%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU921^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:37:45 AM UTC 2026
% Result : Theorem 1.45s 1.25s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 9 ~; 2 |; 1 &; 40 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 7 ^; 13 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
h: $i > $i ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f12,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( f @ X0 )
= ( h @ ( g @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ( h @ X1 )
= ( f @ X0 ) )
| ( ( g @ X0 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( ( h @ X1 )
= ( f @ X0 ) )
| ( ( g @ X0 )
!= X1 ) )
& ( f
!= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( f
= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( f
= ( ^ [X2: $i] : ( h @ ( g @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( f
= ( ^ [X0: $i] : ( h @ ( g @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( f
= ( ^ [X0: $i] : ( h @ ( g @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CFu2yDgKUD/DTF2THF_22618.p',cTHM588LEM2_pme) ).
thf(f11,plain,
( ( h @ ( g @ sK2 ) )
!= ( f @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) )
@ sK2 )
!= ( f @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( f
!= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU921^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 07:36:55 EST 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.33 ---- Original DTF file ---
% 0.07/0.33 thf(spec,logic,$$dhol).
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 % File : SEU921^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.33 % Domain : Set Theory (Functions)
% 0.07/0.33 % Problem : TPS problem THM588LEM2
% 0.07/0.33 % Version : Especial.
% 0.07/0.33 % English : Another possible lemma for THM588, for manipulating composite
% 0.07/0.33 % functions.
% 0.07/0.33
% 0.07/0.33 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.33 % Source : [Bro09]
% 0.07/0.33 % Names : tps_0117 [Bro09]
% 0.07/0.33 % : THM588LEM2 [TPS]
% 0.07/0.33
% 0.07/0.33 % Status : Theorem
% 0.07/0.33 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.07/0.33 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.07/0.33 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.07/0.33 % Maximal formula atoms : 3 ( 3 avg)
% 0.07/0.33 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 5 @)
% 0.07/0.33 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.07/0.33 % Maximal formula depth : 5 ( 5 avg)
% 0.07/0.33 % Number of types : 1 ( 0 usr)
% 0.07/0.33 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.07/0.33 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.07/0.33 % Number of variables : 3 ( 1 ^; 2 !; 0 ?; 3 :)
% 0.07/0.33 % SPC : TH0_THM_EQU_NAR
% 0.07/0.33
% 0.07/0.33 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.33 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.33 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.33 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.33 % : Polymorphic definitions expanded.
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 thf(f,type,
% 0.07/0.33 f: $i > $i ).
% 0.07/0.33
% 0.07/0.33 thf(g,type,
% 0.07/0.33 g: $i > $i ).
% 0.07/0.33
% 0.07/0.33 thf(h,type,
% 0.07/0.33 h: $i > $i ).
% 0.07/0.33
% 0.07/0.33 thf(cTHM588LEM2_pme,conjecture,
% 0.07/0.33 ( ! [Xx: $i,Xy: $i] :
% 0.07/0.33 ( ( ( g @ Xx )
% 0.07/0.33 = Xy )
% 0.07/0.33 => ( ( h @ Xy )
% 0.07/0.33 = ( f @ Xx ) ) )
% 0.07/0.33 => ( ( ^ [Xx: $i] : ( h @ ( g @ Xx ) ) )
% 0.07/0.33 = f ) ) ).
% 0.07/0.33
% 0.07/0.33 %------------------------------------------------------------------------------
% 0.07/0.33 ------------------------
% 1.45/1.22 ---- Embedded in THF ---
% 1.45/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.22 %%% Generated on Tue Feb 24 07:36:56 EST 2026
% 1.45/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.22 %%% Logic specification used:
% 1.45/1.22 %%% thf(spec, logic, $$dhol).
% 1.45/1.22
% 1.45/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CFu2yDgKUD/DTF2DTF22618.p
% See solution above
% 1.45/1.22 ------------------------
% 1.45/1.23 ---- Cleaned THF ---
% 1.45/1.23 thf(f,type,
% 1.45/1.23 f: $i > $i ).
% 1.45/1.23
% 1.45/1.23 thf(g,type,
% 1.45/1.23 g: $i > $i ).
% 1.45/1.23
% 1.45/1.23 thf(h,type,
% 1.45/1.23 h: $i > $i ).
% 1.45/1.23
% 1.45/1.23 thf(cTHM588LEM2_pme,conjecture,
% 1.45/1.23 ( ! [Xx: $i,Xy: $i] :
% 1.45/1.23 ( ( ( g @ Xx )
% 1.45/1.23 = Xy )
% 1.45/1.23 => ( ( h @ Xy )
% 1.45/1.23 = ( f @ Xx ) ) )
% 1.45/1.23 => ( ( ^ [Xx: $i] : ( h @ ( g @ Xx ) ) )
% 1.45/1.23 = f ) ) ).
% 1.45/1.23 ------------------------
% 1.45/1.25 % (22735)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_22618 for (3000ds/27Mi)
% 1.45/1.25 % (22733)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22618 for (3000ds/183Mi)
% 1.45/1.25 % (22734)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_22618 for (3000ds/4Mi)
% 1.45/1.25 % (22736)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22618 for (3000ds/2Mi)
% 1.45/1.25 % (22738)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_22618 for (3000ds/275Mi)
% 1.45/1.25 % (22737)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_22618 for (3000ds/2Mi)
% 1.45/1.25 % (22739)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22618 for (3000ds/18Mi)
% 1.45/1.25 % (22733)First to succeed.
% 1.45/1.25 % (22737)Instruction limit reached!
% 1.45/1.25 % (22737)------------------------------
% 1.45/1.25 % (22737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.25 % (22737)Termination reason: Unknown
% 1.45/1.25 % (22737)Termination phase: Saturation
% 1.45/1.25
% 1.45/1.25 % (22737)Memory used [KB]: 5500
% 1.45/1.25 % (22737)Time elapsed: 0.003 s
% 1.45/1.25 % (22737)Instructions burned: 2 (million)
% 1.45/1.25 % (22734)Also succeeded, but the first one will report.
% 1.45/1.25 % (22737)------------------------------
% 1.45/1.25 % (22737)------------------------------
% 1.45/1.25 % (22735)Also succeeded, but the first one will report.
% 1.45/1.25 % (22733)Refutation found. Thanks to Tanya!
% 1.45/1.25 % SZS status Theorem for DTF2THF_22618
% 1.45/1.25 % SZS output start Proof for DTF2THF_22618
% 1.45/1.25 thf(func_def_0, type, f: $i > $i).
% 1.45/1.25 thf(func_def_1, type, g: $i > $i).
% 1.45/1.25 thf(func_def_2, type, h: $i > $i).
% 1.45/1.25 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.45/1.25 thf(f12,plain,(
% 1.45/1.25 $false),
% 1.45/1.25 inference(subsumption_resolution,[status(thm)],[f11,f9])).
% 1.45/1.25 thf(f9,plain,(
% 1.45/1.25 ( ! [X0 : $i] : (((f @ X0) = (h @ (g @ X0)))) )),
% 1.45/1.25 inference(equality_resolution,[status(thm)],[f8])).
% 1.45/1.25 thf(f8,plain,(
% 1.45/1.25 ( ! [X0 : $i,X1 : $i] : (((h @ X1) = (f @ X0)) | ((g @ X0) != X1)) )),
% 1.45/1.25 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.25 thf(f6,plain,(
% 1.45/1.25 ! [X0 : $i,X1 : $i] : (((h @ X1) = (f @ X0)) | ((g @ X0) != X1)) & (f != (^[Y0 : $i]: (h @ (g @ Y0))))),
% 1.45/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.25 thf(f5,plain,(
% 1.45/1.25 ~(! [X0 : $i,X1 : $i] : (((g @ X0) = X1) => ((h @ X1) = (f @ X0))) => (f = (^[Y0 : $i]: (h @ (g @ Y0)))))),
% 1.45/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.25 thf(f4,plain,(
% 1.45/1.25 ~(! [X0 : $i,X1 : $i] : (((g @ X0) = X1) => ((h @ X1) = (f @ X0))) => (f = (^[X2 : $i] : (h @ (g @ X2)))))),
% 1.45/1.25 inference(rectify,[status(thm)],[f2])).
% 1.45/1.25 thf(f2,negated_conjecture,(
% 1.45/1.25 ~(! [X0 : $i,X1 : $i] : (((g @ X0) = X1) => ((h @ X1) = (f @ X0))) => (f = (^[X0 : $i] : (h @ (g @ X0)))))),
% 1.45/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.25 thf(f1,conjecture,(
% 1.45/1.25 ! [X0 : $i,X1 : $i] : (((g @ X0) = X1) => ((h @ X1) = (f @ X0))) => (f = (^[X0 : $i] : (h @ (g @ X0))))),
% 1.45/1.25 file('/export/starexec/sandbox/tmp/tmp.CFu2yDgKUD/DTF2THF_22618.p',cTHM588LEM2_pme)).
% 1.45/1.25 thf(f11,plain,(
% 1.45/1.25 ((h @ (g @ sK2)) != (f @ sK2))),
% 1.45/1.25 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.45/1.25 thf(f10,plain,(
% 1.45/1.25 (((^[Y0 : $i]: (h @ (g @ Y0))) @ sK2) != (f @ sK2))),
% 1.45/1.25 inference(negative_extensionality,[status(thm)],[f7])).
% 1.45/1.25 thf(f7,plain,(
% 1.45/1.25 (f != (^[Y0 : $i]: (h @ (g @ Y0))))),
% 1.45/1.25 inference(cnf_transformation,[status(thm)],[f6])).
% 1.45/1.25 % SZS output end Proof for DTF2THF_22618
% 1.45/1.25 % (22733)------------------------------
% 1.45/1.25 % (22733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.25 % (22733)Termination reason: Refutation
% 1.45/1.25
% 1.45/1.25 % (22733)Memory used [KB]: 5500
% 1.45/1.25 % (22733)Time elapsed: 0.003 s
% 1.45/1.25 % (22733)Instructions burned: 1 (million)
% 1.45/1.25 % (22733)------------------------------
% 1.45/1.25 % (22733)------------------------------
% 1.45/1.25 % (22732)Success in time 0.017 s
%------------------------------------------------------------------------------