
% 1.36/1.30 % (19486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.30 % (19486)Termination reason: Refutation
% 1.36/1.30
% 1.36/1.30 % (19486)Memory used [KB]: 5500
% 1.36/1.30 % (19486)Time elapsed: 0.005 s
% 1.36/1.30 % (19486)Instructions burned: 4 (million)
% 1.36/1.30 % (19486)------------------------------
% 1.36/1.30 % (19486)------------------------------
% 1.36/1.30 % (19480)Success in time 0.02 s
%------------------------------------------------------------------------------