%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN996^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:51:42 AM UTC 2026
% Result : Theorem 0.30s 1.23s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 71 ( 9 ~; 0 |; 2 &; 54 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 16 !; 12 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
r: $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(func_def_5,type,
sK1: ( $i > $i ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true != $true,
inference(superposition,[status(thm)],[f10,f11]) ).
thf(f11,plain,
! [X0: $i] :
( ( r @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( r @ X0 @ ( sK0 @ X0 ) )
= $true )
& ! [X2: $i > $i] :
( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( r @ X0 @ X1 )
= $true )
=> ( ( r @ X0 @ ( sK0 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X2: $i > $i] :
( ? [X3: $i] :
( ( r @ X3 @ ( X2 @ X3 ) )
!= $true )
=> ( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 @ X1 )
= $true )
& ! [X2: $i > $i] :
? [X3: $i] :
( ( r @ X3 @ ( X2 @ X3 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( r @ X0 @ X1 )
= $true )
=> ? [X2: $i > $i] :
! [X3: $i] :
( ( r @ X3 @ ( X2 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 )
=> ? [X2: $i > $i] :
! [X3: $i] : ( r @ X3 @ ( X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 )
=> ? [X2: $i > $i] :
! [X0: $i] : ( r @ X0 @ ( X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 )
=> ? [X2: $i > $i] :
! [X0: $i] : ( r @ X0 @ ( X2 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z7IqIVT9dr/DTF2THF_24922.p',conj) ).
thf(f10,plain,
! [X2: $i > $i] :
( ( r @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN996^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n001.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 14:22:05 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYN996^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : Test for naive Skolemization
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.30/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Ben09]
% 0.30/0.46 % Names : Example 4 [BB05]
% 0.30/0.46 % : choice2 [Bro09]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % : Without choice : CounterSatisfiable
% 0.30/0.46 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 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, 0.50 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.33 v4.0.1, 1.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 5 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(r_decl,type,
% 0.30/0.46 r: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(conj,conjecture,
% 0.30/0.46 ( ! [X: $i] :
% 0.30/0.46 ? [Y: $i] : ( r @ X @ Y )
% 0.30/0.46 => ? [F: $i > $i] :
% 0.30/0.46 ! [X: $i] : ( r @ X @ ( F @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.30/1.20 ---- Embedded in THF ---
% 0.30/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.20 %%% Generated on Tue Feb 24 14:22:06 EST 2026
% 0.30/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.20 %%% Logic specification used:
% 0.30/1.20 %%% thf(spec, logic, $$dhol).
% 0.30/1.20
% 0.30/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Z7IqIVT9dr/DTF2DTF24922.p
% See solution above
% 0.30/1.20 ------------------------
% 0.30/1.21 ---- Cleaned THF ---
% 0.30/1.21 thf(r_decl,type,
% 0.30/1.21 r: $i > $i > $o ).
% 0.30/1.21
% 0.30/1.21 thf(conj,conjecture,
% 0.30/1.21 ( ! [X: $i] :
% 0.30/1.21 ? [Y: $i] : ( r @ X @ Y )
% 0.30/1.21 => ? [F: $i > $i] :
% 0.30/1.21 ! [X: $i] : ( r @ X @ ( F @ X ) ) ) ).
% 0.30/1.21 ------------------------
% 0.30/1.23 % (25211)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_24922 for (3000ds/4Mi)
% 0.30/1.23 % (25212)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_24922 for (3000ds/27Mi)
% 0.30/1.23 % (25211)First to succeed.
% 0.30/1.23 % (25212)Also succeeded, but the first one will report.
% 0.30/1.23 % (25211)Refutation found. Thanks to Tanya!
% 0.30/1.23 % SZS status Theorem for DTF2THF_24922
% 0.30/1.23 % SZS output start Proof for DTF2THF_24922
% 0.30/1.23 thf(func_def_0, type, r: $i > $i > $o).
% 0.30/1.23 thf(func_def_4, type, sK0: $i > $i).
% 0.30/1.23 thf(func_def_5, type, sK1: ($i > $i) > $i).
% 0.30/1.23 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 0.30/1.23 thf(f16,plain,(
% 0.30/1.23 $false),
% 0.30/1.23 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 0.30/1.23 thf(f14,plain,(
% 0.30/1.23 ($true != $true)),
% 0.30/1.23 inference(superposition,[status(thm)],[f10,f11])).
% 0.30/1.23 thf(f11,plain,(
% 0.30/1.23 ( ! [X0 : $i] : (((r @ X0 @ (sK0 @ X0)) = $true)) )),
% 0.30/1.23 inference(cnf_transformation,[status(thm)],[f9])).
% 0.30/1.23 thf(f9,plain,(
% 0.30/1.23 ! [X0 : $i] : ((r @ X0 @ (sK0 @ X0)) = $true) & ! [X2 : $i > $i] : ((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)),
% 0.30/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 0.30/1.23 thf(f7,plain,(
% 0.30/1.23 ! [X0 : $i] : (? [X1 : $i] : ((r @ X0 @ X1) = $true) => ((r @ X0 @ (sK0 @ X0)) = $true))),
% 0.30/1.23 introduced(definition,[],[choice_axiom])).
% 0.30/1.23 thf(f8,plain,(
% 0.30/1.23 ! [X2 : $i > $i] : (? [X3 : $i] : ((r @ X3 @ (X2 @ X3)) != $true) => ((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true))),
% 0.30/1.23 introduced(definition,[],[choice_axiom])).
% 0.30/1.23 thf(f6,plain,(
% 0.30/1.23 ! [X0 : $i] : ? [X1 : $i] : ((r @ X0 @ X1) = $true) & ! [X2 : $i > $i] : ? [X3 : $i] : ((r @ X3 @ (X2 @ X3)) != $true)),
% 0.30/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 0.30/1.23 thf(f5,plain,(
% 0.30/1.23 ~(! [X0 : $i] : ? [X1 : $i] : ((r @ X0 @ X1) = $true) => ? [X2 : $i > $i] : ! [X3 : $i] : ((r @ X3 @ (X2 @ X3)) = $true))),
% 0.30/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 0.30/1.23 thf(f4,plain,(
% 0.30/1.23 ~(! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : $i > $i] : ! [X3 : $i] : (r @ X3 @ (X2 @ X3)))),
% 0.30/1.23 inference(rectify,[status(thm)],[f2])).
% 0.30/1.23 thf(f2,negated_conjecture,(
% 0.30/1.23 ~(! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : $i > $i] : ! [X0 : $i] : (r @ X0 @ (X2 @ X0)))),
% 0.30/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 0.30/1.23 thf(f1,conjecture,(
% 0.30/1.23 ! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1) => ? [X2 : $i > $i] : ! [X0 : $i] : (r @ X0 @ (X2 @ X0))),
% 0.30/1.23 file('/export/starexec/sandbox/tmp/tmp.Z7IqIVT9dr/DTF2THF_24922.p',conj)).
% 0.30/1.23 thf(f10,plain,(
% 0.30/1.23 ( ! [X2 : $i > $i] : (((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)) )),
% 0.30/1.23 inference(cnf_transformation,[status(thm)],[f9])).
% 0.30/1.23 % SZS output end Proof for DTF2THF_24922
% 0.30/1.23 % (25211)------------------------------
% 0.30/1.23 % (25211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.23 % (25211)Termination reason: Refutation
% 0.30/1.23
% 0.30/1.23 % (25211)Memory used [KB]: 5500
% 0.30/1.23 % (25211)Time elapsed: 0.002 s
% 0.30/1.23 % (25211)Instructions burned: 1 (million)
% 0.30/1.23 % (25211)------------------------------
% 0.30/1.23 % (25211)------------------------------
% 0.30/1.23 % (25209)Success in time 0.011 s
%------------------------------------------------------------------------------