%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU798^2 : 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 : n022.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 09:37:17 AM UTC 2026
% Result : Theorem 1.30s 1.14s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 293 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 431 ( 20 ~; 13 |; 13 &; 327 @)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 9 con; 0-3 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 41 ^; 36 !; 9 ?; 86 :)
% 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(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f46,f52,f59]) ).
thf(f59,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f18,f41]) ).
thf(f41,plain,
( ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl3_1
<=> ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f18,plain,
( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( dsetconstrI = $true )
& ( ( in @ sK0 @ ( injFuncSet @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true )
& ( ( injective @ sK1 @ sK2 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
& ( ( injective @ X1 @ X2 @ X0 )
= $true ) )
=> ( ( ( in @ sK0 @ ( injFuncSet @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $true )
& ( ( injective @ sK1 @ sK2 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
& ( ( injective @ X1 @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) )
!= $true )
& ( ( injective @ X1 @ X2 @ X0 )
= $true )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
=> ( ( ( injective @ X1 @ X2 @ X0 )
= $true )
=> ( ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
=> ( ( injective @ X1 @ X2 @ X0 )
=> ( in @ X0 @ ( injFuncSet @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X5: $i,X0: $i,X4: $i] :
( ( in @ X5 @ ( funcSet @ X0 @ X4 ) )
=> ( ( injective @ X0 @ X4 @ X5 )
=> ( in @ X5 @ ( injFuncSet @ X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X5: $i,X0: $i,X4: $i] :
( ( in @ X5 @ ( funcSet @ X0 @ X4 ) )
=> ( ( injective @ X0 @ X4 @ X5 )
=> ( in @ X5 @ ( injFuncSet @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2THF_31113.p',injFuncInInjFuncSet) ).
thf(f52,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f17,f45]) ).
thf(f45,plain,
( ( ( injective @ sK1 @ sK2 @ sK0 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl3_2
<=> ( ( injective @ sK1 @ sK2 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f17,plain,
( ( injective @ sK1 @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f46,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f37,f43,f39]) ).
thf(f37,plain,
( ( ( injective @ sK1 @ sK2 @ sK0 )
= $false )
| ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( in @ sK0 @ ( funcSet @ sK1 @ sK2 ) )
= $false )
| ( ( injective @ sK1 @ sK2 @ sK0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
= $true )
| ( ( X3 @ X1 )
= $false )
| ( ( in @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ X2 )
= $false )
| ( ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f21,f20]) ).
thf(f20,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f21,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2THF_31113.p',dsetconstrI) ).
thf(f24,plain,
( ( in @ sK0 @ ( dsetconstr @ ( funcSet @ sK1 @ sK2 ) @ ( injective @ sK1 @ sK2 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) )
@ sK1
@ sK2 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f19,f16]) ).
thf(f16,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.pSbC6IkBpM/DTF2THF_31113.p',injFuncSet) ).
thf(f19,plain,
( ( in @ sK0 @ ( injFuncSet @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU798^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Feb 24 12:34:21 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEU798^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : More about Functions - Injective Functions
% 0.16/0.42 % Version : Especial > Reduced > Especial.
% 0.16/0.42 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> injective A B f ->
% 0.16/0.42 % in f (injFuncSet A B))
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.42 % Source : [Bro08]
% 0.16/0.42 % Names : ZFC300l [Bro08]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.2.0, 0.23 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 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.16/0.42 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.16/0.42 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 4 ( 3 avg)
% 0.16/0.42 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 26 @)
% 0.16/0.42 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 10 ( 4 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% 0.16/0.42 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : http://mathgate.info/detsetitem.php?id=423
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(in_type,type,
% 0.16/0.42 in: $i > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(dsetconstr_type,type,
% 0.16/0.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.42
% 0.16/0.42 thf(dsetconstrI_type,type,
% 0.16/0.42 dsetconstrI: $o ).
% 0.16/0.42
% 0.16/0.42 thf(dsetconstrI,definition,
% 0.16/0.42 ( dsetconstrI
% 0.16/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.42 ( ( in @ Xx @ A )
% 0.16/0.42 => ( ( Xphi @ Xx )
% 0.16/0.42 => ( in @ Xx
% 0.16/0.42 @ ( dsetconstr @ A
% 0.16/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(funcSet_type,type,
% 0.16/0.42 funcSet: $i > $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(injective_type,type,
% 0.16/0.42 injective: $i > $i > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(injFuncSet_type,type,
% 0.16/0.42 injFuncSet: $i > $i > $i ).
% 0.16/0.42
% 0.16/0.42 thf(injFuncSet,definition,
% 0.16/0.42 ( injFuncSet
% 0.16/0.42 = ( ^ [A: $i,B: $i] :
% 0.16/0.42 ( dsetconstr @ ( funcSet @ A @ B )
% 0.16/0.42 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(injFuncInInjFuncSet,conjecture,
% 0.16/0.42 ( dsetconstrI
% 0.16/0.42 => ! [A: $i,B: $i,Xf: $i] :
% 0.16/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.16/0.42 => ( ( injective @ A @ B @ Xf )
% 0.16/0.42 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.30/1.12 ---- Embedded in THF ---
% 1.30/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.12 %%% Generated on Tue Feb 24 12:34:21 EST 2026
% 1.30/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.12 %%% Logic specification used:
% 1.30/1.12 %%% thf(spec, logic, $$dhol).
% 1.30/1.12
% 1.30/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2DTF31113.p
% See solution above
% 1.30/1.12 ------------------------
% 1.30/1.13 ---- Cleaned THF ---
% 1.30/1.13 thf(in_type,type,
% 1.30/1.13 in: $i > $i > $o ).
% 1.30/1.13
% 1.30/1.13 thf(dsetconstr_type,type,
% 1.30/1.13 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.30/1.13
% 1.30/1.13 thf(dsetconstrI_type,type,
% 1.30/1.13 dsetconstrI: $o ).
% 1.30/1.13
% 1.30/1.13 thf(dsetconstrI,definition,
% 1.30/1.13 ( dsetconstrI
% 1.30/1.13 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.30/1.13 ( ( in @ Xx @ A )
% 1.30/1.13 => ( ( Xphi @ Xx )
% 1.30/1.13 => ( in @ Xx
% 1.30/1.13 @ ( dsetconstr @ A
% 1.30/1.13 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.30/1.13
% 1.30/1.13 thf(funcSet_type,type,
% 1.30/1.13 funcSet: $i > $i > $i ).
% 1.30/1.13
% 1.30/1.13 thf(injective_type,type,
% 1.30/1.13 injective: $i > $i > $i > $o ).
% 1.30/1.13
% 1.30/1.13 thf(injFuncSet_type,type,
% 1.30/1.13 injFuncSet: $i > $i > $i ).
% 1.30/1.13
% 1.30/1.13 thf(injFuncSet,definition,
% 1.30/1.13 ( injFuncSet
% 1.30/1.13 = ( ^ [A: $i,B: $i] :
% 1.30/1.13 ( dsetconstr @ ( funcSet @ A @ B )
% 1.30/1.13 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 1.30/1.13
% 1.30/1.13 thf(injFuncInInjFuncSet,conjecture,
% 1.30/1.13 ( dsetconstrI
% 1.30/1.13 => ! [A: $i,B: $i,Xf: $i] :
% 1.30/1.13 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.30/1.13 => ( ( injective @ A @ B @ Xf )
% 1.30/1.13 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ).
% 1.30/1.13 ------------------------
% 1.30/1.14 % (31215)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31113 for (3000ds/183Mi)
% 1.30/1.14 % (31215)First to succeed.
% 1.30/1.14 % (31215)Refutation found. Thanks to Tanya!
% 1.30/1.14 % SZS status Theorem for DTF2THF_31113
% 1.30/1.14 % SZS output start Proof for DTF2THF_31113
% 1.30/1.14 thf(func_def_0, type, in: $i > $i > $o).
% 1.30/1.14 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.30/1.14 thf(func_def_4, type, funcSet: $i > $i > $i).
% 1.30/1.14 thf(func_def_5, type, injective: $i > $i > $i > $o).
% 1.30/1.14 thf(func_def_6, type, injFuncSet: $i > $i > $i).
% 1.30/1.14 thf(func_def_20, type, ph4: !>[X0: $tType]:(X0)).
% 1.30/1.14 thf(f60,plain,(
% 1.30/1.14 $false),
% 1.30/1.14 inference(avatar_sat_refutation,[status(thm)],[f46,f52,f59])).
% 1.30/1.14 thf(f59,plain,(
% 1.30/1.14 ~spl3_1),
% 1.30/1.14 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.30/1.14 thf(f58,plain,(
% 1.30/1.14 $false | ~spl3_1),
% 1.30/1.14 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.30/1.14 thf(f55,plain,(
% 1.30/1.14 ($false = $true) | ~spl3_1),
% 1.30/1.14 inference(superposition,[status(thm)],[f18,f41])).
% 1.30/1.14 thf(f41,plain,(
% 1.30/1.14 ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $false) | ~spl3_1),
% 1.30/1.14 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.30/1.14 thf(f39,definition,(
% 1.30/1.14 spl3_1 <=> ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $false)),
% 1.30/1.14 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.30/1.14 thf(f18,plain,(
% 1.30/1.14 ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true)),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.30/1.14 thf(f15,plain,(
% 1.30/1.14 (dsetconstrI = $true) & (((in @ sK0 @ (injFuncSet @ sK1 @ sK2)) != $true) & ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true) & ((injective @ sK1 @ sK2 @ sK0) = $true))),
% 1.30/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.30/1.14 thf(f14,plain,(
% 1.30/1.14 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (injFuncSet @ X1 @ X2)) != $true) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true) & ((injective @ X1 @ X2 @ X0) = $true)) => (((in @ sK0 @ (injFuncSet @ sK1 @ sK2)) != $true) & ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $true) & ((injective @ sK1 @ sK2 @ sK0) = $true))),
% 1.30/1.14 introduced(definition,[],[choice_axiom])).
% 1.30/1.14 thf(f13,plain,(
% 1.30/1.14 (dsetconstrI = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (injFuncSet @ X1 @ X2)) != $true) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true) & ((injective @ X1 @ X2 @ X0) = $true))),
% 1.30/1.14 inference(flattening,[status(thm)],[f12])).
% 1.30/1.14 thf(f12,plain,(
% 1.30/1.14 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (injFuncSet @ X1 @ X2)) != $true) & ((injective @ X1 @ X2 @ X0) = $true)) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true)) & (dsetconstrI = $true)),
% 1.30/1.14 inference(ennf_transformation,[status(thm)],[f9])).
% 1.30/1.14 thf(f9,plain,(
% 1.30/1.14 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (funcSet @ X1 @ X2)) = $true) => (((injective @ X1 @ X2 @ X0) = $true) => ((in @ X0 @ (injFuncSet @ X1 @ X2)) = $true))))),
% 1.30/1.14 inference(fool_elimination,[status(thm)],[f8])).
% 1.30/1.14 thf(f8,plain,(
% 1.30/1.14 ~(dsetconstrI => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X1 @ X2)) => ((injective @ X1 @ X2 @ X0) => (in @ X0 @ (injFuncSet @ X1 @ X2)))))),
% 1.30/1.14 inference(rectify,[status(thm)],[f4])).
% 1.30/1.14 thf(f4,negated_conjecture,(
% 1.30/1.14 ~(dsetconstrI => ! [X5 : $i,X0 : $i,X4 : $i] : ((in @ X5 @ (funcSet @ X0 @ X4)) => ((injective @ X0 @ X4 @ X5) => (in @ X5 @ (injFuncSet @ X0 @ X4)))))),
% 1.30/1.14 inference(negated_conjecture,[status(cth)],[f3])).
% 1.30/1.14 thf(f3,conjecture,(
% 1.30/1.14 dsetconstrI => ! [X5 : $i,X0 : $i,X4 : $i] : ((in @ X5 @ (funcSet @ X0 @ X4)) => ((injective @ X0 @ X4 @ X5) => (in @ X5 @ (injFuncSet @ X0 @ X4))))),
% 1.30/1.14 file('/export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2THF_31113.p',injFuncInInjFuncSet)).
% 1.30/1.14 thf(f52,plain,(
% 1.30/1.14 ~spl3_2),
% 1.30/1.14 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.30/1.14 thf(f51,plain,(
% 1.30/1.14 $false | ~spl3_2),
% 1.30/1.14 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.30/1.14 thf(f48,plain,(
% 1.30/1.14 ($false = $true) | ~spl3_2),
% 1.30/1.14 inference(superposition,[status(thm)],[f17,f45])).
% 1.30/1.14 thf(f45,plain,(
% 1.30/1.14 ((injective @ sK1 @ sK2 @ sK0) = $false) | ~spl3_2),
% 1.30/1.14 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.30/1.14 thf(f43,definition,(
% 1.30/1.14 spl3_2 <=> ((injective @ sK1 @ sK2 @ sK0) = $false)),
% 1.30/1.14 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.30/1.14 thf(f17,plain,(
% 1.30/1.14 ((injective @ sK1 @ sK2 @ sK0) = $true)),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.30/1.14 thf(f46,plain,(
% 1.30/1.14 spl3_1 | spl3_2),
% 1.30/1.14 inference(avatar_split_clause,[status(thm)],[f37,f43,f39])).
% 1.30/1.14 thf(f37,plain,(
% 1.30/1.14 ((injective @ sK1 @ sK2 @ sK0) = $false) | ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $false)),
% 1.30/1.14 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.30/1.14 thf(f36,plain,(
% 1.30/1.14 ((in @ sK0 @ (funcSet @ sK1 @ sK2)) = $false) | ((injective @ sK1 @ sK2 @ sK0) = $false) | ($true != $true)),
% 1.30/1.14 inference(superposition,[status(thm)],[f24,f33])).
% 1.30/1.14 thf(f33,plain,(
% 1.30/1.14 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ X3)) = $true) | ((X3 @ X1) = $false) | ((in @ X1 @ X2) = $false)) )),
% 1.30/1.14 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.30/1.14 thf(f32,plain,(
% 1.30/1.14 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X1 @ X2) = $false) | (((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3))) = $true)) )),
% 1.30/1.14 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.30/1.14 thf(f31,plain,(
% 1.30/1.14 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ X2) => ((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3)))) = $true)) )),
% 1.30/1.14 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.30/1.14 thf(f30,plain,(
% 1.30/1.14 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0))))) @ X3) = $true)) )),
% 1.30/1.14 inference(pi_clausification,[status(thm)],[f29])).
% 1.30/1.14 thf(f29,plain,(
% 1.30/1.14 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0)))))) = $true)) )),
% 1.30/1.14 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.30/1.14 thf(f28,plain,(
% 1.30/1.14 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1))))))) @ X2) = $true)) )),
% 1.30/1.14 inference(pi_clausification,[status(thm)],[f27])).
% 1.30/1.14 thf(f27,plain,(
% 1.30/1.14 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1)))))))) = $true)) )),
% 1.30/1.14 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.30/1.14 thf(f26,plain,(
% 1.30/1.14 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))) @ X1) = $true)) )),
% 1.30/1.14 inference(pi_clausification,[status(thm)],[f25])).
% 1.30/1.14 thf(f25,plain,(
% 1.30/1.14 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) = $true)),
% 1.30/1.14 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.30/1.14 thf(f23,plain,(
% 1.30/1.14 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 1.30/1.14 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.30/1.14 thf(f20,plain,(
% 1.30/1.14 (dsetconstrI = $true)),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.30/1.14 thf(f21,plain,(
% 1.30/1.14 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f11])).
% 1.30/1.14 thf(f11,plain,(
% 1.30/1.14 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.30/1.14 inference(fool_elimination,[status(thm)],[f10])).
% 1.30/1.14 thf(f10,plain,(
% 1.30/1.14 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
% 1.30/1.14 inference(rectify,[status(thm)],[f1])).
% 1.30/1.14 thf(f1,axiom,(
% 1.30/1.14 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.30/1.14 file('/export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2THF_31113.p',dsetconstrI)).
% 1.30/1.14 thf(f24,plain,(
% 1.30/1.14 ((in @ sK0 @ (dsetconstr @ (funcSet @ sK1 @ sK2) @ (injective @ sK1 @ sK2))) != $true)),
% 1.30/1.14 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.30/1.14 thf(f22,plain,(
% 1.30/1.14 ((in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))) @ sK1 @ sK2)) != $true)),
% 1.30/1.14 inference(definition_unfolding,[status(thm)],[f19,f16])).
% 1.30/1.14 thf(f16,plain,(
% 1.30/1.14 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f7])).
% 1.30/1.14 thf(f7,plain,(
% 1.30/1.14 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.30/1.14 inference(fool_elimination,[status(thm)],[f6])).
% 1.30/1.14 thf(f6,plain,(
% 1.30/1.14 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (injective @ X0 @ X1 @ X2)))) = injFuncSet)),
% 1.30/1.14 inference(rectify,[status(thm)],[f2])).
% 1.30/1.14 thf(f2,axiom,(
% 1.30/1.14 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (injective @ X0 @ X4 @ X5)))) = injFuncSet)),
% 1.30/1.14 file('/export/starexec/sandbox2/tmp/tmp.pSbC6IkBpM/DTF2THF_31113.p',injFuncSet)).
% 1.30/1.14 thf(f19,plain,(
% 1.30/1.14 ((in @ sK0 @ (injFuncSet @ sK1 @ sK2)) != $true)),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 1.30/1.14 % SZS output end Proof for DTF2THF_31113
% 1.30/1.14 % (31215)------------------------------
% 1.30/1.14 % (31215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.14 % (31215)Termination reason: Refutation
% 1.30/1.14
% 1.30/1.14 % (31215)Memory used [KB]: 5500
% 1.30/1.14 % (31215)Time elapsed: 0.005 s
% 1.30/1.14 % (31215)Instructions burned: 5 (million)
% 1.30/1.14 % (31215)------------------------------
% 1.30/1.14 % (31215)------------------------------
% 1.30/1.14 % (31214)Success in time 0.014 s
%------------------------------------------------------------------------------