%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO009^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:53:07 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 8 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 30 ( 6 ~; 0 |; 1 &; 19 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 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 : 6 ( 6 ^; 0 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
p: ( $i > $i ) > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
$true != $true,
inference(superposition,[status(thm)],[f8,f9]) ).
thf(f9,plain,
( ( p @ f )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( p @ f )
!= $true )
& ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true )
=> ( ( p @ f )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( p @ f ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( p @ f ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( p @ f ) ),
file('/export/starexec/sandbox2/tmp/tmp.hwQV8iTbWV/DTF2THF_15993.p',conj) ).
thf(f8,plain,
( ( p @ f )
!= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO009^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n009.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 14:21:10 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
% 0.25/0.46 ---- Original DTF file ---
% 0.25/0.46 thf(spec,logic,$$dhol).
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 % File : SYO009^1 : TPTP v9.2.1. Released v3.7.0.
% 0.25/0.46 % Domain : Syntactic
% 0.25/0.46 % Problem : Eta-equality using Leibniz equality
% 0.25/0.46 % Version : Especial.
% 0.25/0.46 % English :
% 0.25/0.46
% 0.25/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.25/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.25/0.46 % Source : [Ben09]
% 0.25/0.46 % Names : Example 12 [BB05]
% 0.25/0.46
% 0.25/0.46 % Status : Theorem
% 0.25/0.46 % : Without eta extensionality : CounterSatisfiable
% 0.25/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v3.7.0
% 0.25/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.25/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.25/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.25/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 3 @)
% 0.25/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.25/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.25/0.46 % Number of types : 2 ( 0 usr)
% 0.25/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.25/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.25/0.46 % Number of variables : 1 ( 1 ^; 0 !; 0 ?; 1 :)
% 0.25/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.25/0.46
% 0.25/0.46 % Comments :
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 thf(p,type,
% 0.25/0.46 p: ( $i > $i ) > $o ).
% 0.25/0.46
% 0.25/0.46 thf(f,type,
% 0.25/0.46 f: $i > $i ).
% 0.25/0.46
% 0.25/0.46 thf(conj,conjecture,
% 0.25/0.46 ( ( p
% 0.25/0.46 @ ^ [X: $i] : ( f @ X ) )
% 0.25/0.46 => ( p @ f ) ) ).
% 0.25/0.46
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:21:11 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.hwQV8iTbWV/DTF2DTF15993.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(p,type,
% 1.48/1.26 p: ( $i > $i ) > $o ).
% 1.48/1.26
% 1.48/1.26 thf(f,type,
% 1.48/1.26 f: $i > $i ).
% 1.48/1.26
% 1.48/1.26 thf(conj,conjecture,
% 1.48/1.26 ( ( p
% 1.48/1.26 @ ^ [X: $i] : ( f @ X ) )
% 1.48/1.26 => ( p @ f ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (16109)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15993 for (2999ds/27Mi)
% 1.48/1.28 % (16108)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15993 for (2999ds/4Mi)
% 1.48/1.28 % (16109)First to succeed.
% 1.48/1.28 % (16108)Also succeeded, but the first one will report.
% 1.48/1.28 % (16109)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_15993
% 1.48/1.28 % SZS output start Proof for DTF2THF_15993
% 1.48/1.28 thf(func_def_0, type, p: ($i > $i) > $o).
% 1.48/1.28 thf(func_def_1, type, f: $i > $i).
% 1.48/1.28 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.48/1.28 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f8,f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ((p @ f) = $true)),
% 1.48/1.28 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ((p @ f) != $true) & ((p @ (^[Y0 : $i]: (f @ Y0))) = $true)),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~(((p @ (^[Y0 : $i]: (f @ Y0))) = $true) => ((p @ f) = $true))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~((p @ (^[X0 : $i] : (f @ X0))) => (p @ f))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~((p @ (^[X0 : $i] : (f @ X0))) => (p @ f))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 (p @ (^[X0 : $i] : (f @ X0))) => (p @ f)),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.hwQV8iTbWV/DTF2THF_15993.p',conj)).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ((p @ f) != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_15993
% 1.48/1.28 % (16109)------------------------------
% 1.48/1.28 % (16109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (16109)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (16109)Memory used [KB]: 5500
% 1.48/1.28 % (16109)Time elapsed: 0.002 s
% 1.48/1.28 % (16109)Instructions burned: 1 (million)
% 1.48/1.28 % (16109)------------------------------
% 1.48/1.28 % (16109)------------------------------
% 1.48/1.28 % (16106)Success in time 0.004 s
%------------------------------------------------------------------------------