%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO360^5 : 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 : n015.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 09:54:02 AM UTC 2026
% Result : Theorem 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 10 ~; 0 |; 9 &; 66 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
j: a > a ).
thf(func_def_2,type,
g: ( a > a ) > a > a ).
thf(func_def_3,type,
h: a > a ).
thf(func_def_4,type,
f: ( a > a ) > a > a ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK2: a ).
thf(func_def_11,type,
sK3: a ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f8]) ).
thf(f8,plain,
! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: a,X1: a > a] :
( ( g @ X1 @ X0 )
= ( f @ X1 @ X0 ) )
& ( ( f @ h )
!= ( g @ j ) )
& ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X1: a,X2: a > a] :
( ( f @ X2 @ X1 )
= ( g @ X2 @ X1 ) )
& ( ( f @ h )
!= ( g @ j ) )
& ! [X0: a] :
( ( h @ X0 )
= ( j @ X0 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ( f @ h )
!= ( g @ j ) )
& ! [X0: a] :
( ( h @ X0 )
= ( j @ X0 ) )
& ! [X1: a,X2: a > a] :
( ( f @ X2 @ X1 )
= ( g @ X2 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a] :
( ( h @ X0 )
= ( j @ X0 ) )
& ! [X1: a,X2: a > a] :
( ( f @ X2 @ X1 )
= ( g @ X2 @ X1 ) ) )
=> ( ( f @ h )
= ( g @ j ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) )
& ! [X1: a,X0: a > a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) ) )
=> ( ( f @ h )
= ( g @ j ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: a] :
( ( h @ X2 )
= ( j @ X2 ) )
& ! [X1: a,X0: a > a] :
( ( f @ X0 @ X1 )
= ( g @ X0 @ X1 ) ) )
=> ( ( f @ h )
= ( g @ j ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NGN5LuUnpA/DTF2THF_32552.p',cEDEC1) ).
thf(f14,plain,
( ( j @ sK3 )
!= ( h @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
h != j,
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
( ( g @ h @ sK2 )
!= ( g @ j @ sK2 ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X0: a,X1: a > a] :
( ( g @ X1 @ X0 )
= ( f @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f11,plain,
( ( f @ h @ sK2 )
!= ( g @ j @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO360^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % 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 14:28:46 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO360^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem EDEC1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : A version of EDEC from [Ben99] using = instead of LeibEq.
% 0.30/0.46
% 0.30/0.46 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0290 [Bro09]
% 0.30/0.46 % : EDEC1 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.3.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.30/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.30/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 1 &; 8 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.30/0.46 % Number of types : 1 ( 1 usr)
% 0.30/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(j,type,
% 0.30/0.46 j: a > a ).
% 0.30/0.46
% 0.30/0.46 thf(g,type,
% 0.30/0.46 g: ( a > a ) > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(h,type,
% 0.30/0.46 h: a > a ).
% 0.30/0.46
% 0.30/0.46 thf(f,type,
% 0.30/0.46 f: ( a > a ) > a > a ).
% 0.30/0.46
% 0.30/0.46 thf(cEDEC1,conjecture,
% 0.30/0.46 ( ( ! [X: a > a,Y: a] :
% 0.30/0.46 ( ( f @ X @ Y )
% 0.30/0.46 = ( g @ X @ Y ) )
% 0.30/0.46 & ! [Z: a] :
% 0.30/0.46 ( ( h @ Z )
% 0.30/0.46 = ( j @ Z ) ) )
% 0.30/0.46 => ( ( f @ h )
% 0.30/0.46 = ( g @ j ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 14:28:47 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NGN5LuUnpA/DTF2DTF32552.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(a_type,type,
% 1.45/1.27 a: $tType ).
% 1.45/1.27
% 1.45/1.27 thf(j,type,
% 1.45/1.27 j: a > a ).
% 1.45/1.27
% 1.45/1.27 thf(g,type,
% 1.45/1.27 g: ( a > a ) > a > a ).
% 1.45/1.27
% 1.45/1.27 thf(h,type,
% 1.45/1.27 h: a > a ).
% 1.45/1.27
% 1.45/1.27 thf(f,type,
% 1.45/1.27 f: ( a > a ) > a > a ).
% 1.45/1.27
% 1.45/1.27 thf(cEDEC1,conjecture,
% 1.45/1.27 ( ( ! [X: a > a,Y: a] :
% 1.45/1.27 ( ( f @ X @ Y )
% 1.45/1.27 = ( g @ X @ Y ) )
% 1.45/1.27 & ! [Z: a] :
% 1.45/1.27 ( ( h @ Z )
% 1.45/1.27 = ( j @ Z ) ) )
% 1.45/1.27 => ( ( f @ h )
% 1.45/1.27 = ( g @ j ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.28 % (32762)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_32552 for (3000ds/4Mi)
% 1.45/1.28 % (32762)Refutation not found, incomplete strategy
% 1.45/1.28 % (32762)------------------------------
% 1.45/1.28 % (32762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (32762)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (32762)Memory used [KB]: 5500
% 1.45/1.28 % (32762)Time elapsed: 0.002 s
% 1.45/1.28 % (32762)Instructions burned: 1 (million)
% 1.45/1.28 % (32762)------------------------------
% 1.45/1.28 % (32762)------------------------------
% 1.45/1.29 % (32761)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32552 for (3000ds/183Mi)
% 1.45/1.29 % (32763)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_32552 for (3000ds/27Mi)
% 1.45/1.29 % (32764)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32552 for (3000ds/2Mi)
% 1.45/1.29 % (32766)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_32552 for (3000ds/275Mi)
% 1.45/1.29 % (32767)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32552 for (3000ds/18Mi)
% 1.45/1.29 % (32765)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_32552 for (3000ds/2Mi)
% 1.45/1.29 % (32761)First to succeed.
% 1.45/1.29 % (32764)Instruction limit reached!
% 1.45/1.29 % (32764)------------------------------
% 1.45/1.29 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (32764)Termination reason: Unknown
% 1.45/1.29 % (32764)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (32764)Memory used [KB]: 5500
% 1.45/1.29 % (32764)Time elapsed: 0.004 s
% 1.45/1.29 % (32764)Instructions burned: 2 (million)
% 1.45/1.29 % (32764)------------------------------
% 1.45/1.29 % (32764)------------------------------
% 1.45/1.29 % (32765)Instruction limit reached!
% 1.45/1.29 % (32765)------------------------------
% 1.45/1.29 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (32765)Termination reason: Unknown
% 1.45/1.29 % (32765)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (32765)Memory used [KB]: 5500
% 1.45/1.29 % (32765)Time elapsed: 0.004 s
% 1.45/1.29 % (32765)Instructions burned: 2 (million)
% 1.45/1.29 % (32765)------------------------------
% 1.45/1.29 % (32765)------------------------------
% 1.45/1.29 % (32766)Refutation not found, incomplete strategy
% 1.45/1.29 % (32766)------------------------------
% 1.45/1.29 % (32766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (32766)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (32766)Memory used [KB]: 5500
% 1.45/1.29 % (32766)Time elapsed: 0.004 s
% 1.45/1.29 % (32766)Instructions burned: 1 (million)
% 1.45/1.29 % (32766)------------------------------
% 1.45/1.29 % (32766)------------------------------
% 1.45/1.29 % (32763)Refutation not found, incomplete strategy
% 1.45/1.29 % (32763)------------------------------
% 1.45/1.29 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (32763)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (32763)Memory used [KB]: 5500
% 1.45/1.29 % (32763)Time elapsed: 0.004 s
% 1.45/1.29 % (32763)Instructions burned: 2 (million)
% 1.45/1.29 % (32763)------------------------------
% 1.45/1.29 % (32763)------------------------------
% 1.45/1.29 % (32767)Also succeeded, but the first one will report.
% 1.45/1.29 % (301)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32552 for (2999ds/3Mi)
% 1.45/1.29 % (32761)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_32552
% 1.45/1.29 % SZS output start Proof for DTF2THF_32552
% 1.45/1.29 thf(type_def_5, type, a: $tType).
% 1.45/1.29 thf(func_def_0, type, a: $tType).
% 1.45/1.29 thf(func_def_1, type, j: a > a).
% 1.45/1.29 thf(func_def_2, type, g: (a > a) > a > a).
% 1.45/1.29 thf(func_def_3, type, h: a > a).
% 1.45/1.29 thf(func_def_4, type, f: (a > a) > a > a).
% 1.45/1.29 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.45/1.29 thf(func_def_10, type, sK2: a).
% 1.45/1.29 thf(func_def_11, type, sK3: a).
% 1.45/1.29 thf(f15,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f14,f8])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ( ! [X2 : a] : (((h @ X2) = (j @ X2))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ! [X0 : a,X1 : a > a] : ((g @ X1 @ X0) = (f @ X1 @ X0)) & ((f @ h) != (g @ j)) & ! [X2 : a] : ((h @ X2) = (j @ X2))),
% 1.45/1.29 inference(rectify,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 ! [X1 : a,X2 : a > a] : ((f @ X2 @ X1) = (g @ X2 @ X1)) & ((f @ h) != (g @ j)) & ! [X0 : a] : ((h @ X0) = (j @ X0))),
% 1.45/1.29 inference(flattening,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 ((f @ h) != (g @ j)) & (! [X0 : a] : ((h @ X0) = (j @ X0)) & ! [X1 : a,X2 : a > a] : ((f @ X2 @ X1) = (g @ X2 @ X1)))),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f4])).
% 1.45/1.29 thf(f4,plain,(
% 1.45/1.29 ~((! [X0 : a] : ((h @ X0) = (j @ X0)) & ! [X1 : a,X2 : a > a] : ((f @ X2 @ X1) = (g @ X2 @ X1))) => ((f @ h) = (g @ j)))),
% 1.45/1.29 inference(rectify,[status(thm)],[f2])).
% 1.45/1.29 thf(f2,negated_conjecture,(
% 1.45/1.29 ~((! [X2 : a] : ((h @ X2) = (j @ X2)) & ! [X1 : a,X0 : a > a] : ((f @ X0 @ X1) = (g @ X0 @ X1))) => ((f @ h) = (g @ j)))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.29 thf(f1,conjecture,(
% 1.45/1.29 (! [X2 : a] : ((h @ X2) = (j @ X2)) & ! [X1 : a,X0 : a > a] : ((f @ X0 @ X1) = (g @ X0 @ X1))) => ((f @ h) = (g @ j))),
% 1.45/1.29 file('/export/starexec/sandbox2/tmp/tmp.NGN5LuUnpA/DTF2THF_32552.p',cEDEC1)).
% 1.45/1.29 thf(f14,plain,(
% 1.45/1.29 ((j @ sK3) != (h @ sK3))),
% 1.45/1.29 inference(negative_extensionality,[status(thm)],[f13])).
% 1.45/1.29 thf(f13,plain,(
% 1.45/1.29 (h != j)),
% 1.45/1.29 inference(equality_resolution,[status(thm)],[f12])).
% 1.45/1.29 thf(f12,plain,(
% 1.45/1.29 ((g @ h @ sK2) != (g @ j @ sK2))),
% 1.45/1.29 inference(superposition,[status(thm)],[f11,f10])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ( ! [X0 : a,X1 : a > a] : (((g @ X1 @ X0) = (f @ X1 @ X0))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 ((f @ h @ sK2) != (g @ j @ sK2))),
% 1.45/1.29 inference(negative_extensionality,[status(thm)],[f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ((f @ h) != (g @ j))),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 % SZS output end Proof for DTF2THF_32552
% 1.45/1.29 % (32761)------------------------------
% 1.45/1.29 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (32761)Termination reason: Refutation
% 1.45/1.29
% 1.45/1.29 % (32761)Memory used [KB]: 5500
% 1.45/1.29 % (32761)Time elapsed: 0.004 s
% 1.45/1.29 % (32761)Instructions burned: 2 (million)
% 1.45/1.29 % (32761)------------------------------
% 1.45/1.29 % (32761)------------------------------
% 1.45/1.29 % (32760)Success in time 0.019 s
%------------------------------------------------------------------------------