%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV476^1 : 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 : n008.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 09:41:20 AM UTC 2026
% Result : Theorem 1.83s 1.54s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 197 ( 19 ~; 10 |; 7 &; 153 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 56 ( 0 ^; 50 !; 6 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK1: sK0 > $o ).
thf(func_def_8,type,
sK2: sK0 > $o ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
$true != $true,
inference(superposition,[status(thm)],[f20,f24]) ).
thf(f24,plain,
! [X0: sK0 > $o] :
( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: sK0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f22,f19]) ).
thf(f19,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) )
=> ( ( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
=> ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2THF_29178.p','thm/sets/FINITE_DIFF_') ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f17]) ).
thf(f17,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2THF_29178.p','thm/sets/SUBSET_DIFF_') ).
thf(f18,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,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)],[f11]) ).
thf(f11,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)],[f10]) ).
thf(f10,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)],[f2]) ).
thf(f2,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.5F96JIXiq9/DTF2THF_29178.p','thm/sets/FINITE_SUBSET_') ).
thf(f20,plain,
( ( 'const/sets/FINITE' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV476^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n008.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 12:47:39 EST 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : SEV476^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.47 % Domain : Analysis
% 0.18/0.47 % Problem : FINITE_DIFF
% 0.18/0.47 % Version : Especial.
% 0.18/0.47 % English :
% 0.18/0.47
% 0.18/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.47 % Source : [Kal16]
% 0.18/0.47 % Names : FINITE_DIFF_.p [Kal16]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : 0.00 v7.1.0
% 0.18/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 3 typ; 0 def)
% 0.18/0.47 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.18/0.47 % Maximal formula atoms : 3 ( 2 avg)
% 0.18/0.47 % Number of connectives : 23 ( 0 ~; 0 |; 1 &; 20 @)
% 0.18/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.47 % Number of types : 1 ( 0 usr)
% 0.18/0.47 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 3 ( 3 usr; 0 con; 2-4 aty)
% 0.18/0.47 % Number of variables : 12 ( 0 ^; 9 !; 0 ?; 12 :)
% 0.18/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.47 % SPC : TH1_THM_NEQ_NAR
% 0.18/0.47
% 0.18/0.47 % Comments : Exported from core HOL Light.
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 thf('thf_const_const/sets/SUBSET',type,
% 0.18/0.47 'const/sets/SUBSET':
% 0.18/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.18/0.47
% 0.18/0.47 thf('thf_const_const/sets/FINITE',type,
% 0.18/0.47 'const/sets/FINITE':
% 0.18/0.47 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.18/0.47
% 0.18/0.47 thf('thf_const_const/sets/DIFF',type,
% 0.18/0.47 'const/sets/DIFF':
% 0.18/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.18/0.47
% 0.18/0.47 thf('thm/sets/SUBSET_DIFF_',axiom,
% 0.18/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) @ A0 ) ).
% 0.18/0.47
% 0.18/0.47 thf('thm/sets/FINITE_SUBSET_',axiom,
% 0.18/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.47 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.18/0.47 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 0.18/0.47 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf('thm/sets/FINITE_DIFF_',conjecture,
% 0.18/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.47 ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.18/0.47 => ( 'const/sets/FINITE' @ A @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) ) ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 1.83/1.51 ---- Embedded in THF ---
% 1.83/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.83/1.51 %%% Generated on Tue Feb 24 12:47:40 EST 2026
% 1.83/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 1.83/1.51 %%% Logic specification used:
% 1.83/1.51 %%% thf(spec, logic, $$dhol).
% 1.83/1.51
% 1.83/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2DTF29178.p
% See solution above
% 1.83/1.51 ------------------------
% 1.83/1.52 ---- Cleaned THF ---
% 1.83/1.52 thf('thf_const_const/sets/SUBSET',type,
% 1.83/1.52 'const/sets/SUBSET':
% 1.83/1.52 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.83/1.52
% 1.83/1.52 thf('thf_const_const/sets/FINITE',type,
% 1.83/1.52 'const/sets/FINITE':
% 1.83/1.52 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.83/1.52
% 1.83/1.52 thf('thf_const_const/sets/DIFF',type,
% 1.83/1.52 'const/sets/DIFF':
% 1.83/1.52 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.83/1.52
% 1.83/1.52 thf('thm/sets/SUBSET_DIFF_',axiom,
% 1.83/1.52 ! [A: $tType,A0: A > $o,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) @ A0 ) ).
% 1.83/1.52
% 1.83/1.52 thf('thm/sets/FINITE_SUBSET_',axiom,
% 1.83/1.52 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.83/1.52 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.83/1.52 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 1.83/1.52 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 1.83/1.52
% 1.83/1.52 thf('thm/sets/FINITE_DIFF_',conjecture,
% 1.83/1.52 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.83/1.52 ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.83/1.52 => ( 'const/sets/FINITE' @ A @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) ) ) ).
% 1.83/1.52 ------------------------
% 1.83/1.54 % (29296)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29178 for (2999ds/18Mi)
% 1.83/1.54 % (29294)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_29178 for (2999ds/2Mi)
% 1.83/1.54 % (29292)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_29178 for (2999ds/27Mi)
% 1.83/1.54 % (29291)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_29178 for (2999ds/4Mi)
% 1.83/1.54 % (29295)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_29178 for (2999ds/275Mi)
% 1.83/1.54 % (29290)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29178 for (2999ds/183Mi)
% 1.83/1.54 % (29293)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29178 for (2999ds/2Mi)
% 1.83/1.54 % (29294)Instruction limit reached!
% 1.83/1.54 % (29294)------------------------------
% 1.83/1.54 % (29294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (29294)Termination reason: Unknown
% 1.83/1.54 % (29294)Termination phase: shuffling
% 1.83/1.54
% 1.83/1.54 % (29294)Memory used [KB]: 895
% 1.83/1.54 % (29294)Time elapsed: 0.003 s
% 1.83/1.54 % (29294)Instructions burned: 2 (million)
% 1.83/1.54 % (29294)------------------------------
% 1.83/1.54 % (29294)------------------------------
% 1.83/1.54 % (29295)Refutation not found, incomplete strategy
% 1.83/1.54 % (29295)------------------------------
% 1.83/1.54 % (29295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (29295)Termination reason: Refutation not found, incomplete strategy
% 1.83/1.54
% 1.83/1.54
% 1.83/1.54 % (29295)Memory used [KB]: 5500
% 1.83/1.54 % (29295)Time elapsed: 0.003 s
% 1.83/1.54 % (29295)Instructions burned: 2 (million)
% 1.83/1.54 % (29295)------------------------------
% 1.83/1.54 % (29295)------------------------------
% 1.83/1.54 % (29293)Instruction limit reached!
% 1.83/1.54 % (29293)------------------------------
% 1.83/1.54 % (29293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (29293)Termination reason: Unknown
% 1.83/1.54 % (29293)Termination phase: Saturation
% 1.83/1.54
% 1.83/1.54 % (29293)Memory used [KB]: 5500
% 1.83/1.54 % (29293)Time elapsed: 0.003 s
% 1.83/1.54 % (29293)Instructions burned: 2 (million)
% 1.83/1.54 % (29293)------------------------------
% 1.83/1.54 % (29293)------------------------------
% 1.83/1.54 % (29291)Instruction limit reached!
% 1.83/1.54 % (29291)------------------------------
% 1.83/1.54 % (29291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (29291)Termination reason: Unknown
% 1.83/1.54 % (29291)Termination phase: Saturation
% 1.83/1.54 % (29292)First to succeed.
% 1.83/1.54
% 1.83/1.54 % (29291)Memory used [KB]: 5500
% 1.83/1.54 % (29291)Time elapsed: 0.005 s
% 1.83/1.54 % (29291)Instructions burned: 4 (million)
% 1.83/1.54 % (29291)------------------------------
% 1.83/1.54 % (29291)------------------------------
% 1.83/1.54 % (29292)Refutation found. Thanks to Tanya!
% 1.83/1.54 % SZS status Theorem for DTF2THF_29178
% 1.83/1.54 % SZS output start Proof for DTF2THF_29178
% 1.83/1.54 thf(type_def_6, type, sK0: $tType).
% 1.83/1.54 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.83/1.54 thf(func_def_1, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.83/1.54 thf(func_def_2, type, 'const/sets/DIFF': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.83/1.54 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.83/1.54 thf(func_def_7, type, sK1: sK0 > $o).
% 1.83/1.54 thf(func_def_8, type, sK2: sK0 > $o).
% 1.83/1.54 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 1.83/1.54 thf(f28,plain,(
% 1.83/1.54 $false),
% 1.83/1.54 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.83/1.54 thf(f25,plain,(
% 1.83/1.54 ($true != $true)),
% 1.83/1.54 inference(superposition,[status(thm)],[f20,f24])).
% 1.83/1.54 thf(f24,plain,(
% 1.83/1.54 ( ! [X0 : sK0 > $o] : ((('const/sets/FINITE' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ X0)) = $true)) )),
% 1.83/1.54 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.83/1.54 thf(f23,plain,(
% 1.83/1.54 ( ! [X0 : sK0 > $o] : (($true != $true) | (('const/sets/FINITE' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ X0)) = $true)) )),
% 1.83/1.54 inference(superposition,[status(thm)],[f22,f19])).
% 1.83/1.54 thf(f19,plain,(
% 1.83/1.54 (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 1.83/1.54 inference(cnf_transformation,[status(thm)],[f16])).
% 1.83/1.54 thf(f16,plain,(
% 1.83/1.54 (('const/sets/FINITE' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2)) != $true) & (('const/sets/FINITE' @ sK0 @ sK1) = $true)),
% 1.83/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.83/1.54 thf(f15,plain,(
% 1.83/1.54 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) != $true) & (('const/sets/FINITE' @ X0 @ X1) = $true)) => ((('const/sets/FINITE' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2)) != $true) & (('const/sets/FINITE' @ sK0 @ sK1) = $true))),
% 1.83/1.54 introduced(definition,[],[choice_axiom])).
% 1.83/1.54 thf(f14,plain,(
% 1.83/1.54 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) != $true) & (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.83/1.54 inference(ennf_transformation,[status(thm)],[f7])).
% 1.83/1.54 thf(f7,plain,(
% 1.83/1.54 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) => (('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true))),
% 1.83/1.54 inference(fool_elimination,[status(thm)],[f6])).
% 1.83/1.54 thf(f6,plain,(
% 1.83/1.54 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)))),
% 1.83/1.54 inference(rectify,[status(thm)],[f4])).
% 1.83/1.54 thf(f4,negated_conjecture,(
% 1.83/1.54 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)))),
% 1.83/1.54 inference(negated_conjecture,[status(cth)],[f3])).
% 1.83/1.54 thf(f3,conjecture,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)))),
% 1.83/1.54 file('/export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2THF_29178.p','thm/sets/FINITE_DIFF_')).
% 1.83/1.54 thf(f22,plain,(
% 1.83/1.54 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true)) )),
% 1.83/1.54 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.83/1.54 thf(f21,plain,(
% 1.83/1.54 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) | (('const/sets/FINITE' @ X0 @ X1) != $true) | ($true != $true)) )),
% 1.83/1.54 inference(superposition,[status(thm)],[f18,f17])).
% 1.83/1.54 thf(f17,plain,(
% 1.83/1.54 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X1) = $true)) )),
% 1.83/1.54 inference(cnf_transformation,[status(thm)],[f9])).
% 1.83/1.54 thf(f9,plain,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X1) = $true)),
% 1.83/1.54 inference(fool_elimination,[status(thm)],[f8])).
% 1.83/1.54 thf(f8,plain,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X1)),
% 1.83/1.54 inference(rectify,[status(thm)],[f1])).
% 1.83/1.54 thf(f1,axiom,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X1)),
% 1.83/1.54 file('/export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2THF_29178.p','thm/sets/SUBSET_DIFF_')).
% 1.83/1.54 thf(f18,plain,(
% 1.83/1.54 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.83/1.54 inference(cnf_transformation,[status(thm)],[f13])).
% 1.83/1.54 thf(f13,plain,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.83/1.54 inference(flattening,[status(thm)],[f12])).
% 1.83/1.54 thf(f12,plain,(
% 1.83/1.54 ! [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)))),
% 1.83/1.54 inference(ennf_transformation,[status(thm)],[f11])).
% 1.83/1.54 thf(f11,plain,(
% 1.83/1.54 ! [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))),
% 1.83/1.54 inference(fool_elimination,[status(thm)],[f10])).
% 1.83/1.54 thf(f10,plain,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.83/1.54 inference(rectify,[status(thm)],[f2])).
% 1.83/1.54 thf(f2,axiom,(
% 1.83/1.54 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.83/1.54 file('/export/starexec/sandbox/tmp/tmp.5F96JIXiq9/DTF2THF_29178.p','thm/sets/FINITE_SUBSET_')).
% 1.83/1.54 thf(f20,plain,(
% 1.83/1.54 (('const/sets/FINITE' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2)) != $true)),
% 1.83/1.54 inference(cnf_transformation,[status(thm)],[f16])).
% 1.83/1.54 % SZS output end Proof for DTF2THF_29178
% 1.83/1.54 % (29292)------------------------------
% 1.83/1.54 % (29292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.83/1.54 % (29292)Termination reason: Refutation
% 1.83/1.54
% 1.83/1.54 % (29292)Memory used [KB]: 5500
% 1.83/1.54 % (29292)Time elapsed: 0.005 s
% 1.83/1.54 % (29292)Instructions burned: 2 (million)
% 1.83/1.54 % (29292)------------------------------
% 1.83/1.54 % (29292)------------------------------
% 1.83/1.54 % (29289)Success in time 0.019 s
%------------------------------------------------------------------------------