%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU799^2 : 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 : n006.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 09:37:18 AM UTC 2026
% Result : Theorem 1.33s 1.25s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 304 ( 8 ~; 2 |; 6 &; 249 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 7 con; 0-3 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 41 ^; 33 !; 6 ?; 80 :)
% 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,
funcSet: $i > $i > $i ).
thf(func_def_5,type,
injective: $i > $i > $i > $o ).
thf(func_def_6,type,
injFuncSet: $i > $i > $i ).
thf(func_def_20,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f35,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f34,f17]) ).
thf(f17,plain,
( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
!= $true )
& ( dsetconstrEL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( injFuncSet @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
!= $true ) )
=> ( ( ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( injFuncSet @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
!= $true ) )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( injFuncSet @ X1 @ X0 ) )
= $true )
=> ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( injFuncSet @ X1 @ X0 ) )
=> ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ! [X4: $i,X0: $i,X5: $i] :
( ( in @ X5 @ ( injFuncSet @ X0 @ X4 ) )
=> ( in @ X5 @ ( funcSet @ X0 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrEL
=> ! [X4: $i,X0: $i,X5: $i] :
( ( in @ X5 @ ( injFuncSet @ X0 @ X4 ) )
=> ( in @ X5 @ ( funcSet @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',injFuncSetFuncIn) ).
thf(f34,plain,
( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $false = $true )
| ( ( in @ sK2 @ ( funcSet @ sK1 @ sK0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f22,f30]) ).
thf(f30,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f16]) ).
thf(f16,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f19,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X1: $i > $o,X0: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',dsetconstrEL) ).
thf(f22,plain,
( ( in @ sK2 @ ( dsetconstr @ ( funcSet @ sK1 @ sK0 ) @ ( injective @ sK1 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) )
@ sK1
@ sK0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f18,f15]) ).
thf(f15,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) )
= injFuncSet ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( funcSet @ X0 @ X4 )
@ ^ [X5: $i] : ( injective @ X0 @ X4 @ X5 ) ) )
= injFuncSet ),
file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',injFuncSet) ).
thf(f18,plain,
( ( in @ sK2 @ ( injFuncSet @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU799^2 : TPTP v9.2.1. Released v3.7.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n006.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:34:15 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEU799^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : More about Functions - Injective Functions
% 0.17/0.44 % Version : Especial > Reduced > Especial.
% 0.17/0.44 % English : (! A:i.! B:i.! f:i.in f (injFuncSet A B) -> in f (funcSet A B))
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.44 % Source : [Bro08]
% 0.17/0.44 % Names : ZFC301l [Bro08]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 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 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.17/0.44 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.17/0.44 % Number of atoms : 9 ( 2 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 3 ( 3 avg)
% 0.17/0.44 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 22 @)
% 0.17/0.44 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 9 ( 4 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% 0.17/0.44 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : http://mathgate.info/detsetitem.php?id=424
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(in_type,type,
% 0.17/0.44 in: $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstr_type,type,
% 0.17/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrEL_type,type,
% 0.17/0.44 dsetconstrEL: $o ).
% 0.17/0.44
% 0.17/0.44 thf(dsetconstrEL,definition,
% 0.17/0.44 ( dsetconstrEL
% 0.17/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.44 ( ( in @ Xx
% 0.17/0.44 @ ( dsetconstr @ A
% 0.17/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(funcSet_type,type,
% 0.17/0.44 funcSet: $i > $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(injective_type,type,
% 0.17/0.44 injective: $i > $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(injFuncSet_type,type,
% 0.17/0.44 injFuncSet: $i > $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(injFuncSet,definition,
% 0.17/0.44 ( injFuncSet
% 0.17/0.44 = ( ^ [A: $i,B: $i] :
% 0.17/0.44 ( dsetconstr @ ( funcSet @ A @ B )
% 0.17/0.44 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(injFuncSetFuncIn,conjecture,
% 0.17/0.44 ( dsetconstrEL
% 0.17/0.44 => ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.44 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.17/0.44 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.33/1.22 ---- Embedded in THF ---
% 1.33/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.33/1.22 %%% Generated on Tue Feb 24 12:34:16 EST 2026
% 1.33/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.33/1.22 %%% Logic specification used:
% 1.33/1.22 %%% thf(spec, logic, $$dhol).
% 1.33/1.22
% 1.33/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2DTF19321.p
% See solution above
% 1.33/1.22 ------------------------
% 1.33/1.23 ---- Cleaned THF ---
% 1.33/1.23 thf(in_type,type,
% 1.33/1.23 in: $i > $i > $o ).
% 1.33/1.23
% 1.33/1.23 thf(dsetconstr_type,type,
% 1.33/1.23 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.33/1.23
% 1.33/1.23 thf(dsetconstrEL_type,type,
% 1.33/1.23 dsetconstrEL: $o ).
% 1.33/1.23
% 1.33/1.23 thf(dsetconstrEL,definition,
% 1.33/1.23 ( dsetconstrEL
% 1.33/1.23 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.33/1.23 ( ( in @ Xx
% 1.33/1.23 @ ( dsetconstr @ A
% 1.33/1.23 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.33/1.23 => ( in @ Xx @ A ) ) ) ) ).
% 1.33/1.23
% 1.33/1.23 thf(funcSet_type,type,
% 1.33/1.23 funcSet: $i > $i > $i ).
% 1.33/1.23
% 1.33/1.23 thf(injective_type,type,
% 1.33/1.23 injective: $i > $i > $i > $o ).
% 1.33/1.23
% 1.33/1.23 thf(injFuncSet_type,type,
% 1.33/1.23 injFuncSet: $i > $i > $i ).
% 1.33/1.23
% 1.33/1.23 thf(injFuncSet,definition,
% 1.33/1.23 ( injFuncSet
% 1.33/1.23 = ( ^ [A: $i,B: $i] :
% 1.33/1.23 ( dsetconstr @ ( funcSet @ A @ B )
% 1.33/1.23 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 1.33/1.23
% 1.33/1.23 thf(injFuncSetFuncIn,conjecture,
% 1.33/1.23 ( dsetconstrEL
% 1.33/1.23 => ! [A: $i,B: $i,Xf: $i] :
% 1.33/1.23 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 1.33/1.23 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ).
% 1.33/1.23 ------------------------
% 1.33/1.24 % (19422)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19321 for (2999ds/183Mi)
% 1.33/1.25 % (19422)First to succeed.
% 1.33/1.25 % (19422)Refutation found. Thanks to Tanya!
% 1.33/1.25 % SZS status Theorem for DTF2THF_19321
% 1.33/1.25 % SZS output start Proof for DTF2THF_19321
% 1.33/1.25 thf(func_def_0, type, in: $i > $i > $o).
% 1.33/1.25 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.33/1.25 thf(func_def_4, type, funcSet: $i > $i > $i).
% 1.33/1.25 thf(func_def_5, type, injective: $i > $i > $i > $o).
% 1.33/1.25 thf(func_def_6, type, injFuncSet: $i > $i > $i).
% 1.33/1.25 thf(func_def_20, type, ph4: !>[X0: $tType]:(X0)).
% 1.33/1.25 thf(f35,plain,(
% 1.33/1.25 $false),
% 1.33/1.25 inference(subsumption_resolution,[status(thm)],[f34,f17])).
% 1.33/1.25 thf(f17,plain,(
% 1.33/1.25 ((in @ sK2 @ (funcSet @ sK1 @ sK0)) != $true)),
% 1.33/1.25 inference(cnf_transformation,[status(thm)],[f14])).
% 1.33/1.25 thf(f14,plain,(
% 1.33/1.25 (((in @ sK2 @ (injFuncSet @ sK1 @ sK0)) = $true) & ((in @ sK2 @ (funcSet @ sK1 @ sK0)) != $true)) & (dsetconstrEL = $true)),
% 1.33/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13])).
% 1.33/1.25 thf(f13,plain,(
% 1.33/1.25 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (injFuncSet @ X1 @ X0)) = $true) & ((in @ X2 @ (funcSet @ X1 @ X0)) != $true)) => (((in @ sK2 @ (injFuncSet @ sK1 @ sK0)) = $true) & ((in @ sK2 @ (funcSet @ sK1 @ sK0)) != $true))),
% 1.33/1.25 introduced(definition,[],[choice_axiom])).
% 1.33/1.25 thf(f12,plain,(
% 1.33/1.25 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (injFuncSet @ X1 @ X0)) = $true) & ((in @ X2 @ (funcSet @ X1 @ X0)) != $true)) & (dsetconstrEL = $true)),
% 1.33/1.25 inference(ennf_transformation,[status(thm)],[f9])).
% 1.33/1.25 thf(f9,plain,(
% 1.33/1.25 ~((dsetconstrEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (injFuncSet @ X1 @ X0)) = $true) => ((in @ X2 @ (funcSet @ X1 @ X0)) = $true)))),
% 1.33/1.25 inference(fool_elimination,[status(thm)],[f8])).
% 1.33/1.25 thf(f8,plain,(
% 1.33/1.25 ~(dsetconstrEL => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (injFuncSet @ X1 @ X0)) => (in @ X2 @ (funcSet @ X1 @ X0))))),
% 1.33/1.25 inference(rectify,[status(thm)],[f4])).
% 1.33/1.25 thf(f4,negated_conjecture,(
% 1.33/1.25 ~(dsetconstrEL => ! [X4 : $i,X0 : $i,X5 : $i] : ((in @ X5 @ (injFuncSet @ X0 @ X4)) => (in @ X5 @ (funcSet @ X0 @ X4))))),
% 1.33/1.25 inference(negated_conjecture,[status(cth)],[f3])).
% 1.33/1.25 thf(f3,conjecture,(
% 1.33/1.25 dsetconstrEL => ! [X4 : $i,X0 : $i,X5 : $i] : ((in @ X5 @ (injFuncSet @ X0 @ X4)) => (in @ X5 @ (funcSet @ X0 @ X4)))),
% 1.33/1.25 file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',injFuncSetFuncIn)).
% 1.33/1.25 thf(f34,plain,(
% 1.33/1.25 ((in @ sK2 @ (funcSet @ sK1 @ sK0)) = $true)),
% 1.33/1.25 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.33/1.25 thf(f31,plain,(
% 1.33/1.25 ($false = $true) | ((in @ sK2 @ (funcSet @ sK1 @ sK0)) = $true)),
% 1.33/1.25 inference(superposition,[status(thm)],[f22,f30])).
% 1.33/1.25 thf(f30,plain,(
% 1.33/1.25 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $true)) )),
% 1.33/1.25 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.33/1.25 thf(f29,plain,(
% 1.33/1.25 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X3 @ (dsetconstr @ X1 @ X2)) => (in @ X3 @ X1)) = $true)) )),
% 1.33/1.25 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.33/1.25 thf(f28,plain,(
% 1.33/1.25 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1))) @ X3) = $true)) )),
% 1.33/1.25 inference(pi_clausification,[status(thm)],[f27])).
% 1.33/1.25 thf(f27,plain,(
% 1.33/1.25 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1)))) = $true)) )),
% 1.33/1.25 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.33/1.25 thf(f26,plain,(
% 1.33/1.25 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1))))) @ X2) = $true)) )),
% 1.33/1.25 inference(pi_clausification,[status(thm)],[f25])).
% 1.33/1.25 thf(f25,plain,(
% 1.33/1.25 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1)))))) = $true)) )),
% 1.33/1.25 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.33/1.25 thf(f24,plain,(
% 1.33/1.25 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 1.33/1.25 inference(pi_clausification,[status(thm)],[f23])).
% 1.33/1.25 thf(f23,plain,(
% 1.33/1.25 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) = $true)),
% 1.33/1.25 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.33/1.25 thf(f21,plain,(
% 1.33/1.25 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))) = $true)),
% 1.33/1.25 inference(definition_unfolding,[status(thm)],[f19,f16])).
% 1.33/1.25 thf(f16,plain,(
% 1.33/1.25 (dsetconstrEL = $true)),
% 1.33/1.25 inference(cnf_transformation,[status(thm)],[f14])).
% 1.33/1.25 thf(f19,plain,(
% 1.33/1.25 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 1.33/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.33/1.25 thf(f11,plain,(
% 1.33/1.25 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 1.33/1.25 inference(fool_elimination,[status(thm)],[f10])).
% 1.33/1.25 thf(f10,plain,(
% 1.33/1.25 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)) = dsetconstrEL)),
% 1.33/1.25 inference(rectify,[status(thm)],[f1])).
% 1.33/1.25 thf(f1,axiom,(
% 1.33/1.25 (! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.33/1.25 file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',dsetconstrEL)).
% 1.33/1.25 thf(f22,plain,(
% 1.33/1.25 ((in @ sK2 @ (dsetconstr @ (funcSet @ sK1 @ sK0) @ (injective @ sK1 @ sK0))) = $true)),
% 1.33/1.25 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.33/1.25 thf(f20,plain,(
% 1.33/1.25 ((in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))) @ sK1 @ sK0)) = $true)),
% 1.33/1.25 inference(definition_unfolding,[status(thm)],[f18,f15])).
% 1.33/1.25 thf(f15,plain,(
% 1.33/1.25 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.33/1.25 inference(cnf_transformation,[status(thm)],[f7])).
% 1.33/1.25 thf(f7,plain,(
% 1.33/1.25 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.33/1.25 inference(fool_elimination,[status(thm)],[f6])).
% 1.33/1.25 thf(f6,plain,(
% 1.33/1.25 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (injective @ X0 @ X1 @ X2)))) = injFuncSet)),
% 1.33/1.25 inference(rectify,[status(thm)],[f2])).
% 1.33/1.25 thf(f2,axiom,(
% 1.33/1.25 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (injective @ X0 @ X4 @ X5)))) = injFuncSet)),
% 1.33/1.25 file('/export/starexec/sandbox2/tmp/tmp.6FFO1j2Xl1/DTF2THF_19321.p',injFuncSet)).
% 1.33/1.25 thf(f18,plain,(
% 1.33/1.25 ((in @ sK2 @ (injFuncSet @ sK1 @ sK0)) = $true)),
% 1.33/1.25 inference(cnf_transformation,[status(thm)],[f14])).
% 1.33/1.25 % SZS output end Proof for DTF2THF_19321
% 1.33/1.25 % (19422)------------------------------
% 1.33/1.25 % (19422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.33/1.25 % (19422)Termination reason: Refutation
% 1.33/1.25
% 1.33/1.25 % (19422)Memory used [KB]: 5500
% 1.33/1.25 % (19422)Time elapsed: 0.003 s
% 1.33/1.25 % (19422)Instructions burned: 2 (million)
% 1.33/1.25 % (19422)------------------------------
% 1.33/1.25 % (19422)------------------------------
% 1.33/1.25 % (19421)Success in time 0.012 s
%------------------------------------------------------------------------------