%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU801^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:37:19 AM UTC 2026
% Result : Theorem 1.82s 1.58s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 311 ( 27 ~; 17 |; 14 &; 238 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 90 ( 30 ^; 45 !; 15 ?; 90 :)
% 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,
ap: $i > $i > $i > $i > $i ).
thf(func_def_6,type,
surjective: $i > $i > $i > $o ).
thf(func_def_7,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_24,type,
sK3: $i > $o ).
thf(func_def_29,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f39,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f38,f24]) ).
thf(f24,plain,
( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( dsetconstrEL = $true )
& ( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ sK1 @ ( surjFuncSet @ sK0 @ sK2 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) )
= $true ) )
=> ( ( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
!= $true )
& ( ( in @ sK1 @ ( surjFuncSet @ sK0 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) )
& ( ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( dsetconstrEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) )
= $true )
=> ( $true
= ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( dsetconstrEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) )
=> ( in @ X1 @ ( funcSet @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dsetconstrEL
=> ! [X0: $i,X5: $i,X4: $i] :
( ( in @ X5 @ ( surjFuncSet @ X0 @ X4 ) )
=> ( in @ X5 @ ( funcSet @ X0 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dsetconstrEL
=> ! [X0: $i,X5: $i,X4: $i] :
( ( in @ X5 @ ( surjFuncSet @ X0 @ X4 ) )
=> ( in @ X5 @ ( funcSet @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',surjFuncSetFuncIn) ).
thf(f38,plain,
( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f35,f36]) ).
thf(f36,plain,
( ( in @ sK1 @ ( dsetconstr @ ( funcSet @ sK0 @ sK2 ) @ ( surjective @ sK0 @ sK2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) )
@ sK0
@ sK2 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f23,f26]) ).
thf(f26,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) )
= surjFuncSet ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( funcSet @ X0 @ X4 )
@ ^ [X5: $i] : ( surjective @ X0 @ X4 @ X5 ) ) )
= surjFuncSet ),
file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',surjFuncSet) ).
thf(f23,plain,
( ( in @ sK1 @ ( surjFuncSet @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f35,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f25]) ).
thf(f25,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f29,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f20,f21]) ).
thf(f21,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
& ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) )
=> ( ( $true
!= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
& ( ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( $true
= ( in @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X1: $i > $o,X2: $i,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',dsetconstrEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU801^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n010.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:34:03 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.50 thf(spec,logic,$$dhol).
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 % File : SEU801^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.50 % Domain : Set Theory
% 0.32/0.50 % Problem : More about Functions - Surjective Functions
% 0.32/0.50 % Version : Especial > Reduced > Especial.
% 0.32/0.50 % English : (! A:i.! B:i.! f:i.in f (surjFuncSet A B) -> in f (funcSet A B))
% 0.32/0.50
% 0.32/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.50 % Source : [Bro08]
% 0.32/0.50 % Names : ZFC303l [Bro08]
% 0.32/0.50
% 0.32/0.50 % Status : Theorem
% 0.32/0.50 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.36 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, 0.29 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
% 0.32/0.50 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.32/0.50 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.32/0.50 % Maximal formula atoms : 3 ( 3 avg)
% 0.32/0.50 % Number of connectives : 35 ( 0 ~; 0 |; 1 &; 30 @)
% 0.32/0.50 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.32/0.50 % Maximal formula depth : 9 ( 3 avg)
% 0.32/0.50 % Number of types : 2 ( 0 usr)
% 0.32/0.50 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.32/0.50 % Number of symbols : 8 ( 7 usr; 1 con; 0-4 aty)
% 0.32/0.50 % Number of variables : 15 ( 7 ^; 7 !; 1 ?; 15 :)
% 0.32/0.50 % SPC : TH0_THM_EQU_NAR
% 0.32/0.50
% 0.32/0.50 % Comments : http://mathgate.info/detsetitem.php?id=484
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 thf(in_type,type,
% 0.32/0.50 in: $i > $i > $o ).
% 0.32/0.50
% 0.32/0.50 thf(dsetconstr_type,type,
% 0.32/0.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/0.50
% 0.32/0.50 thf(dsetconstrEL_type,type,
% 0.32/0.50 dsetconstrEL: $o ).
% 0.32/0.50
% 0.32/0.50 thf(dsetconstrEL,definition,
% 0.32/0.50 ( dsetconstrEL
% 0.32/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.50 ( ( in @ Xx
% 0.32/0.50 @ ( dsetconstr @ A
% 0.32/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.50 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(funcSet_type,type,
% 0.32/0.50 funcSet: $i > $i > $i ).
% 0.32/0.50
% 0.32/0.50 thf(ap_type,type,
% 0.32/0.50 ap: $i > $i > $i > $i > $i ).
% 0.32/0.50
% 0.32/0.50 thf(surjective_type,type,
% 0.32/0.50 surjective: $i > $i > $i > $o ).
% 0.32/0.50
% 0.32/0.50 thf(surjective,definition,
% 0.32/0.50 ( surjective
% 0.32/0.50 = ( ^ [A: $i,B: $i,Xf: $i] :
% 0.32/0.50 ! [Xx: $i] :
% 0.32/0.50 ( ( in @ Xx @ B )
% 0.32/0.50 => ? [Xy: $i] :
% 0.32/0.50 ( ( in @ Xy @ A )
% 0.32/0.50 & ( ( ap @ A @ B @ Xf @ Xy )
% 0.32/0.50 = Xx ) ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(surjFuncSet_type,type,
% 0.32/0.50 surjFuncSet: $i > $i > $i ).
% 0.32/0.50
% 0.32/0.50 thf(surjFuncSet,definition,
% 0.32/0.50 ( surjFuncSet
% 0.32/0.50 = ( ^ [A: $i,B: $i] :
% 0.32/0.50 ( dsetconstr @ ( funcSet @ A @ B )
% 0.32/0.50 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(surjFuncSetFuncIn,conjecture,
% 0.32/0.50 ( dsetconstrEL
% 0.32/0.50 => ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.50 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.32/0.50 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 ------------------------
% 1.82/1.54 ---- Embedded in THF ---
% 1.82/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.82/1.54 %%% Generated on Tue Feb 24 12:34:04 EST 2026
% 1.82/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 1.82/1.54 %%% Logic specification used:
% 1.82/1.54 %%% thf(spec, logic, $$dhol).
% 1.82/1.54
% 1.82/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2DTF23024.p
% See solution above
% 1.82/1.54 ------------------------
% 1.82/1.55 ---- Cleaned THF ---
% 1.82/1.55 thf(in_type,type,
% 1.82/1.55 in: $i > $i > $o ).
% 1.82/1.55
% 1.82/1.55 thf(dsetconstr_type,type,
% 1.82/1.55 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.82/1.55
% 1.82/1.55 thf(dsetconstrEL_type,type,
% 1.82/1.55 dsetconstrEL: $o ).
% 1.82/1.55
% 1.82/1.55 thf(dsetconstrEL,definition,
% 1.82/1.55 ( dsetconstrEL
% 1.82/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.82/1.55 ( ( in @ Xx
% 1.82/1.55 @ ( dsetconstr @ A
% 1.82/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.82/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 1.82/1.55
% 1.82/1.55 thf(funcSet_type,type,
% 1.82/1.55 funcSet: $i > $i > $i ).
% 1.82/1.55
% 1.82/1.55 thf(ap_type,type,
% 1.82/1.55 ap: $i > $i > $i > $i > $i ).
% 1.82/1.55
% 1.82/1.55 thf(surjective_type,type,
% 1.82/1.55 surjective: $i > $i > $i > $o ).
% 1.82/1.55
% 1.82/1.55 thf(surjective,definition,
% 1.82/1.55 ( surjective
% 1.82/1.55 = ( ^ [A: $i,B: $i,Xf: $i] :
% 1.82/1.55 ! [Xx: $i] :
% 1.82/1.55 ( ( in @ Xx @ B )
% 1.82/1.55 => ? [Xy: $i] :
% 1.82/1.55 ( ( in @ Xy @ A )
% 1.82/1.55 & ( ( ap @ A @ B @ Xf @ Xy )
% 1.82/1.55 = Xx ) ) ) ) ) ).
% 1.82/1.55
% 1.82/1.55 thf(surjFuncSet_type,type,
% 1.82/1.55 surjFuncSet: $i > $i > $i ).
% 1.82/1.55
% 1.82/1.55 thf(surjFuncSet,definition,
% 1.82/1.55 ( surjFuncSet
% 1.82/1.55 = ( ^ [A: $i,B: $i] :
% 1.82/1.55 ( dsetconstr @ ( funcSet @ A @ B )
% 1.82/1.55 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 1.82/1.56
% 1.82/1.56 thf(surjFuncSetFuncIn,conjecture,
% 1.82/1.56 ( dsetconstrEL
% 1.82/1.56 => ! [A: $i,B: $i,Xf: $i] :
% 1.82/1.56 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 1.82/1.56 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ).
% 1.82/1.56 ------------------------
% 1.82/1.58 % (23125)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_23024 for (2999ds/2Mi)
% 1.82/1.58 % (23124)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23024 for (2999ds/2Mi)
% 1.82/1.58 % (23123)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_23024 for (2999ds/27Mi)
% 1.82/1.58 % (23121)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23024 for (2999ds/183Mi)
% 1.82/1.58 % (23122)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_23024 for (2999ds/4Mi)
% 1.82/1.58 % (23127)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23024 for (2999ds/18Mi)
% 1.82/1.58 % (23126)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_23024 for (2999ds/275Mi)
% 1.82/1.58 % (23124)Instruction limit reached!
% 1.82/1.58 % (23124)------------------------------
% 1.82/1.58 % (23124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.58 % (23124)Termination reason: Unknown
% 1.82/1.58 % (23124)Termination phase: Preprocessing 3
% 1.82/1.58
% 1.82/1.58 % (23124)Memory used [KB]: 1023
% 1.82/1.58 % (23124)Time elapsed: 0.003 s
% 1.82/1.58 % (23124)Instructions burned: 2 (million)
% 1.82/1.58 % (23124)------------------------------
% 1.82/1.58 % (23124)------------------------------
% 1.82/1.58 % (23125)Instruction limit reached!
% 1.82/1.58 % (23125)------------------------------
% 1.82/1.58 % (23125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.58 % (23125)Termination reason: Unknown
% 1.82/1.58 % (23125)Termination phase: Property scanning
% 1.82/1.58
% 1.82/1.58 % (23125)Memory used [KB]: 895
% 1.82/1.58 % (23125)Time elapsed: 0.003 s
% 1.82/1.58 % (23125)Instructions burned: 2 (million)
% 1.82/1.58 % (23125)------------------------------
% 1.82/1.58 % (23125)------------------------------
% 1.82/1.58 % (23126)First to succeed.
% 1.82/1.58 % (23122)Instruction limit reached!
% 1.82/1.58 % (23122)------------------------------
% 1.82/1.58 % (23122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.58 % (23122)Termination reason: Unknown
% 1.82/1.58 % (23122)Termination phase: Saturation
% 1.82/1.58
% 1.82/1.58 % (23122)Memory used [KB]: 5500
% 1.82/1.58 % (23122)Time elapsed: 0.005 s
% 1.82/1.58 % (23122)Instructions burned: 5 (million)
% 1.82/1.58 % (23122)------------------------------
% 1.82/1.58 % (23122)------------------------------
% 1.82/1.58 % (23121)Also succeeded, but the first one will report.
% 1.82/1.58 % (23127)Also succeeded, but the first one will report.
% 1.82/1.58 % (23126)Refutation found. Thanks to Tanya!
% 1.82/1.58 % SZS status Theorem for DTF2THF_23024
% 1.82/1.58 % SZS output start Proof for DTF2THF_23024
% 1.82/1.58 thf(func_def_0, type, in: $i > $i > $o).
% 1.82/1.58 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.82/1.58 thf(func_def_4, type, funcSet: $i > $i > $i).
% 1.82/1.58 thf(func_def_5, type, ap: $i > $i > $i > $i > $i).
% 1.82/1.58 thf(func_def_6, type, surjective: $i > $i > $i > $o).
% 1.82/1.58 thf(func_def_7, type, surjFuncSet: $i > $i > $i).
% 1.82/1.58 thf(func_def_24, type, sK3: $i > $o).
% 1.82/1.58 thf(func_def_29, type, ph7: !>[X0: $tType]:(X0)).
% 1.82/1.58 thf(f39,plain,(
% 1.82/1.58 $false),
% 1.82/1.58 inference(subsumption_resolution,[status(thm)],[f38,f24])).
% 1.82/1.58 thf(f24,plain,(
% 1.82/1.58 ((in @ sK1 @ (funcSet @ sK0 @ sK2)) != $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f18])).
% 1.82/1.58 thf(f18,plain,(
% 1.82/1.58 (dsetconstrEL = $true) & (((in @ sK1 @ (funcSet @ sK0 @ sK2)) != $true) & ((in @ sK1 @ (surjFuncSet @ sK0 @ sK2)) = $true))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17])).
% 1.82/1.58 thf(f17,plain,(
% 1.82/1.58 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (funcSet @ X0 @ X2))) & ((in @ X1 @ (surjFuncSet @ X0 @ X2)) = $true)) => (((in @ sK1 @ (funcSet @ sK0 @ sK2)) != $true) & ((in @ sK1 @ (surjFuncSet @ sK0 @ sK2)) = $true))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f15,plain,(
% 1.82/1.58 (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (funcSet @ X0 @ X2))) & ((in @ X1 @ (surjFuncSet @ X0 @ X2)) = $true))),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f12])).
% 1.82/1.58 thf(f12,plain,(
% 1.82/1.58 ~((dsetconstrEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (surjFuncSet @ X0 @ X2)) = $true) => ($true = (in @ X1 @ (funcSet @ X0 @ X2)))))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f11])).
% 1.82/1.58 thf(f11,plain,(
% 1.82/1.58 ~(dsetconstrEL => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (surjFuncSet @ X0 @ X2)) => (in @ X1 @ (funcSet @ X0 @ X2))))),
% 1.82/1.58 inference(rectify,[status(thm)],[f5])).
% 1.82/1.58 thf(f5,negated_conjecture,(
% 1.82/1.58 ~(dsetconstrEL => ! [X0 : $i,X5 : $i,X4 : $i] : ((in @ X5 @ (surjFuncSet @ X0 @ X4)) => (in @ X5 @ (funcSet @ X0 @ X4))))),
% 1.82/1.58 inference(negated_conjecture,[status(cth)],[f4])).
% 1.82/1.58 thf(f4,conjecture,(
% 1.82/1.58 dsetconstrEL => ! [X0 : $i,X5 : $i,X4 : $i] : ((in @ X5 @ (surjFuncSet @ X0 @ X4)) => (in @ X5 @ (funcSet @ X0 @ X4)))),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',surjFuncSetFuncIn)).
% 1.82/1.58 thf(f38,plain,(
% 1.82/1.58 ((in @ sK1 @ (funcSet @ sK0 @ sK2)) = $true)),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.82/1.58 thf(f37,plain,(
% 1.82/1.58 ($true != $true) | ((in @ sK1 @ (funcSet @ sK0 @ sK2)) = $true)),
% 1.82/1.58 inference(superposition,[status(thm)],[f35,f36])).
% 1.82/1.58 thf(f36,plain,(
% 1.82/1.58 ((in @ sK1 @ (dsetconstr @ (funcSet @ sK0 @ sK2) @ (surjective @ sK0 @ sK2))) = $true)),
% 1.82/1.58 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.82/1.58 thf(f30,plain,(
% 1.82/1.58 ((in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))) @ sK0 @ sK2)) = $true)),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f23,f26])).
% 1.82/1.58 thf(f26,plain,(
% 1.82/1.58 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f8])).
% 1.82/1.58 thf(f8,plain,(
% 1.82/1.58 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f7])).
% 1.82/1.58 thf(f7,plain,(
% 1.82/1.58 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (surjective @ X0 @ X1 @ X2)))) = surjFuncSet)),
% 1.82/1.58 inference(rectify,[status(thm)],[f3])).
% 1.82/1.58 thf(f3,axiom,(
% 1.82/1.58 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (surjective @ X0 @ X4 @ X5)))) = surjFuncSet)),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',surjFuncSet)).
% 1.82/1.58 thf(f23,plain,(
% 1.82/1.58 ((in @ sK1 @ (surjFuncSet @ sK0 @ sK2)) = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f18])).
% 1.82/1.58 thf(f35,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ X0)) != $true) | ($true = (in @ X1 @ X2))) )),
% 1.82/1.58 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.82/1.58 thf(f34,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2))) )),
% 1.82/1.58 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.82/1.58 thf(f31,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2)) | ($true != $true)) )),
% 1.82/1.58 inference(definition_unfolding,[status(thm)],[f29,f25])).
% 1.82/1.58 thf(f25,plain,(
% 1.82/1.58 (dsetconstrEL = $true)),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f18])).
% 1.82/1.58 thf(f29,plain,(
% 1.82/1.58 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | (dsetconstrEL != $true)) )),
% 1.82/1.58 inference(cnf_transformation,[status(thm)],[f22])).
% 1.82/1.58 thf(f22,plain,(
% 1.82/1.58 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (($true != (in @ sK4 @ sK5)) & ((in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK3 @ Y0)))) = $true)))),
% 1.82/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f20,f21])).
% 1.82/1.58 thf(f21,plain,(
% 1.82/1.58 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X5)) & ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)) => (($true != (in @ sK4 @ sK5)) & ((in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK3 @ Y0)))) = $true))),
% 1.82/1.58 introduced(definition,[],[choice_axiom])).
% 1.82/1.58 thf(f20,plain,(
% 1.82/1.58 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (in @ X4 @ X5)) & ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f19])).
% 1.82/1.58 thf(f19,plain,(
% 1.82/1.58 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) & ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)))),
% 1.82/1.58 inference(nnf_transformation,[status(thm)],[f16])).
% 1.82/1.58 thf(f16,plain,(
% 1.82/1.58 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) <=> (dsetconstrEL = $true)),
% 1.82/1.58 inference(ennf_transformation,[status(thm)],[f14])).
% 1.82/1.58 thf(f14,plain,(
% 1.82/1.58 (dsetconstrEL = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ($true = (in @ X1 @ X2)))),
% 1.82/1.58 inference(fool_elimination,[status(thm)],[f13])).
% 1.82/1.58 thf(f13,plain,(
% 1.82/1.58 (dsetconstrEL = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X1 @ X2)))),
% 1.82/1.58 inference(rectify,[status(thm)],[f1])).
% 1.82/1.58 thf(f1,axiom,(
% 1.82/1.58 (dsetconstrEL = ! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 1.82/1.58 file('/export/starexec/sandbox/tmp/tmp.wSYZKIM69s/DTF2THF_23024.p',dsetconstrEL)).
% 1.82/1.58 % SZS output end Proof for DTF2THF_23024
% 1.82/1.58 % (23126)------------------------------
% 1.82/1.58 % (23126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.58 % (23126)Termination reason: Refutation
% 1.82/1.58
% 1.82/1.58 % (23126)Memory used [KB]: 5500
% 1.82/1.58 % (23126)Time elapsed: 0.005 s
% 1.82/1.58 % (23126)Instructions burned: 3 (million)
% 1.82/1.58 % (23126)------------------------------
% 1.82/1.58 % (23126)------------------------------
% 1.82/1.58 % (23120)Success in time 0.021 s
%------------------------------------------------------------------------------