%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV487^1 : 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 : n006.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 0.30s 1.34s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 45 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 336 ( 24 ~; 9 |; 21 &; 264 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 3 con; 0-3 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 74 ( 10 ^; 60 !; 4 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/pairwise':
!>[X0: $tType] : ( ( X0 > X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK1: sK0 > sK0 > $o ).
thf(func_def_17,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_19,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
$true != $true,
inference(superposition,[status(thm)],[f17,f49]) ).
thf(f49,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( $true != $true )
| ( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f16,f37]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( $true
= ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( ( sK4 @ X0 @ X1 @ X2 )
!= ( sK3 @ X0 @ X1 @ X2 ) ) ) )
| ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( ( sK4 @ X0 @ X1 @ X2 )
!= ( sK3 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ ( sK4 @ X0 @ X1 @ X2 ) @ ( sK3 @ X0 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( ^ [Y0: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( Y0
!= ( sK3 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ Y0 @ ( sK3 @ X0 @ X1 @ X2 ) ) )
@ ( sK4 @ X0 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( 'const/sets/IN' @ X0 @ ( sK3 @ X0 @ X1 @ X2 ) @ X1 )
& ( Y0
!= ( sK3 @ X0 @ X1 @ X2 ) ) )
=> ( X2 @ Y0 @ ( sK3 @ X0 @ X1 @ X2 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( ( ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) )
@ ( sK3 @ X0 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X2: X0 > X0 > $o,X1: X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X2 @ X1 )
= ( !! @ X0
@ ^ [Y0: X0] :
( !! @ X0
@ ^ [Y1: X0] :
( ( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
& ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
& ( Y1 != Y0 ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o,X3: X0,X4: X0] :
( ( ( ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) )
= ( 'const/sets/pairwise' @ X0 @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > X0 > $o,X3: X0,X4: X0] :
( ( ( ( X3 != X4 )
& ( 'const/sets/IN' @ X0 @ X4 @ X1 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( X2 @ X3 @ X4 ) )
= ( 'const/sets/pairwise' @ X0 @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/pairwise_') ).
thf(f16,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f17,plain,
( $true
!= ( 'const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
!= ( 'const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true )
=> ( $true
!= ( 'const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( 'const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
= $true ),
file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/PAIRWISE_EMPTY_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV487^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:47:45 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV487^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : PAIRWISE_EMPTY
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : PAIRWISE_EMPTY_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 2 ( 3 avg)
% 0.19/0.45 % Number of connectives : 24 ( 2 ~; 0 |; 2 &; 19 @)
% 0.19/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 7 ( 5 avg)
% 0.19/0.45 % Number of types : 1 ( 0 usr)
% 0.19/0.45 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 5 ( 3 usr; 1 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 12 ( 0 ^; 9 !; 0 ?; 12 :)
% 0.19/0.45 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_const_const/sets/pairwise',type,
% 0.19/0.45 'const/sets/pairwise':
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/IN',type,
% 0.19/0.45 'const/sets/IN':
% 0.19/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thf_const_const/sets/EMPTY',type,
% 0.19/0.45 'const/sets/EMPTY':
% 0.19/0.45 !>[A: $tType] : ( A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.19/0.45 ! [A: $tType,A0: A] :
% 0.19/0.45 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/pairwise_',axiom,
% 0.19/0.45 ! [A: $tType,A0: A > $o,A1: A > A > $o] :
% 0.19/0.45 ( ( 'const/sets/pairwise' @ A @ A1 @ A0 )
% 0.19/0.45 = ( ! [A2: A,A3: A] :
% 0.19/0.45 ( ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.19/0.45 & ( 'const/sets/IN' @ A @ A3 @ A0 )
% 0.19/0.45 & ( A2 != A3 ) )
% 0.19/0.45 => ( A1 @ A2 @ A3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/PAIRWISE_EMPTY_',conjecture,
% 0.19/0.45 ! [A: $tType,A0: A > A > $o] :
% 0.19/0.45 ( ( 'const/sets/pairwise' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
% 0.19/0.45 = $true ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 0.30/1.30 ---- Embedded in THF ---
% 0.30/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.30 %%% Generated on Tue Feb 24 12:47:46 EST 2026
% 0.30/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.30 %%% Logic specification used:
% 0.30/1.30 %%% thf(spec, logic, $$dhol).
% 0.30/1.30
% 0.30/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2DTF1143.p
% See solution above
% 0.30/1.30 ------------------------
% 0.30/1.31 ---- Cleaned THF ---
% 0.30/1.31 thf('thf_const_const/sets/pairwise',type,
% 0.30/1.31 'const/sets/pairwise':
% 0.30/1.31 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf('thf_const_const/sets/IN',type,
% 0.30/1.31 'const/sets/IN':
% 0.30/1.31 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf('thf_const_const/sets/EMPTY',type,
% 0.30/1.31 'const/sets/EMPTY':
% 0.30/1.31 !>[A: $tType] : ( A > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.30/1.31 ! [A: $tType,A0: A] :
% 0.30/1.31 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.30/1.31
% 0.30/1.31 thf('thm/sets/pairwise_',axiom,
% 0.30/1.31 ! [A: $tType,A0: A > $o,A1: A > A > $o] :
% 0.30/1.31 ( ( 'const/sets/pairwise' @ A @ A1 @ A0 )
% 0.30/1.31 = ( ! [A2: A,A3: A] :
% 0.30/1.31 ( ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.30/1.31 & ( 'const/sets/IN' @ A @ A3 @ A0 )
% 0.30/1.31 & ( A2 != A3 ) )
% 0.30/1.31 => ( A1 @ A2 @ A3 ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf('thm/sets/PAIRWISE_EMPTY_',conjecture,
% 0.30/1.31 ! [A: $tType,A0: A > A > $o] :
% 0.30/1.31 ( ( 'const/sets/pairwise' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
% 0.30/1.31 = $true ) ).
% 0.30/1.31 ------------------------
% 0.30/1.33 % (1332)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_1143 for (2999ds/27Mi)
% 0.30/1.33 % (1335)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_1143 for (2999ds/275Mi)
% 0.30/1.34 % (1333)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1143 for (2999ds/2Mi)
% 0.30/1.34 % (1335)Refutation not found, incomplete strategy
% 0.30/1.34 % (1335)------------------------------
% 0.30/1.34 % (1335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (1334)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_1143 for (2999ds/2Mi)
% 0.30/1.34 % (1335)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.34
% 0.30/1.34
% 0.30/1.34 % (1335)Memory used [KB]: 5500
% 0.30/1.34 % (1335)Time elapsed: 0.003 s
% 0.30/1.34 % (1336)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1143 for (2999ds/18Mi)
% 0.30/1.34 % (1335)Instructions burned: 3 (million)
% 0.30/1.34 % (1335)------------------------------
% 0.30/1.34 % (1335)------------------------------
% 0.30/1.34 % (1330)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1143 for (2999ds/183Mi)
% 0.30/1.34 % Exception at run slice level
% 0.30/1.34 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
% 0.30/1.34 % (1333)Instruction limit reached!
% 0.30/1.34 % (1333)------------------------------
% 0.30/1.34 % (1333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (1333)Termination reason: Unknown
% 0.30/1.34 % (1333)Termination phase: Saturation
% 0.30/1.34
% 0.30/1.34 % (1333)Memory used [KB]: 5500
% 0.30/1.34 % (1333)Time elapsed: 0.003 s
% 0.30/1.34 % (1333)Instructions burned: 2 (million)
% 0.30/1.34 % (1333)------------------------------
% 0.30/1.34 % (1333)------------------------------
% 0.30/1.34 % (1331)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_1143 for (2999ds/4Mi)
% 0.30/1.34 % (1332)First to succeed.
% 0.30/1.34 % (1331)Instruction limit reached!
% 0.30/1.34 % (1331)------------------------------
% 0.30/1.34 % (1331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (1331)Termination reason: Unknown
% 0.30/1.34 % (1331)Termination phase: Saturation
% 0.30/1.34
% 0.30/1.34 % (1331)Memory used [KB]: 5500
% 0.30/1.34 % (1331)Time elapsed: 0.004 s
% 0.30/1.34 % (1331)Instructions burned: 5 (million)
% 0.30/1.34 % (1331)------------------------------
% 0.30/1.34 % (1331)------------------------------
% 0.30/1.34 % (1336)Also succeeded, but the first one will report.
% 0.30/1.34 % (1332)Refutation found. Thanks to Tanya!
% 0.30/1.34 % SZS status Theorem for DTF2THF_1143
% 0.30/1.34 % SZS output start Proof for DTF2THF_1143
% 0.30/1.34 thf(type_def_6, type, sK0: $tType).
% 0.30/1.34 thf(func_def_0, type, 'const/sets/pairwise': !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > $o)).
% 0.30/1.34 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.30/1.34 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 0.30/1.34 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.30/1.34 thf(func_def_15, type, sK1: sK0 > sK0 > $o).
% 0.30/1.34 thf(func_def_17, type, sK3: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 0.30/1.34 thf(func_def_18, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 0.30/1.34 thf(func_def_19, type, ph5: !>[X0: $tType]:(X0)).
% 0.30/1.34 thf(f53,plain,(
% 0.30/1.34 $false),
% 0.30/1.34 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 0.30/1.34 thf(f51,plain,(
% 0.30/1.34 ($true != $true)),
% 0.30/1.34 inference(superposition,[status(thm)],[f17,f49])).
% 0.30/1.34 thf(f49,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)) )),
% 0.30/1.34 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 0.30/1.34 thf(f48,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true != $true) | (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)) )),
% 0.30/1.34 inference(superposition,[status(thm)],[f16,f37])).
% 0.30/1.34 thf(f37,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1) = $true) | (('const/sets/pairwise' @ X0 @ X2 @ X1) = $true)) )),
% 0.30/1.34 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 0.30/1.34 thf(f36,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | ($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X1) & ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1)))) )),
% 0.30/1.34 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 0.30/1.34 thf(f34,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : (($true = ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X1) & ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1)) & (~ ((sK4 @ X0 @ X1 @ X2) = (sK3 @ X0 @ X1 @ X2))))) | (('const/sets/pairwise' @ X0 @ X2 @ X1) = $true)) )),
% 0.30/1.34 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.30/1.34 thf(f32,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | ((((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X1) & ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1)) & (~ ((sK4 @ X0 @ X1 @ X2) = (sK3 @ X0 @ X1 @ X2)))) => (X2 @ (sK4 @ X0 @ X1 @ X2) @ (sK3 @ X0 @ X1 @ X2))) = $false)) )),
% 0.30/1.34 inference(beta_eta_normalization,[status(thm)],[f31])).
% 0.30/1.34 thf(f31,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | (((^[Y0 : X0]: (((('const/sets/IN' @ X0 @ Y0 @ X1) & ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1)) & (~ (Y0 = (sK3 @ X0 @ X1 @ X2)))) => (X2 @ Y0 @ (sK3 @ X0 @ X1 @ X2)))) @ (sK4 @ X0 @ X1 @ X2)) = $false)) )),
% 0.30/1.34 inference(sigma_clausification,[status(thm)],[f30])).
% 0.30/1.34 thf(f30,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | ((!! @ X0 @ (^[Y0 : X0]: (((('const/sets/IN' @ X0 @ Y0 @ X1) & ('const/sets/IN' @ X0 @ (sK3 @ X0 @ X1 @ X2) @ X1)) & (~ (Y0 = (sK3 @ X0 @ X1 @ X2)))) => (X2 @ Y0 @ (sK3 @ X0 @ X1 @ X2))))) = $false)) )),
% 0.30/1.34 inference(beta_eta_normalization,[status(thm)],[f29])).
% 0.30/1.34 thf(f29,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | (((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: (((('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ X0 @ Y0 @ X1)) & (~ (Y1 = Y0))) => (X2 @ Y1 @ Y0))))) @ (sK3 @ X0 @ X1 @ X2)) = $false)) )),
% 0.30/1.34 inference(sigma_clausification,[status(thm)],[f18])).
% 0.30/1.34 thf(f18,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = $true) | ($false = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: (((('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ X0 @ Y0 @ X1)) & (~ (Y1 = Y0))) => (X2 @ Y1 @ Y0)))))))) )),
% 0.30/1.34 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 0.30/1.34 thf(f15,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X1 : X0 > $o] : ((('const/sets/pairwise' @ X0 @ X2 @ X1) = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: (((('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ X0 @ Y0 @ X1)) & (~ (Y1 = Y0))) => (X2 @ Y1 @ Y0)))))))) )),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 0.30/1.34 thf(f10,plain,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X2 @ X1) = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: (((('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ X0 @ Y0 @ X1)) & (~ (Y1 = Y0))) => (X2 @ Y1 @ Y0)))))))),
% 0.30/1.34 inference(fool_elimination,[status(thm)],[f9])).
% 0.30/1.34 thf(f9,plain,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > X0 > $o] : (! [X3 : X0,X4 : X0] : (((X3 != X4) & ('const/sets/IN' @ X0 @ X4 @ X1) & ('const/sets/IN' @ X0 @ X3 @ X1)) => (X2 @ X3 @ X4)) = ('const/sets/pairwise' @ X0 @ X2 @ X1))),
% 0.30/1.34 inference(rectify,[status(thm)],[f2])).
% 0.30/1.34 thf(f2,axiom,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > X0 > $o] : (! [X3 : X0,X4 : X0] : (((X3 != X4) & ('const/sets/IN' @ X0 @ X4 @ X1) & ('const/sets/IN' @ X0 @ X3 @ X1)) => (X2 @ X3 @ X4)) = ('const/sets/pairwise' @ X0 @ X2 @ X1))),
% 0.30/1.34 file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/pairwise_')).
% 0.30/1.34 thf(f16,plain,(
% 0.30/1.34 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)) )),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f11])).
% 0.30/1.34 thf(f11,plain,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 0.30/1.34 inference(flattening,[status(thm)],[f7])).
% 0.30/1.34 thf(f7,plain,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0] : ~(('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 0.30/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 0.30/1.34 thf(f6,plain,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.30/1.34 inference(rectify,[status(thm)],[f1])).
% 0.30/1.34 thf(f1,axiom,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.30/1.34 file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/NOT_IN_EMPTY_')).
% 0.30/1.34 thf(f17,plain,(
% 0.30/1.34 ($true != ('const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0))),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 0.30/1.34 thf(f14,plain,(
% 0.30/1.34 ($true != ('const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0))),
% 0.30/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 0.30/1.34 thf(f13,plain,(
% 0.30/1.34 ? [X0 : $tType,X1 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true) => ($true != ('const/sets/pairwise' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0))),
% 0.30/1.34 introduced(definition,[],[choice_axiom])).
% 0.30/1.34 thf(f12,plain,(
% 0.30/1.34 ? [X0 : $tType,X1 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 0.30/1.34 inference(ennf_transformation,[status(thm)],[f8])).
% 0.30/1.34 thf(f8,plain,(
% 0.30/1.34 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 0.30/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 0.30/1.34 thf(f4,negated_conjecture,(
% 0.30/1.34 ~! [X0 : $tType,X1 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 0.30/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 0.30/1.34 thf(f3,conjecture,(
% 0.30/1.34 ! [X0 : $tType,X1 : X0 > X0 > $o] : (('const/sets/pairwise' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 0.30/1.34 file('/export/starexec/sandbox2/tmp/tmp.uXgelazdtt/DTF2THF_1143.p','thm/sets/PAIRWISE_EMPTY_')).
% 0.30/1.34 % SZS output end Proof for DTF2THF_1143
% 0.30/1.34 % (1332)------------------------------
% 0.30/1.34 % (1332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (1332)Termination reason: Refutation
% 0.30/1.34
% 0.30/1.34 % (1332)Memory used [KB]: 5500
% 0.30/1.34 % (1332)Time elapsed: 0.007 s
% 0.30/1.34 % (1332)Instructions burned: 6 (million)
% 0.30/1.34 % (1332)------------------------------
% 0.30/1.34 % (1332)------------------------------
% 0.30/1.34 % (1329)Success in time 0.021 s
%------------------------------------------------------------------------------