%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV485^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:41:21 AM UTC 2026
% Result : Theorem 1.82s 1.52s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 105 ( 5 ~; 3 |; 5 &; 92 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
'const/sets/HAS_SIZE':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/nums/BIT0': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_8,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f31,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f30,f15]) ).
thf(f15,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
!= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o,
file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/FINITE_BOOL_') ).
thf(f30,plain,
( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( 'const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f18,f14]) ).
thf(f14,plain,
( ( 'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( 'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
'const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/HAS_SIZE_BOOL_') ).
thf(f18,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( $true
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/HAS_SIZE_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV485^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.36 % Computer : n029.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Tue Feb 24 12:47:59 EST 2026
% 0.18/0.36 % CPUTime :
% 0.18/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEV485^1 : TPTP v9.2.1. Released v7.0.0.
% 0.27/0.47 % Domain : Analysis
% 0.27/0.47 % Problem : FINITE_BOOL
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Kal16]
% 0.27/0.47 % Names : FINITE_BOOL_.p [Kal16]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v7.1.0
% 0.27/0.47 % Syntax : Number of formulae : 12 ( 1 unt; 9 typ; 0 def)
% 0.27/0.47 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.27/0.47 % Number of connectives : 18 ( 0 ~; 0 |; 1 &; 17 @)
% 0.27/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 5 ( 4 avg)
% 0.27/0.47 % Number of types : 2 ( 1 usr)
% 0.27/0.47 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 9 ( 8 usr; 1 con; 0-3 aty)
% 0.27/0.47 % Number of variables : 7 ( 0 ^; 3 !; 0 ?; 7 :)
% 0.27/0.47 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.47 % SPC : TH1_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : Exported from core HOL Light.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf('thf_type_type/nums/num',type,
% 0.27/0.47 'type/nums/num': $tType ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/UNIV',type,
% 0.27/0.47 'const/sets/UNIV':
% 0.27/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/HAS_SIZE',type,
% 0.27/0.47 'const/sets/HAS_SIZE':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/FINITE',type,
% 0.27/0.47 'const/sets/FINITE':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/sets/CARD',type,
% 0.27/0.47 'const/sets/CARD':
% 0.27/0.47 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/nums/NUMERAL',type,
% 0.27/0.47 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/nums/BIT1',type,
% 0.27/0.47 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/nums/BIT0',type,
% 0.27/0.47 'const/nums/BIT0': 'type/nums/num' > 'type/nums/num' ).
% 0.27/0.47
% 0.27/0.47 thf('thf_const_const/nums/_0',type,
% 0.27/0.47 'const/nums/_0': 'type/nums/num' ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/HAS_SIZE_',axiom,
% 0.27/0.47 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 0.27/0.47 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 0.27/0.47 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.27/0.47 & ( ( 'const/sets/CARD' @ A @ A0 )
% 0.27/0.47 = A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/HAS_SIZE_BOOL_',axiom,
% 0.27/0.47 'const/sets/HAS_SIZE' @ $o @ ( 'const/sets/UNIV' @ $o ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf('thm/sets/FINITE_BOOL_',conjecture,
% 0.27/0.47 'const/sets/FINITE' @ $o @ ( 'const/sets/UNIV' @ $o ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.63/1.49 ---- Embedded in THF ---
% 1.63/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.49 %%% Generated on Tue Feb 24 12:48:00 EST 2026
% 1.63/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.49 %%% Logic specification used:
% 1.63/1.49 %%% thf(spec, logic, $$dhol).
% 1.63/1.49
% 1.63/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2DTF6524.p
% See solution above
% 1.63/1.49 ------------------------
% 1.82/1.50 ---- Cleaned THF ---
% 1.82/1.50 thf('thf_type_type/nums/num',type,
% 1.82/1.50 'type/nums/num': $tType ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/sets/UNIV',type,
% 1.82/1.50 'const/sets/UNIV':
% 1.82/1.50 !>[A: $tType] : ( A > $o ) ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/sets/HAS_SIZE',type,
% 1.82/1.50 'const/sets/HAS_SIZE':
% 1.82/1.50 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/sets/FINITE',type,
% 1.82/1.50 'const/sets/FINITE':
% 1.82/1.50 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/sets/CARD',type,
% 1.82/1.50 'const/sets/CARD':
% 1.82/1.50 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/nums/NUMERAL',type,
% 1.82/1.50 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/nums/BIT1',type,
% 1.82/1.50 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/nums/BIT0',type,
% 1.82/1.50 'const/nums/BIT0': 'type/nums/num' > 'type/nums/num' ).
% 1.82/1.50
% 1.82/1.50 thf('thf_const_const/nums/_0',type,
% 1.82/1.50 'const/nums/_0': 'type/nums/num' ).
% 1.82/1.50
% 1.82/1.50 thf('thm/sets/HAS_SIZE_',axiom,
% 1.82/1.50 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 1.82/1.50 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 1.82/1.50 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.82/1.50 & ( ( 'const/sets/CARD' @ A @ A0 )
% 1.82/1.50 = A1 ) ) ) ).
% 1.82/1.50
% 1.82/1.50 thf('thm/sets/HAS_SIZE_BOOL_',axiom,
% 1.82/1.50 'const/sets/HAS_SIZE' @ $o @ ( 'const/sets/UNIV' @ $o ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) ).
% 1.82/1.50
% 1.82/1.50 thf('thm/sets/FINITE_BOOL_',conjecture,
% 1.82/1.50 'const/sets/FINITE' @ $o @ ( 'const/sets/UNIV' @ $o ) ).
% 1.82/1.50 ------------------------
% 1.82/1.52 % (6621)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6524 for (3000ds/183Mi)
% 1.82/1.52 % (6625)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_6524 for (3000ds/2Mi)
% 1.82/1.52 % (6623)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_6524 for (3000ds/27Mi)
% 1.82/1.52 % (6627)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6524 for (3000ds/18Mi)
% 1.82/1.52 % (6626)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_6524 for (3000ds/275Mi)
% 1.82/1.52 % (6624)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6524 for (3000ds/2Mi)
% 1.82/1.52 % (6626)Refutation not found, incomplete strategy
% 1.82/1.52 % (6626)------------------------------
% 1.82/1.52 % (6626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (6626)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.52
% 1.82/1.52
% 1.82/1.52 % (6626)Memory used [KB]: 5373
% 1.82/1.52 % (6626)Time elapsed: 0.002 s
% 1.82/1.52 % (6626)Instructions burned: 1 (million)
% 1.82/1.52 % (6626)------------------------------
% 1.82/1.52 % (6626)------------------------------
% 1.82/1.52 % (6622)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_6524 for (3000ds/4Mi)
% 1.82/1.52 % (6625)Refutation not found, incomplete strategy
% 1.82/1.52 % (6625)------------------------------
% 1.82/1.52 % (6625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (6624)Instruction limit reached!
% 1.82/1.52 % (6624)------------------------------
% 1.82/1.52 % (6624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (6624)Termination reason: Unknown
% 1.82/1.52 % (6625)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.52
% 1.82/1.52
% 1.82/1.52 % (6624)Termination phase: Saturation
% 1.82/1.52
% 1.82/1.52 % (6625)Memory used [KB]: 5500
% 1.82/1.52 % (6624)Memory used [KB]: 5500
% 1.82/1.52 % (6625)Time elapsed: 0.002 s
% 1.82/1.52 % (6624)Time elapsed: 0.003 s
% 1.82/1.52 % (6625)Instructions burned: 1 (million)
% 1.82/1.52 % (6624)Instructions burned: 2 (million)
% 1.82/1.52 % (6625)------------------------------
% 1.82/1.52 % (6625)------------------------------
% 1.82/1.52 % (6624)------------------------------
% 1.82/1.52 % (6624)------------------------------
% 1.82/1.52 % (6621)First to succeed.
% 1.82/1.52 % (6623)Also succeeded, but the first one will report.
% 1.82/1.52 % (6621)Refutation found. Thanks to Tanya!
% 1.82/1.52 % SZS status Theorem for DTF2THF_6524
% 1.82/1.52 % SZS output start Proof for DTF2THF_6524
% 1.82/1.52 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.82/1.52 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.82/1.52 thf(func_def_1, type, 'const/sets/UNIV': !>[X0: $tType]:(X0 > $o)).
% 1.82/1.52 thf(func_def_2, type, 'const/sets/HAS_SIZE': !>[X0: $tType]:((X0 > $o) > 'type/nums/num' > $o)).
% 1.82/1.52 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.82/1.52 thf(func_def_4, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.82/1.52 thf(func_def_5, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.82/1.52 thf(func_def_6, type, 'const/nums/BIT1': 'type/nums/num' > 'type/nums/num').
% 1.82/1.52 thf(func_def_7, type, 'const/nums/BIT0': 'type/nums/num' > 'type/nums/num').
% 1.82/1.52 thf(func_def_8, type, 'const/nums/_0': 'type/nums/num').
% 1.82/1.52 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.82/1.52 thf(f31,plain,(
% 1.82/1.52 $false),
% 1.82/1.52 inference(subsumption_resolution,[status(thm)],[f30,f15])).
% 1.82/1.52 thf(f15,plain,(
% 1.82/1.52 (('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o) != $true)),
% 1.82/1.52 inference(cnf_transformation,[status(thm)],[f12])).
% 1.82/1.52 thf(f12,plain,(
% 1.82/1.52 (('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o) != $true)),
% 1.82/1.52 inference(flattening,[status(thm)],[f7])).
% 1.82/1.52 thf(f7,plain,(
% 1.82/1.52 ~(('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o) = $true)),
% 1.82/1.52 inference(fool_elimination,[status(thm)],[f6])).
% 1.82/1.52 thf(f6,plain,(
% 1.82/1.52 ~('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o)),
% 1.82/1.52 inference(rectify,[status(thm)],[f4])).
% 1.82/1.52 thf(f4,negated_conjecture,(
% 1.82/1.52 ~('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o)),
% 1.82/1.52 inference(negated_conjecture,[status(cth)],[f3])).
% 1.82/1.52 thf(f3,conjecture,(
% 1.82/1.52 ('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o)),
% 1.82/1.52 file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/FINITE_BOOL_')).
% 1.82/1.52 thf(f30,plain,(
% 1.82/1.52 (('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o) = $true)),
% 1.82/1.52 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.82/1.52 thf(f26,plain,(
% 1.82/1.52 (('const/sets/FINITE' @ $o @ 'const/sets/UNIV' @ $o) = $true) | ($false = $true)),
% 1.82/1.52 inference(superposition,[status(thm)],[f18,f14])).
% 1.82/1.52 thf(f14,plain,(
% 1.82/1.52 (('const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ('const/nums/NUMERAL' @ ('const/nums/BIT0' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = $true)),
% 1.82/1.52 inference(cnf_transformation,[status(thm)],[f9])).
% 1.82/1.52 thf(f9,plain,(
% 1.82/1.52 (('const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ('const/nums/NUMERAL' @ ('const/nums/BIT0' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = $true)),
% 1.82/1.52 inference(fool_elimination,[status(thm)],[f8])).
% 1.82/1.52 thf(f8,plain,(
% 1.82/1.52 ('const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ('const/nums/NUMERAL' @ ('const/nums/BIT0' @ ('const/nums/BIT1' @ 'const/nums/_0'))))),
% 1.82/1.52 inference(rectify,[status(thm)],[f2])).
% 1.82/1.52 thf(f2,axiom,(
% 1.82/1.52 ('const/sets/HAS_SIZE' @ $o @ 'const/sets/UNIV' @ $o @ ('const/nums/NUMERAL' @ ('const/nums/BIT0' @ ('const/nums/BIT1' @ 'const/nums/_0'))))),
% 1.82/1.52 file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/HAS_SIZE_BOOL_')).
% 1.82/1.52 thf(f18,plain,(
% 1.82/1.52 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $false) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.82/1.52 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.82/1.52 thf(f17,plain,(
% 1.82/1.52 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : (($true = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1))) | (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $false)) )),
% 1.82/1.52 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.82/1.52 thf(f13,plain,(
% 1.82/1.52 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1)))) )),
% 1.82/1.52 inference(cnf_transformation,[status(thm)],[f11])).
% 1.82/1.52 thf(f11,plain,(
% 1.82/1.52 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1)))),
% 1.82/1.52 inference(fool_elimination,[status(thm)],[f10])).
% 1.82/1.52 thf(f10,plain,(
% 1.82/1.52 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2) = ('const/sets/HAS_SIZE' @ X0 @ X1 @ X2))),
% 1.82/1.52 inference(rectify,[status(thm)],[f1])).
% 1.82/1.52 thf(f1,axiom,(
% 1.82/1.52 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2) = ('const/sets/HAS_SIZE' @ X0 @ X1 @ X2))),
% 1.82/1.52 file('/export/starexec/sandbox2/tmp/tmp.utNar50f9c/DTF2THF_6524.p','thm/sets/HAS_SIZE_')).
% 1.82/1.52 % SZS output end Proof for DTF2THF_6524
% 1.82/1.52 % (6621)------------------------------
% 1.82/1.52 % (6621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (6621)Termination reason: Refutation
% 1.82/1.52
% 1.82/1.52 % (6621)Memory used [KB]: 5500
% 1.82/1.52 % (6621)Time elapsed: 0.004 s
% 1.82/1.52 % (6621)Instructions burned: 2 (million)
% 1.82/1.52 % (6621)------------------------------
% 1.82/1.52 % (6621)------------------------------
% 1.82/1.52 % (6620)Success in time 0.018 s
%------------------------------------------------------------------------------