%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU702^2 : 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 : n005.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 09:36:31 AM UTC 2026
% Result : Theorem 1.58s 1.34s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 451 ( 144 equ; 1 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 462 ( 66 ~; 45 |; 65 &; 258 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 108 ( 33 ^; 52 !; 23 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_14,type,
sK2: $i > $o ).
thf(func_def_20,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f45,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44,f28]) ).
thf(f28,plain,
( ( in @ sK4 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( in @ sK4 @ sK5 )
= $true )
& ( $true
= ( in @ sK6 @ sK5 ) )
& ( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK3 )
| ( ~ sK3
& ( sK6 = Y0 ) ) ) ) ) )
& ( sK3 = $true )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f12,f18,f17]) ).
thf(f17,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) )
& ( $true = X0 ) ) )
=> ( ( ( in @ sK4 @ sK5 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK3 )
| ( ~ sK3
& ( X3 = Y0 ) ) ) ) ) )
& ( sK3 = $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK5 ) )
& ( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK3 )
| ( ~ sK3
& ( X3 = Y0 ) ) ) ) ) )
& ( sK3 = $true ) )
=> ( ( $true
= ( in @ sK6 @ sK5 ) )
& ( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK3 )
| ( ~ sK3
& ( sK6 = Y0 ) ) ) ) ) )
& ( sK3 = $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) )
& ( $true = X0 ) ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) )
& ( $true = X0 )
& ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( $true = X0 )
=> ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( dsetconstrI
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X0 )
| ( X0
& ( X1 = X4 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( dsetconstrI
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( X1
& ( X2 = X4 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( dsetconstrI
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( X1
& ( X2 = X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2oymhsO5Cq/DTF2THF_14680.p',iftrueProp1) ).
thf(f44,plain,
( ( in @ sK4 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( in @ sK4 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
!= ( sK4 = sK4 ) )
| ( ( in @ sK4 @ sK5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true != $true )
| ( ( in @ sK4 @ sK5 )
!= $true )
| ( $true
!= ( sK4 = sK4 ) ) ),
inference(superposition,[status(thm)],[f38,f40]) ).
thf(f40,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $true
!= ( X2 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( X2 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f24]) ).
thf(f24,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f23,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
!= ( in @ sK0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) )
& ( $true
= ( sK2 @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X3 @ X4 ) )
& ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
= ( X5 @ X3 ) ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
!= ( in @ sK0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ) )
& ( $true
= ( sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X3 @ X4 ) )
& ( $true
!= ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
= ( X5 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( $true
= ( X2 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
!= ( X2 @ X0 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
= ( X2 @ X0 ) )
=> ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.2oymhsO5Cq/DTF2THF_14680.p',dsetconstrI) ).
thf(f38,plain,
( $true
!= ( in @ sK4 @ ( dsetconstr @ sK5 @ ( (=) @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK4 = Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( sK4 = Y0 )
& $true ) ) ) ),
inference(boolean_simplification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& $true )
| $false ) ) ) ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& $true )
| ( $false
& ( sK6 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& $true )
| ( ~ $true
& ( sK6 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f26,f25,f25]) ).
thf(f25,plain,
sK3 = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f26,plain,
( $true
!= ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] :
( ( ( sK4 = Y0 )
& sK3 )
| ( ~ sK3
& ( sK6 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU702^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.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 12:31:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU702^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.48 % Domain : Set Theory
% 0.27/0.48 % Problem : Conditionals
% 0.27/0.48 % Version : Especial > Reduced > Especial.
% 0.27/0.48 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> phi ->
% 0.27/0.48 % in x (dsetconstr A (^ z:i.phi & z = x | ~phi & z = y))))
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.48 % Source : [Bro08]
% 0.27/0.48 % Names : ZFC204l [Bro08]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 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
% 0.27/0.48 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.27/0.48 % Number of atoms : 10 ( 3 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 6 ( 5 avg)
% 0.27/0.48 % Number of connectives : 26 ( 1 ~; 1 |; 2 &; 16 @)
% 0.27/0.48 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 15 ( 8 avg)
% 0.27/0.48 % Number of types : 2 ( 0 usr)
% 0.27/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.27/0.48 % Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : http://mathgate.info/detsetitem.php?id=254
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(in_type,type,
% 0.27/0.48 in: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstr_type,type,
% 0.27/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrI_type,type,
% 0.27/0.48 dsetconstrI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrI,definition,
% 0.27/0.48 ( dsetconstrI
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 => ( in @ Xx
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(iftrueProp1,conjecture,
% 0.27/0.49 ( dsetconstrI
% 0.27/0.49 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.49 ( ( in @ Xx @ A )
% 0.27/0.49 => ! [Xy: $i] :
% 0.27/0.49 ( ( in @ Xy @ A )
% 0.27/0.49 => ( Xphi
% 0.27/0.49 => ( in @ Xx
% 0.27/0.49 @ ( dsetconstr @ A
% 0.27/0.49 @ ^ [Xz: $i] :
% 0.27/0.49 ( ( Xphi
% 0.27/0.49 & ( Xz = Xx ) )
% 0.27/0.49 | ( ~ Xphi
% 0.27/0.49 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.58/1.30 ---- Embedded in THF ---
% 1.58/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.30 %%% Generated on Tue Feb 24 12:31:15 EST 2026
% 1.58/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.30 %%% Logic specification used:
% 1.58/1.30 %%% thf(spec, logic, $$dhol).
% 1.58/1.30
% 1.58/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2oymhsO5Cq/DTF2DTF14680.p
% See solution above
% 1.58/1.31 ------------------------
% 1.58/1.31 ---- Cleaned THF ---
% 1.58/1.31 thf(in_type,type,
% 1.58/1.31 in: $i > $i > $o ).
% 1.58/1.31
% 1.58/1.31 thf(dsetconstr_type,type,
% 1.58/1.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.58/1.31
% 1.58/1.31 thf(dsetconstrI_type,type,
% 1.58/1.31 dsetconstrI: $o ).
% 1.58/1.31
% 1.58/1.31 thf(dsetconstrI,definition,
% 1.58/1.31 ( dsetconstrI
% 1.58/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.58/1.31 ( ( in @ Xx @ A )
% 1.58/1.31 => ( ( Xphi @ Xx )
% 1.58/1.31 => ( in @ Xx
% 1.58/1.31 @ ( dsetconstr @ A
% 1.58/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.58/1.31
% 1.58/1.31 thf(iftrueProp1,conjecture,
% 1.58/1.31 ( dsetconstrI
% 1.58/1.31 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.58/1.31 ( ( in @ Xx @ A )
% 1.58/1.31 => ! [Xy: $i] :
% 1.58/1.31 ( ( in @ Xy @ A )
% 1.58/1.31 => ( Xphi
% 1.58/1.31 => ( in @ Xx
% 1.58/1.31 @ ( dsetconstr @ A
% 1.58/1.31 @ ^ [Xz: $i] :
% 1.58/1.31 ( ( Xphi
% 1.58/1.31 & ( Xz = Xx ) )
% 1.58/1.31 | ( ~ Xphi
% 1.58/1.31 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 1.58/1.31 ------------------------
% 1.58/1.33 % (14840)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_14680 for (2999ds/4Mi)
% 1.58/1.33 % (14843)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_14680 for (2999ds/2Mi)
% 1.58/1.33 % (14843)Instruction limit reached!
% 1.58/1.33 % (14843)------------------------------
% 1.58/1.33 % (14843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (14843)Termination reason: Unknown
% 1.58/1.33 % (14843)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (14843)Memory used [KB]: 5500
% 1.58/1.33 % (14843)Time elapsed: 0.002 s
% 1.58/1.33 % (14843)Instructions burned: 3 (million)
% 1.58/1.33 % (14843)------------------------------
% 1.58/1.33 % (14843)------------------------------
% 1.58/1.33 % (14840)Instruction limit reached!
% 1.58/1.33 % (14840)------------------------------
% 1.58/1.33 % (14840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (14840)Termination reason: Unknown
% 1.58/1.33 % (14840)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (14840)Memory used [KB]: 5500
% 1.58/1.33 % (14840)Time elapsed: 0.004 s
% 1.58/1.33 % (14840)Instructions burned: 5 (million)
% 1.58/1.33 % (14840)------------------------------
% 1.58/1.33 % (14840)------------------------------
% 1.58/1.34 % (14842)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14680 for (2999ds/2Mi)
% 1.58/1.34 % (14842)Instruction limit reached!
% 1.58/1.34 % (14842)------------------------------
% 1.58/1.34 % (14842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (14842)Termination reason: Unknown
% 1.58/1.34 % (14842)Termination phase: Property scanning
% 1.58/1.34
% 1.58/1.34 % (14842)Memory used [KB]: 895
% 1.58/1.34 % (14842)Time elapsed: 0.003 s
% 1.58/1.34 % (14842)Instructions burned: 2 (million)
% 1.58/1.34 % (14842)------------------------------
% 1.58/1.34 % (14842)------------------------------
% 1.58/1.34 % (14845)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14680 for (2999ds/18Mi)
% 1.58/1.34 % (14844)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_14680 for (2999ds/275Mi)
% 1.58/1.34 % (14839)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14680 for (2999ds/183Mi)
% 1.58/1.34 % (14844)First to succeed.
% 1.58/1.34 % (14839)Also succeeded, but the first one will report.
% 1.58/1.34 % (14844)Refutation found. Thanks to Tanya!
% 1.58/1.34 % SZS status Theorem for DTF2THF_14680
% 1.58/1.34 % SZS output start Proof for DTF2THF_14680
% 1.58/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.58/1.34 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.58/1.34 thf(func_def_14, type, sK2: $i > $o).
% 1.58/1.34 thf(func_def_20, type, ph8: !>[X0: $tType]:(X0)).
% 1.58/1.34 thf(f45,plain,(
% 1.58/1.34 $false),
% 1.58/1.34 inference(subsumption_resolution,[status(thm)],[f44,f28])).
% 1.58/1.34 thf(f28,plain,(
% 1.58/1.34 ((in @ sK4 @ sK5) = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.34 thf(f19,plain,(
% 1.58/1.34 (((in @ sK4 @ sK5) = $true) & (($true = (in @ sK6 @ sK5)) & ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & sK3) | ((~ sK3) & (sK6 = Y0))))))) & (sK3 = $true))) & (dsetconstrI = $true)),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f12,f18,f17])).
% 1.58/1.34 thf(f17,plain,(
% 1.58/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0))))))) & ($true = X0))) => (((in @ sK4 @ sK5) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & sK3) | ((~ sK3) & (X3 = Y0))))))) & (sK3 = $true)))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f18,plain,(
% 1.58/1.34 ? [X3 : $i] : (($true = (in @ X3 @ sK5)) & ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & sK3) | ((~ sK3) & (X3 = Y0))))))) & (sK3 = $true)) => (($true = (in @ sK6 @ sK5)) & ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & sK3) | ((~ sK3) & (sK6 = Y0))))))) & (sK3 = $true))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f12,plain,(
% 1.58/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0))))))) & ($true = X0))) & (dsetconstrI = $true)),
% 1.58/1.34 inference(flattening,[status(thm)],[f11])).
% 1.58/1.34 thf(f11,plain,(
% 1.58/1.34 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : ((($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0))))))) & ($true = X0)) & ($true = (in @ X3 @ X2))) & ($true = (in @ X1 @ X2))) & (dsetconstrI = $true)),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f8])).
% 1.58/1.34 thf(f8,plain,(
% 1.58/1.34 ~((dsetconstrI = $true) => ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => (($true = X0) => ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))))))))),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 1.58/1.34 thf(f7,plain,(
% 1.58/1.34 ~(dsetconstrI => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => (in @ X1 @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X3 = X4) & ~X0) | (X0 & (X1 = X4))))))))))),
% 1.58/1.34 inference(rectify,[status(thm)],[f3])).
% 1.58/1.34 thf(f3,negated_conjecture,(
% 1.58/1.34 ~(dsetconstrI => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | (X1 & (X2 = X4))))))))))),
% 1.58/1.34 inference(negated_conjecture,[status(cth)],[f2])).
% 1.58/1.34 thf(f2,conjecture,(
% 1.58/1.34 dsetconstrI => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | (X1 & (X2 = X4)))))))))),
% 1.58/1.34 file('/export/starexec/sandbox2/tmp/tmp.2oymhsO5Cq/DTF2THF_14680.p',iftrueProp1)).
% 1.58/1.34 thf(f44,plain,(
% 1.58/1.34 ((in @ sK4 @ sK5) != $true)),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.58/1.34 thf(f43,plain,(
% 1.58/1.34 ((in @ sK4 @ sK5) != $true) | ($true != $true)),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f42])).
% 1.58/1.34 thf(f42,plain,(
% 1.58/1.34 ($true != (sK4 = sK4)) | ((in @ sK4 @ sK5) != $true)),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.58/1.34 thf(f41,plain,(
% 1.58/1.34 ($true != $true) | ((in @ sK4 @ sK5) != $true) | ($true != (sK4 = sK4))),
% 1.58/1.34 inference(superposition,[status(thm)],[f38,f40])).
% 1.58/1.34 thf(f40,plain,(
% 1.58/1.34 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (dsetconstr @ X1 @ X2))) | ($true != (X2 @ X0)) | ($true != (in @ X0 @ X1))) )),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.58/1.34 thf(f39,plain,(
% 1.58/1.34 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (in @ X0 @ X1)) | ($true != (X2 @ X0))) )),
% 1.58/1.34 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.58/1.34 thf(f29,plain,(
% 1.58/1.34 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != $true) | ($true != (X2 @ X0)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))))) )),
% 1.58/1.34 inference(definition_unfolding,[status(thm)],[f23,f24])).
% 1.58/1.34 thf(f24,plain,(
% 1.58/1.34 (dsetconstrI = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.34 thf(f23,plain,(
% 1.58/1.34 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0)) | (dsetconstrI != $true)) )),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f16])).
% 1.58/1.34 thf(f16,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0))) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | (($true = (in @ sK0 @ sK1)) & ($true != (in @ sK0 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))))) & ($true = (sK2 @ sK0))))),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.58/1.34 thf(f15,plain,(
% 1.58/1.34 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X3 @ X4)) & ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true = (X5 @ X3))) => (($true = (in @ sK0 @ sK1)) & ($true != (in @ sK0 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0))))) & ($true = (sK2 @ sK0)))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f14,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0))) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X3 @ X4)) & ($true != (in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true = (X5 @ X3))))),
% 1.58/1.34 inference(rectify,[status(thm)],[f13])).
% 1.58/1.34 thf(f13,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0))) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) & ($true = (X2 @ X0))))),
% 1.58/1.34 inference(nnf_transformation,[status(thm)],[f10])).
% 1.58/1.34 thf(f10,plain,(
% 1.58/1.34 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0))) <=> (dsetconstrI = $true)),
% 1.58/1.34 inference(flattening,[status(thm)],[f9])).
% 1.58/1.34 thf(f9,plain,(
% 1.58/1.34 (dsetconstrI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != (X2 @ X0))) | ($true != (in @ X0 @ X1)))),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.34 thf(f6,plain,(
% 1.58/1.34 (dsetconstrI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X0 @ X1)) => (($true = (X2 @ X0)) => ($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))))))),
% 1.58/1.34 inference(fool_elimination,[status(thm)],[f5])).
% 1.58/1.34 thf(f5,plain,(
% 1.58/1.34 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 1.58/1.34 inference(rectify,[status(thm)],[f1])).
% 1.58/1.34 thf(f1,axiom,(
% 1.58/1.34 (! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.58/1.34 file('/export/starexec/sandbox2/tmp/tmp.2oymhsO5Cq/DTF2THF_14680.p',dsetconstrI)).
% 1.58/1.34 thf(f38,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (= @ sK4))))),
% 1.58/1.34 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.58/1.34 thf(f37,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK4 = Y0)))))),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f36])).
% 1.58/1.34 thf(f36,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: ((sK4 = Y0) & $true)))))),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f35])).
% 1.58/1.34 thf(f35,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & $true) | $false)))))),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f34])).
% 1.58/1.34 thf(f34,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & $true) | ($false & (sK6 = Y0)))))))),
% 1.58/1.34 inference(boolean_simplification,[status(thm)],[f33])).
% 1.58/1.34 thf(f33,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & $true) | ((~ $true) & (sK6 = Y0)))))))),
% 1.58/1.34 inference(definition_unfolding,[status(thm)],[f26,f25,f25])).
% 1.58/1.34 thf(f25,plain,(
% 1.58/1.34 (sK3 = $true)),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.34 thf(f26,plain,(
% 1.58/1.34 ($true != (in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (((sK4 = Y0) & sK3) | ((~ sK3) & (sK6 = Y0)))))))),
% 1.58/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 1.58/1.34 % SZS output end Proof for DTF2THF_14680
% 1.58/1.34 % (14844)------------------------------
% 1.58/1.34 % (14844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (14844)Termination reason: Refutation
% 1.58/1.34
% 1.58/1.34 % (14844)Memory used [KB]: 5500
% 1.58/1.34 % (14844)Time elapsed: 0.005 s
% 1.58/1.34 % (14844)Instructions burned: 3 (million)
% 1.58/1.34 % (14844)------------------------------
% 1.58/1.34 % (14844)------------------------------
% 1.58/1.34 % (14838)Success in time 0.022 s
%------------------------------------------------------------------------------