%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV451^1 : 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 : 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 09:41:16 AM UTC 2026
% Result : Theorem 1.58s 1.33s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 187 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 244 ( 17 ~; 26 |; 0 &; 198 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 67 ( 0 ^; 63 !; 4 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK1: sK0 > $o ).
thf(func_def_14,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK5: sK0 ).
thf(f146,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f69,f136,f145]) ).
thf(f145,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f144]) ).
thf(f144,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $false = $true )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f47,f68]) ).
thf(f68,plain,
( ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl2_4
<=> ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f47,plain,
! [X0: $tType,X1: X0] :
( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0] :
( ( $true
= ( 'const/sets/UNIV' @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f23,f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_UNIV_') ).
thf(f23,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( X1 @ X2 )
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_') ).
thf(f136,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f132,f62,f66]) ).
thf(f62,definition,
( spl2_3
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f132,plain,
( ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ( $false = $true )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f120,f24]) ).
thf(f24,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) )
| ( $false
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f120,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false = $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0 ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f114,f64]) ).
thf(f64,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f114,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( $true
= ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X3 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f28,f23]) ).
thf(f28,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X1 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
| ( 'const/sets/IN' @ X0 @ X4 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_UNION_') ).
thf(f69,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f51,f66,f62]) ).
thf(f51,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) )
| ( $false
= ( 'const/sets/UNIV' @ sK0 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( 'const/sets/UNIV' @ sK0 @ sK5 )
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f22]) ).
thf(f22,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
!= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) )
=> ( 'const/sets/UNIV'
@ ( sK0
!= ( 'const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
!= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > $o] :
( 'const/sets/UNIV'
@ ( X0
= ( 'const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/UNION_UNIV_1') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEV451^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n029.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 12:47:14 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEV451^1 : TPTP v9.2.1. Released v7.0.0.
% 0.26/0.47 % Domain : Analysis
% 0.26/0.47 % Problem : UNION_UNIV_
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English :
% 0.26/0.47
% 0.26/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Kal16]
% 0.26/0.47 % Names : UNION_UNIV_1.p [Kal16]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.00 v7.1.0
% 0.26/0.47 % Syntax : Number of formulae : 8 ( 4 unt; 3 typ; 0 def)
% 0.26/0.47 % Number of atoms : 18 ( 6 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 2 ( 3 avg)
% 0.26/0.47 % Number of connectives : 32 ( 0 ~; 1 |; 0 &; 31 @)
% 0.26/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 6 ( 4 avg)
% 0.26/0.47 % Number of types : 1 ( 0 usr)
% 0.26/0.47 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% 0.26/0.47 % Number of variables : 18 ( 0 ^; 15 !; 0 ?; 18 :)
% 0.26/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.47 % SPC : TH1_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : Exported from core HOL Light.
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf('thf_const_const/sets/UNIV',type,
% 0.26/0.47 'const/sets/UNIV':
% 0.26/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/UNION',type,
% 0.26/0.47 'const/sets/UNION':
% 0.26/0.47 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thf_const_const/sets/IN',type,
% 0.26/0.47 'const/sets/IN':
% 0.26/0.47 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/IN_UNIV_',axiom,
% 0.26/0.47 ! [A: $tType,A0: A] : ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/IN_',axiom,
% 0.26/0.47 ! [A: $tType,P: A > $o,A0: A] :
% 0.26/0.47 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.26/0.47 = ( P @ A0 ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/IN_UNION_',axiom,
% 0.26/0.47 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 0.26/0.47 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) )
% 0.26/0.47 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.26/0.47 | ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/EXTENSION_',axiom,
% 0.26/0.47 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.26/0.47 ( ( A0 = A1 )
% 0.26/0.47 = ( ! [A2: A] :
% 0.26/0.47 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.26/0.47 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf('thm/sets/UNION_UNIV_1',conjecture,
% 0.26/0.47 ! [A: $tType,A0: A > $o] :
% 0.26/0.47 ( ( 'const/sets/UNION' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) )
% 0.26/0.47 = ( 'const/sets/UNIV' @ A ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.43/1.27 ---- Embedded in THF ---
% 1.43/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.27 %%% Generated on Tue Feb 24 12:47:15 EST 2026
% 1.43/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.27 %%% Logic specification used:
% 1.43/1.27 %%% thf(spec, logic, $$dhol).
% 1.43/1.27
% 1.43/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2DTF2370.p
% See solution above
% 1.43/1.27 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.29 thf('thf_const_const/sets/UNIV',type,
% 1.43/1.29 'const/sets/UNIV':
% 1.43/1.29 !>[A: $tType] : ( A > $o ) ).
% 1.43/1.29
% 1.43/1.29 thf('thf_const_const/sets/UNION',type,
% 1.43/1.29 'const/sets/UNION':
% 1.43/1.29 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.43/1.29
% 1.43/1.29 thf('thf_const_const/sets/IN',type,
% 1.43/1.29 'const/sets/IN':
% 1.43/1.29 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.43/1.29
% 1.43/1.29 thf('thm/sets/IN_UNIV_',axiom,
% 1.43/1.29 ! [A: $tType,A0: A] : ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 1.43/1.29
% 1.43/1.29 thf('thm/sets/IN_',axiom,
% 1.43/1.29 ! [A: $tType,P: A > $o,A0: A] :
% 1.43/1.29 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.43/1.29 = ( P @ A0 ) ) ).
% 1.43/1.29
% 1.43/1.29 thf('thm/sets/IN_UNION_',axiom,
% 1.43/1.29 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 1.43/1.29 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) )
% 1.43/1.29 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.43/1.29 | ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 1.43/1.29
% 1.43/1.29 thf('thm/sets/EXTENSION_',axiom,
% 1.43/1.29 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.43/1.29 ( ( A0 = A1 )
% 1.43/1.29 = ( ! [A2: A] :
% 1.43/1.29 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.43/1.29 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.43/1.29
% 1.43/1.29 thf('thm/sets/UNION_UNIV_1',conjecture,
% 1.43/1.29 ! [A: $tType,A0: A > $o] :
% 1.43/1.29 ( ( 'const/sets/UNION' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) )
% 1.43/1.29 = ( 'const/sets/UNIV' @ A ) ) ).
% 1.43/1.29 ------------------------
% 1.58/1.30 % (2467)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/183Mi)
% 1.58/1.31 % (2472)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_2370 for (2999ds/275Mi)
% 1.58/1.31 % (2473)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/18Mi)
% 1.58/1.31 % (2472)Refutation not found, incomplete strategy
% 1.58/1.31 % (2472)------------------------------
% 1.58/1.31 % (2472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (2472)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.31
% 1.58/1.31
% 1.58/1.31 % (2472)Memory used [KB]: 5500
% 1.58/1.31 % (2472)Time elapsed: 0.004 s
% 1.58/1.31 % (2472)Instructions burned: 4 (million)
% 1.58/1.31 % (2472)------------------------------
% 1.58/1.31 % (2472)------------------------------
% 1.58/1.32 % (2470)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/2Mi)
% 1.58/1.32 % (2468)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_2370 for (2999ds/4Mi)
% 1.58/1.32 % (2470)Instruction limit reached!
% 1.58/1.32 % (2470)------------------------------
% 1.58/1.32 % (2470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (2470)Termination reason: Unknown
% 1.58/1.32 % (2470)Termination phase: Property scanning
% 1.58/1.32
% 1.58/1.32 % (2470)Memory used [KB]: 895
% 1.58/1.32 % (2470)Time elapsed: 0.002 s
% 1.58/1.32 % (2470)Instructions burned: 2 (million)
% 1.58/1.32 % (2470)------------------------------
% 1.58/1.32 % (2470)------------------------------
% 1.58/1.32 % (2473)Instruction limit reached!
% 1.58/1.32 % (2473)------------------------------
% 1.58/1.32 % (2473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (2473)Termination reason: Unknown
% 1.58/1.32 % (2473)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (2473)Memory used [KB]: 5628
% 1.58/1.32 % (2473)Time elapsed: 0.012 s
% 1.58/1.32 % (2473)Instructions burned: 18 (million)
% 1.58/1.32 % (2473)------------------------------
% 1.58/1.32 % (2473)------------------------------
% 1.58/1.32 % (2471)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_2370 for (2999ds/2Mi)
% 1.58/1.32 % (2471)Instruction limit reached!
% 1.58/1.32 % (2471)------------------------------
% 1.58/1.32 % (2471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (2471)Termination reason: Unknown
% 1.58/1.32 % (2471)Termination phase: shuffling
% 1.58/1.32
% 1.58/1.32 % (2471)Memory used [KB]: 895
% 1.58/1.32 % (2471)Time elapsed: 0.002 s
% 1.58/1.32 % (2471)Instructions burned: 2 (million)
% 1.58/1.32 % (2471)------------------------------
% 1.58/1.32 % (2471)------------------------------
% 1.58/1.32 % (2468)Instruction limit reached!
% 1.58/1.32 % (2468)------------------------------
% 1.58/1.32 % (2468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (2468)Termination reason: Unknown
% 1.58/1.32 % (2468)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (2468)Memory used [KB]: 5500
% 1.58/1.32 % (2468)Time elapsed: 0.005 s
% 1.58/1.32 % (2468)Instructions burned: 5 (million)
% 1.58/1.32 % (2468)------------------------------
% 1.58/1.32 % (2468)------------------------------
% 1.58/1.32 % (2469)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_2370 for (2999ds/27Mi)
% 1.58/1.33 % (2474)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/3Mi)
% 1.58/1.33 % (2477)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/3Mi)
% 1.58/1.33 % (2474)Instruction limit reached!
% 1.58/1.33 % (2474)------------------------------
% 1.58/1.33 % (2474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (2474)Termination reason: Unknown
% 1.58/1.33 % (2474)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (2474)Memory used [KB]: 5500
% 1.58/1.33 % (2474)Time elapsed: 0.004 s
% 1.58/1.33 % (2474)Instructions burned: 3 (million)
% 1.58/1.33 % (2474)------------------------------
% 1.58/1.33 % (2474)------------------------------
% 1.58/1.33 % (2477)Instruction limit reached!
% 1.58/1.33 % (2477)------------------------------
% 1.58/1.33 % (2477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (2477)Termination reason: Unknown
% 1.58/1.33 % (2477)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (2477)Memory used [KB]: 5500
% 1.58/1.33 % (2477)Time elapsed: 0.004 s
% 1.58/1.33 % (2477)Instructions burned: 5 (million)
% 1.58/1.33 % (2477)------------------------------
% 1.58/1.33 % (2477)------------------------------
% 1.58/1.33 % (2469)First to succeed.
% 1.58/1.33 % (2475)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/37Mi)
% 1.58/1.33 % Exception at run slice level
% 1.58/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.58/1.33 % (2476)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_2370 for (2999ds/15Mi)
% 1.58/1.33 % (2469)Refutation found. Thanks to Tanya!
% 1.58/1.33 % SZS status Theorem for DTF2THF_2370
% 1.58/1.33 % SZS output start Proof for DTF2THF_2370
% 1.58/1.33 thf(type_def_6, type, sK0: $tType).
% 1.58/1.33 thf(func_def_0, type, 'const/sets/UNIV': !>[X0: $tType]:(X0 > $o)).
% 1.58/1.33 thf(func_def_1, type, 'const/sets/UNION': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.58/1.33 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.58/1.33 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.58/1.33 thf(func_def_12, type, sK1: sK0 > $o).
% 1.58/1.33 thf(func_def_14, type, sK3: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.58/1.33 thf(func_def_15, type, ph4: !>[X0: $tType]:(X0)).
% 1.58/1.33 thf(func_def_16, type, sK5: sK0).
% 1.58/1.33 thf(f146,plain,(
% 1.58/1.33 $false),
% 1.58/1.33 inference(avatar_sat_refutation,[status(thm)],[f69,f136,f145])).
% 1.58/1.33 thf(f145,plain,(
% 1.58/1.33 ~spl2_4),
% 1.58/1.33 inference(avatar_contradiction_clause,[status(thm)],[f144])).
% 1.58/1.33 thf(f144,plain,(
% 1.58/1.33 $false | ~spl2_4),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.58/1.33 thf(f139,plain,(
% 1.58/1.33 ($false = $true) | ~spl2_4),
% 1.58/1.33 inference(superposition,[status(thm)],[f47,f68])).
% 1.58/1.33 thf(f68,plain,(
% 1.58/1.33 ($false = ('const/sets/UNIV' @ sK0 @ sK5)) | ~spl2_4),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.58/1.33 thf(f66,definition,(
% 1.58/1.33 spl2_4 <=> ($false = ('const/sets/UNIV' @ sK0 @ sK5))),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.58/1.33 thf(f47,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X1 : X0] : (($true = ('const/sets/UNIV' @ X0 @ X1))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.58/1.33 thf(f45,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X1 : X0] : (($true = ('const/sets/UNIV' @ X0 @ X1)) | ($false = $true)) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f23,f19])).
% 1.58/1.33 thf(f19,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) = $true)) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 1.58/1.33 thf(f13,plain,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) = $true)),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f12])).
% 1.58/1.33 thf(f12,plain,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0] : ('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 1.58/1.33 inference(rectify,[status(thm)],[f1])).
% 1.58/1.33 thf(f1,axiom,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0] : ('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_UNIV_')).
% 1.58/1.33 thf(f23,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = ('const/sets/IN' @ X0 @ X2 @ X1)) | ((X1 @ X2) = $true)) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.58/1.33 thf(f18,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (((X1 @ X2) = ('const/sets/IN' @ X0 @ X2 @ X1))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f14])).
% 1.58/1.33 thf(f14,plain,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((X1 @ X2) = ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.58/1.33 inference(rectify,[status(thm)],[f2])).
% 1.58/1.33 thf(f2,axiom,(
% 1.58/1.33 ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ X2) = (X2 @ X1))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_')).
% 1.58/1.33 thf(f136,plain,(
% 1.58/1.33 spl2_4 | ~spl2_3),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f132,f62,f66])).
% 1.58/1.33 thf(f62,definition,(
% 1.58/1.33 spl2_3 <=> ($false = ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5))),
% 1.58/1.33 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.58/1.33 thf(f132,plain,(
% 1.58/1.33 ($false = ('const/sets/UNIV' @ sK0 @ sK5)) | ~spl2_3),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.58/1.33 thf(f123,plain,(
% 1.58/1.33 ($false = ('const/sets/UNIV' @ sK0 @ sK5)) | ($false = $true) | ~spl2_3),
% 1.58/1.33 inference(superposition,[status(thm)],[f120,f24])).
% 1.58/1.33 thf(f24,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = ('const/sets/IN' @ X0 @ X2 @ X1)) | ($false = (X1 @ X2))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.58/1.33 thf(f120,plain,(
% 1.58/1.33 ($false = ('const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0)) | ~spl2_3),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.58/1.33 thf(f118,plain,(
% 1.58/1.33 ($false = $true) | ($false = ('const/sets/IN' @ sK0 @ sK5 @ 'const/sets/UNIV' @ sK0)) | ~spl2_3),
% 1.58/1.33 inference(superposition,[status(thm)],[f114,f64])).
% 1.58/1.33 thf(f64,plain,(
% 1.58/1.33 ($false = ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5)) | ~spl2_3),
% 1.58/1.33 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.58/1.33 thf(f114,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : (($true = ('const/sets/UNION' @ X0 @ X2 @ X3 @ X1)) | ($false = ('const/sets/IN' @ X0 @ X1 @ X3))) )),
% 1.58/1.33 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.58/1.33 thf(f108,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : (($true = ('const/sets/UNION' @ X0 @ X2 @ X3 @ X1)) | ($false = ('const/sets/IN' @ X0 @ X1 @ X3)) | ($false = $true)) )),
% 1.58/1.33 inference(superposition,[status(thm)],[f28,f23])).
% 1.58/1.33 thf(f28,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true) | ($false = ('const/sets/IN' @ X0 @ X3 @ X2))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.58/1.33 thf(f25,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true) | ($false = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))) )),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.58/1.33 thf(f20,plain,(
% 1.58/1.33 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))) )),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.33 thf(f9,plain,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.58/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.58/1.33 thf(f8,plain,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = ('const/sets/IN' @ X0 @ X3 @ X2) | ('const/sets/IN' @ X0 @ X3 @ X1))),
% 1.58/1.33 inference(rectify,[status(thm)],[f3])).
% 1.58/1.33 thf(f3,axiom,(
% 1.58/1.33 ! [X0 : $tType,X1 : X0 > $o,X3 : X0 > $o,X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/UNION' @ X0 @ X1 @ X3)) = ('const/sets/IN' @ X0 @ X4 @ X3) | ('const/sets/IN' @ X0 @ X4 @ X1))),
% 1.58/1.33 file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/IN_UNION_')).
% 1.58/1.33 thf(f69,plain,(
% 1.58/1.33 spl2_3 | spl2_4),
% 1.58/1.33 inference(avatar_split_clause,[status(thm)],[f51,f66,f62])).
% 1.58/1.33 thf(f51,plain,(
% 1.58/1.33 ($false = ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5)) | ($false = ('const/sets/UNIV' @ sK0 @ sK5))),
% 1.58/1.33 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.58/1.33 thf(f49,plain,(
% 1.58/1.33 (('const/sets/UNIV' @ sK0 @ sK5) != ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 @ sK5))),
% 1.58/1.33 inference(negative_extensionality,[status(thm)],[f22])).
% 1.58/1.33 thf(f22,plain,(
% 1.58/1.33 ('const/sets/UNIV' @ sK0 != ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0))),
% 1.58/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 1.58/1.33 thf(f17,plain,(
% 1.58/1.33 ('const/sets/UNIV' @ sK0 != ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0))),
% 1.58/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16])).
% 1.58/1.34 thf(f16,plain,(
% 1.58/1.34 ? [X0 : $tType,X1 : X0 > $o] : ('const/sets/UNIV' @ X0 != ('const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)) => ('const/sets/UNIV' @ sK0 != ('const/sets/UNION' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0))),
% 1.58/1.34 introduced(definition,[],[choice_axiom])).
% 1.58/1.34 thf(f15,plain,(
% 1.58/1.34 ? [X0 : $tType,X1 : X0 > $o] : ('const/sets/UNIV' @ X0 != ('const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0))),
% 1.58/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.34 thf(f6,negated_conjecture,(
% 1.58/1.34 ~! [X0 : $tType,X1 : X0 > $o] : ('const/sets/UNIV' @ X0 = ('const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0))),
% 1.58/1.34 inference(negated_conjecture,[status(cth)],[f5])).
% 1.58/1.34 thf(f5,conjecture,(
% 1.58/1.34 ! [X0 : $tType,X1 : X0 > $o] : ('const/sets/UNIV' @ X0 = ('const/sets/UNION' @ X0 @ X1 @ 'const/sets/UNIV' @ X0))),
% 1.58/1.34 file('/export/starexec/sandbox/tmp/tmp.DVw3IqPB0o/DTF2THF_2370.p','thm/sets/UNION_UNIV_1')).
% 1.58/1.34 % SZS output end Proof for DTF2THF_2370
% 1.58/1.34 % (2469)------------------------------
% 1.58/1.34 % (2469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (2469)Termination reason: Refutation
% 1.58/1.34
% 1.58/1.34 % (2469)Memory used [KB]: 5628
% 1.58/1.34 % (2469)Time elapsed: 0.014 s
% 1.58/1.34 % (2469)Instructions burned: 16 (million)
% 1.58/1.34 % (2469)------------------------------
% 1.58/1.34 % (2469)------------------------------
% 1.58/1.34 % (2466)Success in time 0.038 s
%------------------------------------------------------------------------------