%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA068^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 08:38:47 AM UTC 2026
% Result : Theorem 1.57s 1.36s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 48 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 246 ( 28 ~; 18 |; 4 &; 188 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 3 con; 0-4 aty)
% ( 0 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 65 ( 8 ^; 55 !; 2 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/INFINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_6,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f46,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
$true != $true,
inference(superposition,[status(thm)],[f26,f36]) ).
thf(f36,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24,f34]) ).
thf(f34,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != $true )
| ( $true
= ( 'const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f32,f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/SUBSET_UNIV_') ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f28]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/INFINITE' @ X0 @ X1 )
!= $true ) )
& ( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
<=> ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/INFINITE' @ X0 @ X1 )
= $true )
<=> ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/INFINITE' @ X0 @ X1 )
= ( ~ ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/INFINITE_') ).
thf(f25,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/FINITE_SUBSET_') ).
thf(f24,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' )
!= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real' ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
'const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real',
file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/real_INFINITE_') ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ( 'const/realax/real_le' @ X0 @ Y1 ) @ Y1 ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ( 'const/realax/real_le' @ X0 @ X2 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA068^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n009.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 03:49:25 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : ANA068^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.39 % Domain : Analysis
% 0.17/0.39 % Problem : real_INFINITE
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Kal16]
% 0.17/0.39 % Names : real_INFINITE_.p [Kal16]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v7.1.0
% 0.17/0.39 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 0.17/0.39 % Number of atoms : 14 ( 1 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 4 ( 2 avg)
% 0.17/0.39 % Number of connectives : 32 ( 2 ~; 0 |; 1 &; 28 @)
% 0.17/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 11 ( 6 avg)
% 0.17/0.39 % Number of types : 2 ( 1 usr)
% 0.17/0.39 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 8 ( 7 usr; 0 con; 2-4 aty)
% 0.17/0.39 % Number of variables : 16 ( 1 ^; 8 !; 1 ?; 16 :)
% 0.17/0.39 % ( 6 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.39 % SPC : TH1_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : Exported from core HOL Light.
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf('thf_type_type/realax/real',type,
% 0.17/0.39 'type/realax/real': $tType ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/UNIV',type,
% 0.17/0.39 'const/sets/UNIV':
% 0.17/0.39 !>[A: $tType] : ( A > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/SUBSET',type,
% 0.17/0.39 'const/sets/SUBSET':
% 0.17/0.39 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/SETSPEC',type,
% 0.17/0.39 'const/sets/SETSPEC':
% 0.17/0.39 !>[A: $tType] : ( A > $o > A > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/INFINITE',type,
% 0.17/0.39 'const/sets/INFINITE':
% 0.17/0.39 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/GSPEC',type,
% 0.17/0.39 'const/sets/GSPEC':
% 0.17/0.39 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/FINITE',type,
% 0.17/0.39 'const/sets/FINITE':
% 0.17/0.39 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/realax/real_le',type,
% 0.17/0.39 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/FINITE_REAL_INTERVAL_1',axiom,
% 0.17/0.39 ! [A: 'type/realax/real'] :
% 0.17/0.39 ~ ( 'const/sets/FINITE' @ 'type/realax/real'
% 0.17/0.39 @ ( 'const/sets/GSPEC' @ 'type/realax/real'
% 0.17/0.39 @ ^ [A0: 'type/realax/real'] :
% 0.17/0.39 ? [A1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ A0 @ ( 'const/realax/real_le' @ A @ A1 ) @ A1 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/SUBSET_UNIV_',axiom,
% 0.17/0.39 ! [A: $tType,A0: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/FINITE_SUBSET_',axiom,
% 0.17/0.39 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.17/0.39 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.17/0.39 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 0.17/0.39 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/INFINITE_',axiom,
% 0.17/0.39 ! [A: $tType,A0: A > $o] :
% 0.17/0.39 ( ( 'const/sets/INFINITE' @ A @ A0 )
% 0.17/0.39 = ( ~ ( 'const/sets/FINITE' @ A @ A0 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/real_INFINITE_',conjecture,
% 0.17/0.39 'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.57/1.33 ---- Embedded in THF ---
% 1.57/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.33 %%% Generated on Tue Feb 24 03:49:26 EST 2026
% 1.57/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.33 %%% Logic specification used:
% 1.57/1.33 %%% thf(spec, logic, $$dhol).
% 1.57/1.33
% 1.57/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2DTF4714.p
% See solution above
% 1.57/1.33 ------------------------
% 1.57/1.34 ---- Cleaned THF ---
% 1.57/1.34 thf('thf_type_type/realax/real',type,
% 1.57/1.34 'type/realax/real': $tType ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/UNIV',type,
% 1.57/1.34 'const/sets/UNIV':
% 1.57/1.34 !>[A: $tType] : ( A > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/SUBSET',type,
% 1.57/1.34 'const/sets/SUBSET':
% 1.57/1.34 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/SETSPEC',type,
% 1.57/1.34 'const/sets/SETSPEC':
% 1.57/1.34 !>[A: $tType] : ( A > $o > A > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/INFINITE',type,
% 1.57/1.34 'const/sets/INFINITE':
% 1.57/1.34 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/GSPEC',type,
% 1.57/1.34 'const/sets/GSPEC':
% 1.57/1.34 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/sets/FINITE',type,
% 1.57/1.34 'const/sets/FINITE':
% 1.57/1.34 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.57/1.34
% 1.57/1.34 thf('thf_const_const/realax/real_le',type,
% 1.57/1.34 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.57/1.34
% 1.57/1.34 thf('thm/sets/FINITE_REAL_INTERVAL_1',axiom,
% 1.57/1.34 ! [A: 'type/realax/real'] :
% 1.57/1.34 ~ ( 'const/sets/FINITE' @ 'type/realax/real'
% 1.57/1.34 @ ( 'const/sets/GSPEC' @ 'type/realax/real'
% 1.57/1.34 @ ^ [A0: 'type/realax/real'] :
% 1.57/1.34 ? [A1: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ A0 @ ( 'const/realax/real_le' @ A @ A1 ) @ A1 ) ) ) ).
% 1.57/1.34
% 1.57/1.34 thf('thm/sets/SUBSET_UNIV_',axiom,
% 1.57/1.34 ! [A: $tType,A0: A > $o] : ( 'const/sets/SUBSET' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 1.57/1.34
% 1.57/1.34 thf('thm/sets/FINITE_SUBSET_',axiom,
% 1.57/1.34 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.57/1.34 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.57/1.34 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 1.57/1.34 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 1.57/1.34
% 1.57/1.34 thf('thm/sets/INFINITE_',axiom,
% 1.57/1.34 ! [A: $tType,A0: A > $o] :
% 1.57/1.34 ( ( 'const/sets/INFINITE' @ A @ A0 )
% 1.57/1.34 = ( ~ ( 'const/sets/FINITE' @ A @ A0 ) ) ) ).
% 1.57/1.34
% 1.57/1.34 thf('thm/sets/real_INFINITE_',conjecture,
% 1.57/1.34 'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ).
% 1.57/1.34 ------------------------
% 1.57/1.36 % (4814)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_4714 for (2999ds/27Mi)
% 1.57/1.36 % (4815)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4714 for (2999ds/2Mi)
% 1.57/1.36 % (4813)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_4714 for (2999ds/4Mi)
% 1.57/1.36 % (4812)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4714 for (2999ds/183Mi)
% 1.57/1.36 % (4816)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_4714 for (2999ds/2Mi)
% 1.57/1.36 % (4817)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_4714 for (2999ds/275Mi)
% 1.57/1.36 % (4818)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4714 for (2999ds/18Mi)
% 1.57/1.36 % (4815)Instruction limit reached!
% 1.57/1.36 % (4815)------------------------------
% 1.57/1.36 % (4815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (4815)Termination reason: Unknown
% 1.57/1.36 % (4815)Termination phase: Saturation
% 1.57/1.36 % (4816)Instruction limit reached!
% 1.57/1.36 % (4816)------------------------------
% 1.57/1.36 % (4816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (4816)Termination reason: Unknown
% 1.57/1.36 % (4816)Termination phase: Saturation
% 1.57/1.36
% 1.57/1.36 % (4816)Memory used [KB]: 1023
% 1.57/1.36 % (4816)Time elapsed: 0.003 s
% 1.57/1.36 % (4816)Instructions burned: 3 (million)
% 1.57/1.36 % (4816)------------------------------
% 1.57/1.36 % (4816)------------------------------
% 1.57/1.36
% 1.57/1.36 % (4815)Memory used [KB]: 5500
% 1.57/1.36 % (4815)Time elapsed: 0.003 s
% 1.57/1.36 % (4815)Instructions burned: 2 (million)
% 1.57/1.36 % (4815)------------------------------
% 1.57/1.36 % (4815)------------------------------
% 1.57/1.36 % (4817)Refutation not found, incomplete strategy
% 1.57/1.36 % (4817)------------------------------
% 1.57/1.36 % (4817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (4817)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.36
% 1.57/1.36
% 1.57/1.36 % (4817)Memory used [KB]: 5500
% 1.57/1.36 % (4817)Time elapsed: 0.003 s
% 1.57/1.36 % (4817)Instructions burned: 2 (million)
% 1.57/1.36 % (4817)------------------------------
% 1.57/1.36 % (4817)------------------------------
% 1.57/1.36 % (4813)Instruction limit reached!
% 1.57/1.36 % (4813)------------------------------
% 1.57/1.36 % (4813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (4813)Termination reason: Unknown
% 1.57/1.36 % (4813)Termination phase: Saturation
% 1.57/1.36
% 1.57/1.36 % (4813)Memory used [KB]: 5500
% 1.57/1.36 % (4813)Time elapsed: 0.004 s
% 1.57/1.36 % (4813)Instructions burned: 4 (million)
% 1.57/1.36 % (4813)------------------------------
% 1.57/1.36 % (4813)------------------------------
% 1.57/1.36 % (4818)First to succeed.
% 1.57/1.36 % (4812)Also succeeded, but the first one will report.
% 1.57/1.36 % (4818)Refutation found. Thanks to Tanya!
% 1.57/1.36 % SZS status Theorem for DTF2THF_4714
% 1.57/1.36 % SZS output start Proof for DTF2THF_4714
% 1.57/1.36 thf(type_def_6, type, 'type/realax/real': $tType).
% 1.57/1.36 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.57/1.36 thf(func_def_1, type, 'const/sets/UNIV': !>[X0: $tType]:(X0 > $o)).
% 1.57/1.36 thf(func_def_2, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.57/1.36 thf(func_def_3, type, 'const/sets/SETSPEC': !>[X0: $tType]:(X0 > $o > X0 > $o)).
% 1.57/1.36 thf(func_def_4, type, 'const/sets/INFINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.57/1.36 thf(func_def_5, type, 'const/sets/GSPEC': !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 1.57/1.36 thf(func_def_6, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.57/1.36 thf(func_def_7, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.57/1.36 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.57/1.36 thf(f46,plain,(
% 1.57/1.36 $false),
% 1.57/1.36 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.57/1.36 thf(f43,plain,(
% 1.57/1.36 ($true != $true)),
% 1.57/1.36 inference(superposition,[status(thm)],[f26,f36])).
% 1.57/1.36 thf(f36,plain,(
% 1.57/1.36 ( ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true)) )),
% 1.57/1.36 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.57/1.36 thf(f35,plain,(
% 1.57/1.36 ( ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) = $true) | ($true != $true)) )),
% 1.57/1.36 inference(superposition,[status(thm)],[f24,f34])).
% 1.57/1.36 thf(f34,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = ('const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0)) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.57/1.36 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.57/1.36 thf(f33,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X1 : X0 > $o] : (($true != $true) | ($true = ('const/sets/INFINITE' @ X0 @ 'const/sets/UNIV' @ X0)) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.57/1.36 inference(superposition,[status(thm)],[f32,f27])).
% 1.57/1.36 thf(f27,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) = $true)) )),
% 1.57/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.57/1.36 thf(f9,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) = $true)),
% 1.57/1.36 inference(fool_elimination,[status(thm)],[f8])).
% 1.57/1.36 thf(f8,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 1.57/1.36 inference(rectify,[status(thm)],[f2])).
% 1.57/1.36 thf(f2,axiom,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 1.57/1.36 file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/SUBSET_UNIV_')).
% 1.57/1.36 thf(f32,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) != $true) | (('const/sets/INFINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X2) = $true)) )),
% 1.57/1.36 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.57/1.36 thf(f31,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/INFINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X2) = $true) | (('const/sets/SUBSET' @ X0 @ X2 @ X1) != $true) | ($true != $true)) )),
% 1.57/1.36 inference(superposition,[status(thm)],[f25,f28])).
% 1.57/1.36 thf(f28,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | (('const/sets/INFINITE' @ X0 @ X1) = $true)) )),
% 1.57/1.36 inference(cnf_transformation,[status(thm)],[f23])).
% 1.57/1.36 thf(f23,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : (((('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/INFINITE' @ X0 @ X1) != $true)) & ((('const/sets/INFINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X1) = $true)))),
% 1.57/1.36 inference(nnf_transformation,[status(thm)],[f18])).
% 1.57/1.36 thf(f18,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) != $true) <=> (('const/sets/INFINITE' @ X0 @ X1) = $true))),
% 1.57/1.36 inference(flattening,[status(thm)],[f11])).
% 1.57/1.36 thf(f11,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/INFINITE' @ X0 @ X1) = $true) <=> ~(('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.57/1.36 inference(fool_elimination,[status(thm)],[f10])).
% 1.57/1.36 thf(f10,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/INFINITE' @ X0 @ X1) = ~('const/sets/FINITE' @ X0 @ X1))),
% 1.57/1.36 inference(rectify,[status(thm)],[f4])).
% 1.57/1.36 thf(f4,axiom,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/INFINITE' @ X0 @ X1) = ~('const/sets/FINITE' @ X0 @ X1))),
% 1.57/1.36 file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/INFINITE_')).
% 1.57/1.36 thf(f25,plain,(
% 1.57/1.36 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.57/1.36 inference(cnf_transformation,[status(thm)],[f22])).
% 1.57/1.36 thf(f22,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X2) != $true))),
% 1.57/1.36 inference(flattening,[status(thm)],[f21])).
% 1.57/1.36 thf(f21,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)))),
% 1.57/1.36 inference(ennf_transformation,[status(thm)],[f15])).
% 1.57/1.36 thf(f15,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) => (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.57/1.36 inference(fool_elimination,[status(thm)],[f14])).
% 1.57/1.36 thf(f14,plain,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.57/1.36 inference(rectify,[status(thm)],[f3])).
% 1.57/1.36 thf(f3,axiom,(
% 1.57/1.36 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.57/1.36 file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/FINITE_SUBSET_')).
% 1.57/1.36 thf(f24,plain,(
% 1.57/1.36 (('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real') != $true)),
% 1.57/1.36 inference(cnf_transformation,[status(thm)],[f20])).
% 1.57/1.36 thf(f20,plain,(
% 1.57/1.36 (('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real') != $true)),
% 1.57/1.36 inference(flattening,[status(thm)],[f17])).
% 1.57/1.36 thf(f17,plain,(
% 1.57/1.36 ~(('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real') = $true)),
% 1.57/1.36 inference(fool_elimination,[status(thm)],[f16])).
% 1.57/1.36 thf(f16,plain,(
% 1.57/1.36 ~('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real')),
% 1.57/1.36 inference(rectify,[status(thm)],[f6])).
% 1.57/1.36 thf(f6,negated_conjecture,(
% 1.57/1.36 ~('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real')),
% 1.57/1.36 inference(negated_conjecture,[status(cth)],[f5])).
% 1.57/1.36 thf(f5,conjecture,(
% 1.57/1.36 ('const/sets/INFINITE' @ 'type/realax/real' @ 'const/sets/UNIV' @ 'type/realax/real')),
% 1.57/1.36 file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/real_INFINITE_')).
% 1.57/1.36 thf(f26,plain,(
% 1.57/1.36 ( ! [X0 : 'type/realax/real'] : ((('const/sets/FINITE' @ 'type/realax/real' @ ('const/sets/GSPEC' @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ('const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ('const/realax/real_le' @ X0 @ Y1) @ Y1)))))) != $true)) )),
% 1.57/1.36 inference(cnf_transformation,[status(thm)],[f19])).
% 1.57/1.36 thf(f19,plain,(
% 1.57/1.36 ! [X0 : 'type/realax/real'] : (('const/sets/FINITE' @ 'type/realax/real' @ ('const/sets/GSPEC' @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ('const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ('const/realax/real_le' @ X0 @ Y1) @ Y1)))))) != $true)),
% 1.57/1.36 inference(flattening,[status(thm)],[f13])).
% 1.57/1.36 thf(f13,plain,(
% 1.57/1.36 ! [X0 : 'type/realax/real'] : ~(('const/sets/FINITE' @ 'type/realax/real' @ ('const/sets/GSPEC' @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ('const/sets/SETSPEC' @ 'type/realax/real' @ Y0 @ ('const/realax/real_le' @ X0 @ Y1) @ Y1)))))) = $true)),
% 1.57/1.36 inference(fool_elimination,[status(thm)],[f12])).
% 1.57/1.36 thf(f12,plain,(
% 1.57/1.36 ! [X0 : 'type/realax/real'] : ~('const/sets/FINITE' @ 'type/realax/real' @ ('const/sets/GSPEC' @ 'type/realax/real' @ (^[X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ('const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ('const/realax/real_le' @ X0 @ X2) @ X2)))))),
% 1.57/1.36 inference(rectify,[status(thm)],[f1])).
% 1.57/1.36 thf(f1,axiom,(
% 1.57/1.36 ! [X0 : 'type/realax/real'] : ~('const/sets/FINITE' @ 'type/realax/real' @ ('const/sets/GSPEC' @ 'type/realax/real' @ (^[X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ('const/sets/SETSPEC' @ 'type/realax/real' @ X1 @ ('const/realax/real_le' @ X0 @ X2) @ X2)))))),
% 1.57/1.36 file('/export/starexec/sandbox/tmp/tmp.77IOBmYOUD/DTF2THF_4714.p','thm/sets/FINITE_REAL_INTERVAL_1')).
% 1.57/1.36 % SZS output end Proof for DTF2THF_4714
% 1.57/1.36 % (4818)------------------------------
% 1.57/1.36 % (4818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (4818)Termination reason: Refutation
% 1.57/1.36
% 1.57/1.36 % (4818)Memory used [KB]: 5500
% 1.57/1.36 % (4818)Time elapsed: 0.006 s
% 1.57/1.36 % (4818)Instructions burned: 5 (million)
% 1.57/1.36 % (4818)------------------------------
% 1.57/1.36 % (4818)------------------------------
% 1.57/1.36 % (4811)Success in time 0.02 s
%------------------------------------------------------------------------------