%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU800^2 : 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 : n009.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 1.63s 1.37s
% Output : Refutation 1.63s
% 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 : 231 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 284 ( 27 ~; 17 |; 14 &; 211 @)
% ( 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 : 16 ( 13 usr; 8 con; 0-3 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,
injective: $i > $i > $i > $o ).
thf(func_def_6,type,
injFuncSet: $i > $i > $i ).
thf(func_def_18,type,
sK5: $i > $o ).
thf(func_def_21,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f21]) ).
thf(f21,plain,
( ( injective @ sK0 @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( in @ sK1 @ ( injFuncSet @ sK0 @ sK2 ) )
= $true )
& ( ( injective @ sK0 @ sK2 @ sK1 )
!= $true )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( injFuncSet @ X0 @ X2 ) )
= $true )
& ( ( injective @ X0 @ X2 @ X1 )
!= $true ) )
=> ( ( ( in @ sK1 @ ( injFuncSet @ sK0 @ sK2 ) )
= $true )
& ( ( injective @ sK0 @ sK2 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( injFuncSet @ X0 @ X2 ) )
= $true )
& ( ( injective @ X0 @ X2 @ X1 )
!= $true ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( injFuncSet @ X0 @ X2 ) )
= $true )
=> ( ( injective @ X0 @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( injFuncSet @ X0 @ X2 ) )
=> ( injective @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X2: $i,X5: $i,X3: $i] :
( ( in @ X5 @ ( injFuncSet @ X2 @ X3 ) )
=> ( injective @ X2 @ X3 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X2: $i,X5: $i,X3: $i] :
( ( in @ X5 @ ( injFuncSet @ X2 @ X3 ) )
=> ( injective @ X2 @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',injFuncSetFuncInj) ).
thf(f35,plain,
( ( injective @ sK0 @ sK2 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( injective @ sK0 @ sK2 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f32,f33]) ).
thf(f33,plain,
( ( in @ sK1 @ ( dsetconstr @ ( funcSet @ sK0 @ sK2 ) @ ( injective @ sK0 @ sK2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) )
@ sK0
@ sK2 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f23]) ).
thf(f23,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( injFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( injective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( injFuncSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( injective @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( injFuncSet
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ ( funcSet @ X0 @ X4 )
@ ^ [X5: $i] : ( injective @ X0 @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',injFuncSet) ).
thf(f22,plain,
( ( in @ sK1 @ ( injFuncSet @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f32,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) )
!= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X0 )
= $true )
| ( $true != $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f26,f20]) ).
thf(f20,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f26,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( sK5 @ sK3 )
!= $true )
& ( ( in @ sK3
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18]) ).
thf(f18,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X5 @ X3 ) )
& ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) )
=> ( ( ( sK5 @ sK3 )
!= $true )
& ( ( in @ sK3
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X5 @ X3 ) )
& ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ( ( X2 @ X0 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X0 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',dsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU800^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.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 12:34:10 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
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU800^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : More about Functions - Injective Functions
% 0.27/0.46 % Version : Especial > Reduced > Especial.
% 0.27/0.46 % English : (! x:i.! y:i.! f:i.in f (injFuncSet x y) -> injective x y f)
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC302l [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v8.2.0, 0.15 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, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.27/0.46 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.27/0.46 % Number of connectives : 23 ( 0 ~; 0 |; 0 &; 20 @)
% 0.27/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 9 ( 4 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 7 ( 6 usr; 1 con; 0-3 aty)
% 0.27/0.46 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=425
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstr_type,type,
% 0.27/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER_type,type,
% 0.27/0.46 dsetconstrER: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER,definition,
% 0.27/0.46 ( dsetconstrER
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(funcSet_type,type,
% 0.27/0.46 funcSet: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(injective_type,type,
% 0.27/0.46 injective: $i > $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(injFuncSet_type,type,
% 0.27/0.46 injFuncSet: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(injFuncSet,definition,
% 0.27/0.46 ( injFuncSet
% 0.27/0.46 = ( ^ [A: $i,B: $i] :
% 0.27/0.46 ( dsetconstr @ ( funcSet @ A @ B )
% 0.27/0.46 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(injFuncSetFuncInj,conjecture,
% 0.27/0.46 ( dsetconstrER
% 0.27/0.46 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.27/0.46 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.27/0.46 => ( injective @ Xx @ Xy @ Xf ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.63/1.33 ---- Embedded in THF ---
% 1.63/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.33 %%% Generated on Tue Feb 24 12:34:11 EST 2026
% 1.63/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.33 %%% Logic specification used:
% 1.63/1.33 %%% thf(spec, logic, $$dhol).
% 1.63/1.33
% 1.63/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2DTF432.p
% See solution above
% 1.63/1.33 ------------------------
% 1.63/1.34 ---- Cleaned THF ---
% 1.63/1.35 thf(in_type,type,
% 1.63/1.35 in: $i > $i > $o ).
% 1.63/1.35
% 1.63/1.35 thf(dsetconstr_type,type,
% 1.63/1.35 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.63/1.35
% 1.63/1.35 thf(dsetconstrER_type,type,
% 1.63/1.35 dsetconstrER: $o ).
% 1.63/1.35
% 1.63/1.35 thf(dsetconstrER,definition,
% 1.63/1.35 ( dsetconstrER
% 1.63/1.35 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.63/1.35 ( ( in @ Xx
% 1.63/1.35 @ ( dsetconstr @ A
% 1.63/1.35 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.63/1.35 => ( Xphi @ Xx ) ) ) ) ).
% 1.63/1.35
% 1.63/1.35 thf(funcSet_type,type,
% 1.63/1.35 funcSet: $i > $i > $i ).
% 1.63/1.35
% 1.63/1.35 thf(injective_type,type,
% 1.63/1.35 injective: $i > $i > $i > $o ).
% 1.63/1.35
% 1.63/1.35 thf(injFuncSet_type,type,
% 1.63/1.35 injFuncSet: $i > $i > $i ).
% 1.63/1.35
% 1.63/1.35 thf(injFuncSet,definition,
% 1.63/1.35 ( injFuncSet
% 1.63/1.35 = ( ^ [A: $i,B: $i] :
% 1.63/1.35 ( dsetconstr @ ( funcSet @ A @ B )
% 1.63/1.35 @ ^ [Xf: $i] : ( injective @ A @ B @ Xf ) ) ) ) ).
% 1.63/1.35
% 1.63/1.35 thf(injFuncSetFuncInj,conjecture,
% 1.63/1.35 ( dsetconstrER
% 1.63/1.35 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 1.63/1.35 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 1.63/1.35 => ( injective @ Xx @ Xy @ Xf ) ) ) ).
% 1.63/1.35 ------------------------
% 1.63/1.37 % (688)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_432 for (2999ds/2Mi)
% 1.63/1.37 % (685)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_432 for (2999ds/183Mi)
% 1.63/1.37 % (689)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_432 for (2999ds/2Mi)
% 1.63/1.37 % (686)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_432 for (2999ds/4Mi)
% 1.63/1.37 % (690)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_432 for (2999ds/275Mi)
% 1.63/1.37 % (687)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_432 for (2999ds/27Mi)
% 1.63/1.37 % (691)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_432 for (2999ds/18Mi)
% 1.63/1.37 % (688)Instruction limit reached!
% 1.63/1.37 % (688)------------------------------
% 1.63/1.37 % (688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (688)Termination reason: Unknown
% 1.63/1.37 % (688)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (688)Memory used [KB]: 5500
% 1.63/1.37 % (688)Time elapsed: 0.004 s
% 1.63/1.37 % (688)Instructions burned: 2 (million)
% 1.63/1.37 % (688)------------------------------
% 1.63/1.37 % (688)------------------------------
% 1.63/1.37 % (689)Instruction limit reached!
% 1.63/1.37 % (689)------------------------------
% 1.63/1.37 % (689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (689)Termination reason: Unknown
% 1.63/1.37 % (689)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (689)Memory used [KB]: 1023
% 1.63/1.37 % (689)Time elapsed: 0.004 s
% 1.63/1.37 % (689)Instructions burned: 2 (million)
% 1.63/1.37 % (689)------------------------------
% 1.63/1.37 % (689)------------------------------
% 1.63/1.37 % (690)Refutation not found, incomplete strategy
% 1.63/1.37 % (690)------------------------------
% 1.63/1.37 % (690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (690)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (690)Memory used [KB]: 5500
% 1.63/1.37 % (690)Time elapsed: 0.004 s
% 1.63/1.37 % (690)Instructions burned: 2 (million)
% 1.63/1.37 % (690)------------------------------
% 1.63/1.37 % (690)------------------------------
% 1.63/1.37 % (691)First to succeed.
% 1.63/1.37 % (686)Instruction limit reached!
% 1.63/1.37 % (686)------------------------------
% 1.63/1.37 % (686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (686)Termination reason: Unknown
% 1.63/1.37 % (686)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (686)Memory used [KB]: 5500
% 1.63/1.37 % (686)Time elapsed: 0.005 s
% 1.63/1.37 % (686)Instructions burned: 4 (million)
% 1.63/1.37 % (686)------------------------------
% 1.63/1.37 % (686)------------------------------
% 1.63/1.37 % (685)Also succeeded, but the first one will report.
% 1.63/1.37 % (691)Refutation found. Thanks to Tanya!
% 1.63/1.37 % SZS status Theorem for DTF2THF_432
% 1.63/1.37 % SZS output start Proof for DTF2THF_432
% 1.63/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.63/1.37 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.63/1.37 thf(func_def_4, type, funcSet: $i > $i > $i).
% 1.63/1.37 thf(func_def_5, type, injective: $i > $i > $i > $o).
% 1.63/1.37 thf(func_def_6, type, injFuncSet: $i > $i > $i).
% 1.63/1.37 thf(func_def_18, type, sK5: $i > $o).
% 1.63/1.37 thf(func_def_21, type, ph7: !>[X0: $tType]:(X0)).
% 1.63/1.37 thf(f36,plain,(
% 1.63/1.37 $false),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f35,f21])).
% 1.63/1.37 thf(f21,plain,(
% 1.63/1.37 ((injective @ sK0 @ sK2 @ sK1) != $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.37 thf(f15,plain,(
% 1.63/1.37 (((in @ sK1 @ (injFuncSet @ sK0 @ sK2)) = $true) & ((injective @ sK0 @ sK2 @ sK1) != $true)) & (dsetconstrER = $true)),
% 1.63/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14])).
% 1.63/1.37 thf(f14,plain,(
% 1.63/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (injFuncSet @ X0 @ X2)) = $true) & ((injective @ X0 @ X2 @ X1) != $true)) => (((in @ sK1 @ (injFuncSet @ sK0 @ sK2)) = $true) & ((injective @ sK0 @ sK2 @ sK1) != $true))),
% 1.63/1.37 introduced(definition,[],[choice_axiom])).
% 1.63/1.37 thf(f12,plain,(
% 1.63/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (injFuncSet @ X0 @ X2)) = $true) & ((injective @ X0 @ X2 @ X1) != $true)) & (dsetconstrER = $true)),
% 1.63/1.37 inference(ennf_transformation,[status(thm)],[f7])).
% 1.63/1.37 thf(f7,plain,(
% 1.63/1.37 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (injFuncSet @ X0 @ X2)) = $true) => ((injective @ X0 @ X2 @ X1) = $true)))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.37 thf(f6,plain,(
% 1.63/1.37 ~(dsetconstrER => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (injFuncSet @ X0 @ X2)) => (injective @ X0 @ X2 @ X1)))),
% 1.63/1.37 inference(rectify,[status(thm)],[f4])).
% 1.63/1.37 thf(f4,negated_conjecture,(
% 1.63/1.37 ~(dsetconstrER => ! [X2 : $i,X5 : $i,X3 : $i] : ((in @ X5 @ (injFuncSet @ X2 @ X3)) => (injective @ X2 @ X3 @ X5)))),
% 1.63/1.37 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.37 thf(f3,conjecture,(
% 1.63/1.37 dsetconstrER => ! [X2 : $i,X5 : $i,X3 : $i] : ((in @ X5 @ (injFuncSet @ X2 @ X3)) => (injective @ X2 @ X3 @ X5))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',injFuncSetFuncInj)).
% 1.63/1.37 thf(f35,plain,(
% 1.63/1.37 ((injective @ sK0 @ sK2 @ sK1) = $true)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.63/1.37 thf(f34,plain,(
% 1.63/1.37 ((injective @ sK0 @ sK2 @ sK1) = $true) | ($true != $true)),
% 1.63/1.37 inference(superposition,[status(thm)],[f32,f33])).
% 1.63/1.37 thf(f33,plain,(
% 1.63/1.37 ((in @ sK1 @ (dsetconstr @ (funcSet @ sK0 @ sK2) @ (injective @ sK0 @ sK2))) = $true)),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.63/1.37 thf(f27,plain,(
% 1.63/1.37 ((in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))) @ sK0 @ sK2)) = $true)),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f22,f23])).
% 1.63/1.37 thf(f23,plain,(
% 1.63/1.37 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.37 thf(f11,plain,(
% 1.63/1.37 (injFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (injective @ Y0 @ Y1 @ Y2)))))))),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.37 thf(f10,plain,(
% 1.63/1.37 (injFuncSet = (^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (injective @ X0 @ X1 @ X2)))))),
% 1.63/1.37 inference(rectify,[status(thm)],[f2])).
% 1.63/1.37 thf(f2,axiom,(
% 1.63/1.37 (injFuncSet = (^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (injective @ X0 @ X4 @ X5)))))),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',injFuncSet)).
% 1.63/1.37 thf(f22,plain,(
% 1.63/1.37 ((in @ sK1 @ (injFuncSet @ sK0 @ sK2)) = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.37 thf(f32,plain,(
% 1.63/1.37 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X0 @ (dsetconstr @ X1 @ X2)) != $true) | ((X2 @ X0) = $true)) )),
% 1.63/1.37 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.63/1.37 thf(f31,plain,(
% 1.63/1.37 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.63/1.37 thf(f28,plain,(
% 1.63/1.37 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X0) = $true) | ($true != $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) )),
% 1.63/1.37 inference(definition_unfolding,[status(thm)],[f26,f20])).
% 1.63/1.37 thf(f20,plain,(
% 1.63/1.37 (dsetconstrER = $true)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f15])).
% 1.63/1.37 thf(f26,plain,(
% 1.63/1.37 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f19])).
% 1.63/1.37 thf(f19,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK5 @ sK3) != $true) & ((in @ sK3 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true)))),
% 1.63/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f17,f18])).
% 1.63/1.37 thf(f18,plain,(
% 1.63/1.37 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (X5 @ X3)) & ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)) => (((sK5 @ sK3) != $true) & ((in @ sK3 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK5 @ Y0)))) = $true))),
% 1.63/1.37 introduced(definition,[],[choice_axiom])).
% 1.63/1.37 thf(f17,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (X5 @ X3)) & ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)))),
% 1.63/1.37 inference(rectify,[status(thm)],[f16])).
% 1.63/1.37 thf(f16,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) != $true) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))),
% 1.63/1.37 inference(nnf_transformation,[status(thm)],[f13])).
% 1.63/1.37 thf(f13,plain,(
% 1.63/1.37 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 1.63/1.37 inference(ennf_transformation,[status(thm)],[f9])).
% 1.63/1.37 thf(f9,plain,(
% 1.63/1.37 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ((X2 @ X0) = $true)) <=> (dsetconstrER = $true)),
% 1.63/1.37 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.37 thf(f8,plain,(
% 1.63/1.37 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)) = dsetconstrER)),
% 1.63/1.37 inference(rectify,[status(thm)],[f1])).
% 1.63/1.37 thf(f1,axiom,(
% 1.63/1.37 (! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.63/1.37 file('/export/starexec/sandbox2/tmp/tmp.6S93X1hddf/DTF2THF_432.p',dsetconstrER)).
% 1.63/1.37 % SZS output end Proof for DTF2THF_432
% 1.63/1.37 % (691)------------------------------
% 1.63/1.37 % (691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (691)Termination reason: Refutation
% 1.63/1.37
% 1.63/1.37 % (691)Memory used [KB]: 5500
% 1.63/1.37 % (691)Time elapsed: 0.006 s
% 1.63/1.37 % (691)Instructions burned: 2 (million)
% 1.63/1.37 % (691)------------------------------
% 1.63/1.37 % (691)------------------------------
% 1.63/1.37 % (684)Success in time 0.021 s
%------------------------------------------------------------------------------