%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV257^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 09:40:41 AM UTC 2026
% Result : Theorem 1.04s 0.92s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 248 ( 67 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 300 ( 24 ~; 20 |; 52 &; 173 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-2 aty)
% ( 0 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 55 ^; 38 !; 6 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cOPEN: ( a > $o ) > $o ).
thf(func_def_10,type,
sK0: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_13,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK3: a ).
thf(func_def_15,type,
sK4: ( ( a > $o ) > $o ) > a ).
thf(func_def_16,type,
sK5: ( ( a > $o ) > $o ) > a > $o ).
thf(f59,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
$false = $true,
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true
= ( ^ [Y0: a > $o] : $false
@ ( sK5
@ ^ [Y0: a > $o] : $false ) ) )
| ( ( ^ [Y0: a > $o] : $false
@ ( sK0
@ ^ [Y0: a > $o] : $false ) )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK5 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $true
= ( ( sK5 @ X0 @ ( sK4 @ X0 ) )
& ( X0 @ ( sK5 @ X0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ ( sK4 @ X0 ) )
& ( X0 @ Y0 ) )
@ ( sK5 @ X0 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: ( a > $o ) > $o] :
( ( $false
!= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ ( sK4 @ X0 ) )
& ( X0 @ Y0 ) ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: ( a > $o ) > $o] :
( ( ( ^ [Y0: a] : $false
@ ( sK4 @ X0 ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) )
@ ( sK4 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(negative_extensionality,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: ( a > $o ) > $o] :
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f13,f14]) ).
thf(f14,plain,
! [X0: ( a > $o ) > $o] :
( ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: ( a > $o ) > $o] :
( ( ( ( cOPEN @ ( sK0 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) )
| ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true ) )
& ( ( cOPEN
@ ^ [Y0: a] : $false )
!= $true )
& ( ( cOPEN
@ ^ [Y0: a] : $true )
= $true )
& ! [X2: a > $o,X3: a > $o] :
( ( ( cOPEN @ X3 )
!= $true )
| ( ( cOPEN @ X2 )
!= $true )
| ( $true
= ( cOPEN
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( cOPEN @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
=> ( ( ( cOPEN @ ( sK0 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( cOPEN @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true ) )
& ( ( cOPEN
@ ^ [Y0: a] : $false )
!= $true )
& ( ( cOPEN
@ ^ [Y0: a] : $true )
= $true )
& ! [X2: a > $o,X3: a > $o] :
( ( ( cOPEN @ X3 )
!= $true )
| ( ( cOPEN @ X2 )
!= $true )
| ( $true
= ( cOPEN
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cOPEN
@ ^ [Y0: a] : $false )
!= $true )
& ! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( cOPEN @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
| ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true ) )
& ! [X2: a > $o,X3: a > $o] :
( ( $true
= ( cOPEN
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) ) )
| ( ( cOPEN @ X3 )
!= $true )
| ( ( cOPEN @ X2 )
!= $true ) )
& ( ( cOPEN
@ ^ [Y0: a] : $true )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cOPEN @ X1 )
= $true ) )
=> ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true ) )
& ! [X2: a > $o,X3: a > $o] :
( ( ( ( cOPEN @ X3 )
= $true )
& ( ( cOPEN @ X2 )
= $true ) )
=> ( $true
= ( cOPEN
@ ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X3 @ Y0 ) ) ) ) )
& ( ( cOPEN
@ ^ [Y0: a] : $true )
= $true ) )
=> ( ( cOPEN
@ ^ [Y0: a] : $false )
= $true ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cOPEN
@ ^ [Y0: a] : $true )
= $true )
& ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( ( X1 @ X2 )
= $true )
=> ( ( cOPEN @ X2 )
= $true ) )
=> ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X1 @ Y1 ) ) ) )
= $true ) )
& ! [X5: a > $o,X6: a > $o] :
( ( ( ( cOPEN @ X5 )
= $true )
& ( ( cOPEN @ X6 )
= $true ) )
=> ( ( cOPEN
@ ^ [Y0: a] :
( ( X5 @ Y0 )
& ( X6 @ Y0 ) ) )
= $true ) ) )
=> ( ( cOPEN
@ ^ [Y0: a] : $false )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cOPEN
@ ^ [X0: a] : $true )
& ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X3: a] :
? [X4: a > $o] :
( ( X1 @ X4 )
& ( X4 @ X3 ) ) ) )
& ! [X5: a > $o,X6: a > $o] :
( ( ( cOPEN @ X5 )
& ( cOPEN @ X6 ) )
=> ( cOPEN
@ ^ [X7: a] :
( ( X6 @ X7 )
& ( X5 @ X7 ) ) ) ) )
=> ( cOPEN
@ ^ [X8: a] : $false ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cOPEN
@ ^ [X0: a] : $true )
& ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X2: a] :
? [X3: a > $o] :
( ( X1 @ X3 )
& ( X3 @ X2 ) ) ) )
& ! [X4: a > $o,X5: a > $o] :
( ( ( cOPEN @ X4 )
& ( cOPEN @ X5 ) )
=> ( cOPEN
@ ^ [X2: a] :
( ( X5 @ X2 )
& ( X4 @ X2 ) ) ) ) )
=> ( cOPEN
@ ^ [X0: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cOPEN
@ ^ [X0: a] : $true )
& ! [X1: ( a > $o ) > $o] :
( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ( cOPEN @ X2 ) )
=> ( cOPEN
@ ^ [X2: a] :
? [X3: a > $o] :
( ( X1 @ X3 )
& ( X3 @ X2 ) ) ) )
& ! [X4: a > $o,X5: a > $o] :
( ( ( cOPEN @ X4 )
& ( cOPEN @ X5 ) )
=> ( cOPEN
@ ^ [X2: a] :
( ( X5 @ X2 )
& ( X4 @ X2 ) ) ) ) )
=> ( cOPEN
@ ^ [X0: a] : $false ) ),
file('/export/starexec/sandbox2/tmp/tmp.89w8oXnglr/DTF2THF_9771.p',cTHM625_pme) ).
thf(f13,plain,
( ( cOPEN
@ ^ [Y0: a] : $false )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV257^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue Feb 24 07:42:40 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : SEV257^5 : TPTP v9.2.1. Released v4.0.0.
% 0.06/0.31 % Domain : Set Theory (Sets of sets)
% 0.06/0.31 % Problem : TPS problem THM625
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English : Empty sets are open in any topology.
% 0.06/0.31
% 0.06/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.06/0.31 % Source : [Bro09]
% 0.06/0.31 % Names : tps_0161 [Bro09]
% 0.06/0.31 % : THM625 [TPS]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.50 v5.3.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.06/0.31 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.06/0.31 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 9 ( 9 avg)
% 0.06/0.31 % Number of connectives : 21 ( 0 ~; 0 |; 5 &; 12 @)
% 0.06/0.31 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 11 ( 11 avg)
% 0.06/0.31 % Number of types : 2 ( 1 usr)
% 0.06/0.31 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 3 ( 1 usr; 2 con; 0-1 aty)
% 0.06/0.31 % Number of variables : 9 ( 4 ^; 4 !; 1 ?; 9 :)
% 0.06/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.06/0.31
% 0.06/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.06/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.06/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.06/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.06/0.31 % : Polymorphic definitions expanded.
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf(a_type,type,
% 0.06/0.31 a: $tType ).
% 0.06/0.31
% 0.06/0.31 thf(cOPEN,type,
% 0.06/0.31 cOPEN: ( a > $o ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(cTHM625_pme,conjecture,
% 0.06/0.31 ( ( ( cOPEN
% 0.06/0.31 @ ^ [Xy: a] : $true )
% 0.06/0.31 & ! [K: ( a > $o ) > $o] :
% 0.06/0.31 ( ! [Xx: a > $o] :
% 0.06/0.31 ( ( K @ Xx )
% 0.06/0.31 => ( cOPEN @ Xx ) )
% 0.06/0.31 => ( cOPEN
% 0.06/0.31 @ ^ [Xx: a] :
% 0.06/0.31 ? [S: a > $o] :
% 0.06/0.31 ( ( K @ S )
% 0.06/0.31 & ( S @ Xx ) ) ) )
% 0.06/0.31 & ! [Y: a > $o,Z: a > $o] :
% 0.06/0.31 ( ( ( cOPEN @ Y )
% 0.06/0.31 & ( cOPEN @ Z ) )
% 0.06/0.31 => ( cOPEN
% 0.06/0.31 @ ^ [Xx: a] :
% 0.06/0.31 ( ( Y @ Xx )
% 0.06/0.31 & ( Z @ Xx ) ) ) ) )
% 0.06/0.31 => ( cOPEN
% 0.06/0.31 @ ^ [Xy: a] : $false ) ) ).
% 0.06/0.31
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 ------------------------
% 0.84/0.88 ---- Embedded in THF ---
% 0.84/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.88 %%% Generated on Tue Feb 24 07:42:41 EST 2026
% 0.84/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.88 %%% Logic specification used:
% 0.84/0.88 %%% thf(spec, logic, $$dhol).
% 0.84/0.88
% 0.84/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.89w8oXnglr/DTF2DTF9771.p
% See solution above
% 0.84/0.88 ------------------------
% 0.84/0.89 ---- Cleaned THF ---
% 0.84/0.89 thf(a_type,type,
% 0.84/0.89 a: $tType ).
% 0.84/0.89
% 0.84/0.89 thf(cOPEN,type,
% 0.84/0.89 cOPEN: ( a > $o ) > $o ).
% 0.84/0.89
% 0.84/0.89 thf(cTHM625_pme,conjecture,
% 0.84/0.89 ( ( ( cOPEN
% 0.84/0.89 @ ^ [Xy: a] : $true )
% 0.84/0.89 & ! [K: ( a > $o ) > $o] :
% 0.84/0.89 ( ! [Xx: a > $o] :
% 0.84/0.89 ( ( K @ Xx )
% 0.84/0.89 => ( cOPEN @ Xx ) )
% 0.84/0.89 => ( cOPEN
% 0.84/0.89 @ ^ [Xx: a] :
% 0.84/0.89 ? [S: a > $o] :
% 0.84/0.89 ( ( K @ S )
% 0.84/0.89 & ( S @ Xx ) ) ) )
% 0.84/0.89 & ! [Y: a > $o,Z: a > $o] :
% 0.84/0.89 ( ( ( cOPEN @ Y )
% 0.84/0.89 & ( cOPEN @ Z ) )
% 0.84/0.89 => ( cOPEN
% 0.84/0.89 @ ^ [Xx: a] :
% 0.84/0.89 ( ( Y @ Xx )
% 0.84/0.89 & ( Z @ Xx ) ) ) ) )
% 0.84/0.89 => ( cOPEN
% 0.84/0.89 @ ^ [Xy: a] : $false ) ) ).
% 0.84/0.89 ------------------------
% 1.04/0.90 % (9930)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9771 for (3000ds/183Mi)
% 1.04/0.91 % (9933)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9771 for (3000ds/2Mi)
% 1.04/0.91 % (9932)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_9771 for (3000ds/27Mi)
% 1.04/0.91 % (9933)Instruction limit reached!
% 1.04/0.91 % (9933)------------------------------
% 1.04/0.91 % (9933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.91 % (9933)Termination reason: Unknown
% 1.04/0.91 % (9933)Termination phase: Saturation
% 1.04/0.91
% 1.04/0.91 % (9933)Memory used [KB]: 5500
% 1.04/0.91 % (9933)Time elapsed: 0.003 s
% 1.04/0.91 % (9933)Instructions burned: 3 (million)
% 1.04/0.91 % (9933)------------------------------
% 1.04/0.91 % (9933)------------------------------
% 1.04/0.91 % (9934)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_9771 for (3000ds/2Mi)
% 1.04/0.91 % (9935)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_9771 for (3000ds/275Mi)
% 1.04/0.91 % (9936)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9771 for (3000ds/18Mi)
% 1.04/0.91 % (9934)Instruction limit reached!
% 1.04/0.91 % (9934)------------------------------
% 1.04/0.91 % (9934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.91 % (9934)Termination reason: Unknown
% 1.04/0.91 % (9934)Termination phase: Property scanning
% 1.04/0.91
% 1.04/0.91 % (9934)Memory used [KB]: 895
% 1.04/0.91 % (9934)Time elapsed: 0.002 s
% 1.04/0.91 % (9934)Instructions burned: 2 (million)
% 1.04/0.91 % (9934)------------------------------
% 1.04/0.91 % (9934)------------------------------
% 1.04/0.91 % (9935)Refutation not found, incomplete strategy
% 1.04/0.91 % (9935)------------------------------
% 1.04/0.91 % (9935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.91 % (9935)Termination reason: Refutation not found, incomplete strategy
% 1.04/0.91
% 1.04/0.91
% 1.04/0.91 % (9935)Memory used [KB]: 5500
% 1.04/0.91 % (9935)Time elapsed: 0.003 s
% 1.04/0.91 % (9935)Instructions burned: 3 (million)
% 1.04/0.91 % (9935)------------------------------
% 1.04/0.91 % (9935)------------------------------
% 1.04/0.91 % (9931)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_9771 for (3000ds/4Mi)
% 1.04/0.92 % (9931)Instruction limit reached!
% 1.04/0.92 % (9931)------------------------------
% 1.04/0.92 % (9931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.92 % (9931)Termination reason: Unknown
% 1.04/0.92 % (9931)Termination phase: Saturation
% 1.04/0.92
% 1.04/0.92 % (9931)Memory used [KB]: 5500
% 1.04/0.92 % (9931)Time elapsed: 0.004 s
% 1.04/0.92 % (9931)Instructions burned: 4 (million)
% 1.04/0.92 % (9931)------------------------------
% 1.04/0.92 % (9931)------------------------------
% 1.04/0.92 % (9936)First to succeed.
% 1.04/0.92 % (9936)Refutation found. Thanks to Tanya!
% 1.04/0.92 % SZS status Theorem for DTF2THF_9771
% 1.04/0.92 % SZS output start Proof for DTF2THF_9771
% 1.04/0.92 thf(type_def_5, type, a: $tType).
% 1.04/0.92 thf(func_def_0, type, a: $tType).
% 1.04/0.92 thf(func_def_1, type, cOPEN: (a > $o) > $o).
% 1.04/0.92 thf(func_def_10, type, sK0: ((a > $o) > $o) > a > $o).
% 1.04/0.92 thf(func_def_13, type, ph2: !>[X0: $tType]:(X0)).
% 1.04/0.92 thf(func_def_14, type, sK3: a).
% 1.04/0.92 thf(func_def_15, type, sK4: ((a > $o) > $o) > a).
% 1.04/0.92 thf(func_def_16, type, sK5: ((a > $o) > $o) > a > $o).
% 1.04/0.92 thf(f59,plain,(
% 1.04/0.92 $false),
% 1.04/0.92 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.04/0.92 thf(f58,plain,(
% 1.04/0.92 ($false = $true)),
% 1.04/0.92 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.04/0.92 thf(f57,plain,(
% 1.04/0.92 ($false = $true) | ($false = $true)),
% 1.04/0.92 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.04/0.92 thf(f44,plain,(
% 1.04/0.92 ($true = ((^[Y0 : a > $o]: ($false)) @ (sK5 @ (^[Y0 : a > $o]: ($false))))) | (((^[Y0 : a > $o]: ($false)) @ (sK0 @ (^[Y0 : a > $o]: ($false)))) = $true)),
% 1.04/0.92 inference(primitive_instantiation,[status(thm)],[f41])).
% 1.04/0.92 thf(f41,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK5 @ X0)) = $true) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.04/0.92 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.04/0.92 thf(f40,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | ($true = ((sK5 @ X0 @ (sK4 @ X0)) & (X0 @ (sK5 @ X0))))) )),
% 1.04/0.92 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.04/0.92 thf(f39,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | (((^[Y0 : a > $o]: ((Y0 @ (sK4 @ X0)) & (X0 @ Y0))) @ (sK5 @ X0)) = $true)) )),
% 1.04/0.92 inference(sigma_clausification,[status(thm)],[f38])).
% 1.04/0.92 thf(f38,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (($false != (?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ (sK4 @ X0)) & (X0 @ Y0))))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.04/0.92 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.04/0.92 thf(f37,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : ((((^[Y0 : a]: ($false)) @ (sK4 @ X0)) != ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))) @ (sK4 @ X0))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.04/0.92 inference(negative_extensionality,[status(thm)],[f30])).
% 1.04/0.92 thf(f30,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.04/0.92 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.04/0.92 thf(f25,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) | ($true != $true)) )),
% 1.04/0.92 inference(constrained_superposition,[status(thm)],[f13,f14])).
% 1.04/0.92 thf(f14,plain,(
% 1.04/0.92 ( ! [X0 : (a > $o) > $o] : (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.04/0.92 inference(cnf_transformation,[status(thm)],[f10])).
% 1.04/0.92 thf(f10,plain,(
% 1.04/0.92 ! [X0 : (a > $o) > $o] : ((((cOPEN @ (sK0 @ X0)) != $true) & ((X0 @ (sK0 @ X0)) = $true)) | ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true)) & ((cOPEN @ (^[Y0 : a]: ($false))) != $true) & ((cOPEN @ (^[Y0 : a]: ($true))) = $true) & ! [X2 : a > $o,X3 : a > $o] : (((cOPEN @ X3) != $true) | ((cOPEN @ X2) != $true) | ($true = (cOPEN @ (^[Y0 : a]: ((X2 @ Y0) & (X3 @ Y0))))))),
% 1.04/0.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.04/0.92 thf(f9,plain,(
% 1.04/0.92 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((cOPEN @ X1) != $true) & ((X0 @ X1) = $true)) => (((cOPEN @ (sK0 @ X0)) != $true) & ((X0 @ (sK0 @ X0)) = $true)))),
% 1.04/0.92 introduced(definition,[],[choice_axiom])).
% 1.04/0.92 thf(f8,plain,(
% 1.04/0.92 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((cOPEN @ X1) != $true) & ((X0 @ X1) = $true)) | ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true)) & ((cOPEN @ (^[Y0 : a]: ($false))) != $true) & ((cOPEN @ (^[Y0 : a]: ($true))) = $true) & ! [X2 : a > $o,X3 : a > $o] : (((cOPEN @ X3) != $true) | ((cOPEN @ X2) != $true) | ($true = (cOPEN @ (^[Y0 : a]: ((X2 @ Y0) & (X3 @ Y0))))))),
% 1.04/0.92 inference(flattening,[status(thm)],[f7])).
% 1.04/0.92 thf(f7,plain,(
% 1.04/0.92 ((cOPEN @ (^[Y0 : a]: ($false))) != $true) & (! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((cOPEN @ X1) != $true) & ((X0 @ X1) = $true)) | ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true)) & ! [X2 : a > $o,X3 : a > $o] : (($true = (cOPEN @ (^[Y0 : a]: ((X2 @ Y0) & (X3 @ Y0))))) | (((cOPEN @ X3) != $true) | ((cOPEN @ X2) != $true))) & ((cOPEN @ (^[Y0 : a]: ($true))) = $true))),
% 1.04/0.92 inference(ennf_transformation,[status(thm)],[f6])).
% 1.04/0.92 thf(f6,plain,(
% 1.04/0.92 ~((! [X0 : (a > $o) > $o] : (! [X1 : a > $o] : (((X0 @ X1) = $true) => ((cOPEN @ X1) = $true)) => ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true)) & ! [X2 : a > $o,X3 : a > $o] : ((((cOPEN @ X3) = $true) & ((cOPEN @ X2) = $true)) => ($true = (cOPEN @ (^[Y0 : a]: ((X2 @ Y0) & (X3 @ Y0)))))) & ((cOPEN @ (^[Y0 : a]: ($true))) = $true)) => ((cOPEN @ (^[Y0 : a]: ($false))) = $true))),
% 1.04/0.92 inference(rectify,[status(thm)],[f5])).
% 1.04/0.92 thf(f5,plain,(
% 1.04/0.92 ~((((cOPEN @ (^[Y0 : a]: ($true))) = $true) & ! [X1 : (a > $o) > $o] : (! [X2 : a > $o] : (((X1 @ X2) = $true) => ((cOPEN @ X2) = $true)) => ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X1 @ Y1)))))) = $true)) & ! [X5 : a > $o,X6 : a > $o] : ((((cOPEN @ X5) = $true) & ((cOPEN @ X6) = $true)) => ((cOPEN @ (^[Y0 : a]: ((X5 @ Y0) & (X6 @ Y0)))) = $true))) => ((cOPEN @ (^[Y0 : a]: ($false))) = $true))),
% 1.04/0.92 inference(fool_elimination,[status(thm)],[f4])).
% 1.04/0.92 thf(f4,plain,(
% 1.04/0.92 ~(((cOPEN @ (^[X0 : a] : ($true))) & ! [X1 : (a > $o) > $o] : (! [X2 : a > $o] : ((X1 @ X2) => (cOPEN @ X2)) => (cOPEN @ (^[X3 : a] : (? [X4 : a > $o] : ((X1 @ X4) & (X4 @ X3)))))) & ! [X5 : a > $o,X6 : a > $o] : (((cOPEN @ X5) & (cOPEN @ X6)) => (cOPEN @ (^[X7 : a] : ((X6 @ X7) & (X5 @ X7)))))) => (cOPEN @ (^[X8 : a] : ($false))))),
% 1.04/0.92 inference(rectify,[status(thm)],[f2])).
% 1.04/0.92 thf(f2,negated_conjecture,(
% 1.04/0.92 ~(((cOPEN @ (^[X0 : a] : ($true))) & ! [X1 : (a > $o) > $o] : (! [X2 : a > $o] : ((X1 @ X2) => (cOPEN @ X2)) => (cOPEN @ (^[X2 : a] : (? [X3 : a > $o] : ((X1 @ X3) & (X3 @ X2)))))) & ! [X4 : a > $o,X5 : a > $o] : (((cOPEN @ X4) & (cOPEN @ X5)) => (cOPEN @ (^[X2 : a] : ((X5 @ X2) & (X4 @ X2)))))) => (cOPEN @ (^[X0 : a] : ($false))))),
% 1.04/0.92 inference(negated_conjecture,[status(cth)],[f1])).
% 1.04/0.92 thf(f1,conjecture,(
% 1.04/0.92 ((cOPEN @ (^[X0 : a] : ($true))) & ! [X1 : (a > $o) > $o] : (! [X2 : a > $o] : ((X1 @ X2) => (cOPEN @ X2)) => (cOPEN @ (^[X2 : a] : (? [X3 : a > $o] : ((X1 @ X3) & (X3 @ X2)))))) & ! [X4 : a > $o,X5 : a > $o] : (((cOPEN @ X4) & (cOPEN @ X5)) => (cOPEN @ (^[X2 : a] : ((X5 @ X2) & (X4 @ X2)))))) => (cOPEN @ (^[X0 : a] : ($false)))),
% 1.04/0.92 file('/export/starexec/sandbox2/tmp/tmp.89w8oXnglr/DTF2THF_9771.p',cTHM625_pme)).
% 1.04/0.92 thf(f13,plain,(
% 1.04/0.92 ((cOPEN @ (^[Y0 : a]: ($false))) != $true)),
% 1.04/0.92 inference(cnf_transformation,[status(thm)],[f10])).
% 1.04/0.92 % SZS output end Proof for DTF2THF_9771
% 1.04/0.92 % (9936)------------------------------
% 1.04/0.92 % (9936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.92 % (9936)Termination reason: Refutation
% 1.04/0.92
% 1.04/0.92 % (9936)Memory used [KB]: 5500
% 1.04/0.92 % (9936)Time elapsed: 0.008 s
% 1.04/0.92 % (9936)Instructions burned: 10 (million)
% 1.04/0.92 % (9936)------------------------------
% 1.04/0.92 % (9936)------------------------------
% 1.04/0.92 % (9928)Success in time 0.009 s
%------------------------------------------------------------------------------