%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO549^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:54:31 AM UTC 2026
% Result : Theorem 0.31s 1.33s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 62 ( 25 ~; 0 |; 0 &; 37 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 11 ^; 0 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
p: ( $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_1,type,
f: $o > $o ).
thf(func_def_2,type,
g: $o > $o ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ~ $true ) = $true ),
inference(forward_demodulation,[status(thm)],[f14,f12]) ).
thf(f12,plain,
( $true
= ( p @ f @ g ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( p
@ ^ [Y0: $o] : ( f @ Y0 )
@ g )
= $true ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( p
@ ^ [Y0: $o] :
( f
@ ~ ~ Y0 )
@ g ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( p
@ ^ [Y0: $o] :
( f
@ ~ ~ Y0 )
@ g ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( p
@ ^ [X0: $o] :
( f
@ ~ ~ X0 )
@ g ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( p
@ ^ [X0: $o] :
( f
@ ~ ~ X0 )
@ g ),
file('/export/starexec/sandbox2/tmp/tmp.IUAxmwGlJX/DTF2THF_3504.p',pfg) ).
thf(f14,plain,
( $true
= ( ~ ( p @ f @ g ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ~ ( p @ f
@ ^ [Y0: $o] : ( g @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ~ ( p @ f
@ ^ [Y0: $o] :
( g
@ ~ ~ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( p @ f
@ ^ [Y0: $o] :
( g
@ ~ ~ Y0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( p @ f
@ ^ [X0: $o] :
( g
@ ~ ~ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( p @ f
@ ^ [X0: $o] :
( g
@ ~ ~ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( p @ f
@ ^ [X0: $o] :
( g
@ ~ ~ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.IUAxmwGlJX/DTF2THF_3504.p',pfgc) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO549^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:34:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO549^1 : TPTP v9.2.1. Released v5.2.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : The eta double negation problem
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro11]
% 0.30/0.46 % Names : ETADN [Bro11]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 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 v5.3.0, 0.25 v5.2.0
% 0.30/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 3 typ; 0 def)
% 0.30/0.46 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.30/0.46 % Number of connectives : 10 ( 4 ~; 0 |; 0 &; 6 @)
% 0.30/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This higher-order problem is immediately solved if one removes
% 0.30/0.46 % double negations embedded inside terms and eta-normalizes.
% 0.30/0.46 % Otherwise, search may be required.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(p,type,
% 0.30/0.46 p: ( $o > $o ) > ( $o > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: $o > $o ).
% 0.30/0.46
% 0.30/0.46 thf(g,type,
% 0.30/0.46 g: $o > $o ).
% 0.30/0.46
% 0.30/0.46 thf(pfg,axiom,
% 0.30/0.46 ( p
% 0.30/0.46 @ ^ [X: $o] :
% 0.30/0.46 ( f
% 0.30/0.46 @ ~ ~ X )
% 0.30/0.46 @ g ) ).
% 0.30/0.46
% 0.30/0.46 thf(pfgc,conjecture,
% 0.30/0.46 ( p @ f
% 0.30/0.46 @ ^ [X: $o] :
% 0.30/0.46 ( g
% 0.30/0.46 @ ~ ~ X ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 14:34:07 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.IUAxmwGlJX/DTF2DTF3504.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(p,type,
% 0.31/1.31 p: ( $o > $o ) > ( $o > $o ) > $o ).
% 0.31/1.31
% 0.31/1.31 thf(f,type,
% 0.31/1.31 f: $o > $o ).
% 0.31/1.31
% 0.31/1.31 thf(g,type,
% 0.31/1.31 g: $o > $o ).
% 0.31/1.31
% 0.31/1.31 thf(pfg,axiom,
% 0.31/1.31 ( p
% 0.31/1.31 @ ^ [X: $o] :
% 0.31/1.31 ( f
% 0.31/1.31 @ ~ ~ X )
% 0.31/1.31 @ g ) ).
% 0.31/1.31
% 0.31/1.31 thf(pfgc,conjecture,
% 0.31/1.31 ( p @ f
% 0.31/1.31 @ ^ [X: $o] :
% 0.31/1.31 ( g
% 0.31/1.31 @ ~ ~ X ) ) ).
% 0.31/1.32 ------------------------
% 0.31/1.33 % (3725)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3504 for (2999ds/2Mi)
% 0.31/1.33 % (3725)First to succeed.
% 0.31/1.33 % (3725)Refutation found. Thanks to Tanya!
% 0.31/1.33 % SZS status Theorem for DTF2THF_3504
% 0.31/1.33 % SZS output start Proof for DTF2THF_3504
% 0.31/1.33 thf(func_def_0, type, p: ($o > $o) > ($o > $o) > $o).
% 0.31/1.33 thf(func_def_1, type, f: $o > $o).
% 0.31/1.33 thf(func_def_2, type, g: $o > $o).
% 0.31/1.33 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 0.31/1.33 thf(f17,plain,(
% 0.31/1.33 $false),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 0.31/1.33 thf(f16,plain,(
% 0.31/1.33 ($false = $true)),
% 0.31/1.33 inference(boolean_simplification,[status(thm)],[f15])).
% 0.31/1.33 thf(f15,plain,(
% 0.31/1.33 ((~ $true) = $true)),
% 0.31/1.33 inference(forward_demodulation,[status(thm)],[f14,f12])).
% 0.31/1.33 thf(f12,plain,(
% 0.31/1.33 ($true = (p @ f @ g))),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f11])).
% 0.31/1.33 thf(f11,plain,(
% 0.31/1.33 ((p @ (^[Y0 : $o]: (f @ Y0)) @ g) = $true)),
% 0.31/1.33 inference(boolean_simplification,[status(thm)],[f9])).
% 0.31/1.33 thf(f9,plain,(
% 0.31/1.33 ($true = (p @ (^[Y0 : $o]: (f @ (~ (~ Y0)))) @ g))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f8])).
% 0.31/1.33 thf(f8,plain,(
% 0.31/1.33 ($true = (p @ (^[Y0 : $o]: (f @ (~ (~ Y0)))) @ g))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 0.31/1.33 thf(f7,plain,(
% 0.31/1.33 (p @ (^[X0 : $o] : (f @ ~~X0)) @ g)),
% 0.31/1.33 inference(rectify,[status(thm)],[f1])).
% 0.31/1.33 thf(f1,axiom,(
% 0.31/1.33 (p @ (^[X0 : $o] : (f @ ~~X0)) @ g)),
% 0.31/1.33 file('/export/starexec/sandbox2/tmp/tmp.IUAxmwGlJX/DTF2THF_3504.p',pfg)).
% 0.31/1.33 thf(f14,plain,(
% 0.31/1.33 ($true = (~ (p @ f @ g)))),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f13])).
% 0.31/1.33 thf(f13,plain,(
% 0.31/1.33 ((~ (p @ f @ (^[Y0 : $o]: (g @ Y0)))) = $true)),
% 0.31/1.33 inference(boolean_simplification,[status(thm)],[f10])).
% 0.31/1.33 thf(f10,plain,(
% 0.31/1.33 ((~ (p @ f @ (^[Y0 : $o]: (g @ (~ (~ Y0)))))) = $true)),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 0.31/1.33 thf(f6,plain,(
% 0.31/1.33 ((~ (p @ f @ (^[Y0 : $o]: (g @ (~ (~ Y0)))))) = $true)),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 0.31/1.33 thf(f5,plain,(
% 0.31/1.33 ~(p @ f @ (^[X0 : $o] : (g @ ~~X0)))),
% 0.31/1.33 inference(rectify,[status(thm)],[f3])).
% 0.31/1.33 thf(f3,negated_conjecture,(
% 0.31/1.33 ~(p @ f @ (^[X0 : $o] : (g @ ~~X0)))),
% 0.31/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 0.31/1.33 thf(f2,conjecture,(
% 0.31/1.33 (p @ f @ (^[X0 : $o] : (g @ ~~X0)))),
% 0.31/1.33 file('/export/starexec/sandbox2/tmp/tmp.IUAxmwGlJX/DTF2THF_3504.p',pfgc)).
% 0.31/1.33 % SZS output end Proof for DTF2THF_3504
% 0.31/1.33 % (3725)------------------------------
% 0.31/1.33 % (3725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (3725)Termination reason: Refutation
% 0.31/1.33
% 0.31/1.33 % (3725)Memory used [KB]: 5373
% 0.31/1.33 % (3725)Time elapsed: 0.002 s
% 0.31/1.33 % (3725)Instructions burned: 1 (million)
% 0.31/1.33 % (3725)------------------------------
% 0.31/1.33 % (3725)------------------------------
% 0.31/1.33 % (3720)Success in time 0.013 s
%------------------------------------------------------------------------------