%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO236^5 : 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 : n007.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 09:53:44 AM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 52 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 19 ~; 17 |; 1 &; 36 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
g: b > a ).
thf(func_def_3,type,
f: b > a ).
thf(func_def_9,type,
sK1: b ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f38,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f15,f34,f37]) ).
thf(f37,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( g @ sK1 )
!= ( g @ sK1 ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f16,f11]) ).
thf(f11,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f10]) ).
thf(f10,definition,
( spl0_1
<=> ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( g @ sK1 )
!= ( f @ sK1 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
f != g,
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( f != g )
& ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
| ! [X1: ( b > a ) > $o] :
( ( ( X1 @ g )
= $true )
| ( $true
!= ( X1 @ f ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
| ! [X1: ( b > a ) > $o] :
( ( $true
= ( X1 @ f ) )
=> ( ( X1 @ g )
= $true ) ) )
=> ( f = g ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
| ! [X1: ( b > a ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( f = g ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: b] :
( ( f @ X1 )
= ( g @ X1 ) )
| ! [X0: ( b > a ) > $o] :
( ( X0 @ f )
=> ( X0 @ g ) ) )
=> ( f = g ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: b] :
( ( f @ X1 )
= ( g @ X1 ) )
| ! [X0: ( b > a ) > $o] :
( ( X0 @ f )
=> ( X0 @ g ) ) )
=> ( f = g ) ),
file('/export/starexec/sandbox2/tmp/tmp.tpNU1h5bjF/DTF2THF_16562.p',cTHM504) ).
thf(f34,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f33]) ).
thf(f33,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f19,f8]) ).
thf(f19,plain,
( ( f = g )
| ~ spl0_2 ),
inference(leibniz_equality_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: ( b > a ) > $o] :
( ( $true
!= ( X1 @ f ) )
| ( ( X1 @ g )
= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl0_2
<=> ! [X1: ( b > a ) > $o] :
( ( ( X1 @ g )
= $true )
| ( $true
!= ( X1 @ f ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f15,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f7,f13,f10]) ).
thf(f7,plain,
! [X0: b,X1: ( b > a ) > $o] :
( ( ( X1 @ g )
= $true )
| ( $true
!= ( X1 @ f ) )
| ( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO236^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n007.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 14:25:53 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO236^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0774 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.47 % Number of connectives : 7 ( 0 ~; 1 |; 0 &; 4 @)
% 0.19/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.47 % Number of types : 3 ( 2 usr)
% 0.19/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.47 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(b_type,type,
% 0.19/0.47 b: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(a_type,type,
% 0.19/0.47 a: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(g,type,
% 0.19/0.47 g: b > a ).
% 0.19/0.47
% 0.19/0.47 thf(f,type,
% 0.19/0.47 f: b > a ).
% 0.19/0.47
% 0.19/0.47 thf(cTHM504,conjecture,
% 0.19/0.47 ( ( ! [Q: ( b > a ) > $o] :
% 0.19/0.47 ( ( Q @ f )
% 0.19/0.47 => ( Q @ g ) )
% 0.19/0.47 | ! [Xx: b] :
% 0.19/0.47 ( ( f @ Xx )
% 0.19/0.47 = ( g @ Xx ) ) )
% 0.19/0.47 => ( f = g ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.42/1.28 ---- Embedded in THF ---
% 1.42/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.28 %%% Generated on Tue Feb 24 14:25:54 EST 2026
% 1.42/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.28 %%% Logic specification used:
% 1.42/1.28 %%% thf(spec, logic, $$dhol).
% 1.42/1.28
% 1.42/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tpNU1h5bjF/DTF2DTF16562.p
% See solution above
% 1.42/1.28 ------------------------
% 1.42/1.29 ---- Cleaned THF ---
% 1.42/1.29 thf(b_type,type,
% 1.42/1.29 b: $tType ).
% 1.42/1.29
% 1.42/1.29 thf(a_type,type,
% 1.42/1.29 a: $tType ).
% 1.42/1.29
% 1.42/1.29 thf(g,type,
% 1.42/1.29 g: b > a ).
% 1.42/1.29
% 1.42/1.29 thf(f,type,
% 1.42/1.29 f: b > a ).
% 1.42/1.29
% 1.42/1.29 thf(cTHM504,conjecture,
% 1.42/1.29 ( ( ! [Q: ( b > a ) > $o] :
% 1.42/1.29 ( ( Q @ f )
% 1.42/1.29 => ( Q @ g ) )
% 1.42/1.29 | ! [Xx: b] :
% 1.42/1.29 ( ( f @ Xx )
% 1.42/1.29 = ( g @ Xx ) ) )
% 1.42/1.29 => ( f = g ) ) ).
% 1.42/1.29 ------------------------
% 1.62/1.30 % (16731)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_16562 for (2999ds/4Mi)
% 1.62/1.30 % (16733)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16562 for (2999ds/2Mi)
% 1.62/1.31 % (16730)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16562 for (2999ds/183Mi)
% 1.62/1.31 % (16733)Instruction limit reached!
% 1.62/1.31 % (16733)------------------------------
% 1.62/1.31 % (16733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16733)Termination reason: Unknown
% 1.62/1.31 % (16733)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (16733)Memory used [KB]: 5500
% 1.62/1.31 % (16733)Time elapsed: 0.002 s
% 1.62/1.31 % (16733)Instructions burned: 2 (million)
% 1.62/1.31 % (16733)------------------------------
% 1.62/1.31 % (16733)------------------------------
% 1.62/1.31 % (16731)First to succeed.
% 1.62/1.31 % (16730)Also succeeded, but the first one will report.
% 1.62/1.31 % (16731)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_16562
% 1.62/1.31 % SZS output start Proof for DTF2THF_16562
% 1.62/1.31 thf(type_def_5, type, b: $tType).
% 1.62/1.31 thf(type_def_6, type, a: $tType).
% 1.62/1.31 thf(func_def_0, type, b: $tType).
% 1.62/1.31 thf(func_def_1, type, a: $tType).
% 1.62/1.31 thf(func_def_2, type, g: b > a).
% 1.62/1.31 thf(func_def_3, type, f: b > a).
% 1.62/1.31 thf(func_def_9, type, sK1: b).
% 1.62/1.31 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.31 thf(f38,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(avatar_sat_refutation,[status(thm)],[f15,f34,f37])).
% 1.62/1.31 thf(f37,plain,(
% 1.62/1.31 ~spl0_1),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.62/1.31 thf(f36,plain,(
% 1.62/1.31 $false | ~spl0_1),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.62/1.31 thf(f35,plain,(
% 1.62/1.31 ((g @ sK1) != (g @ sK1)) | ~spl0_1),
% 1.62/1.31 inference(superposition,[status(thm)],[f16,f11])).
% 1.62/1.31 thf(f11,plain,(
% 1.62/1.31 ( ! [X0 : b] : (((f @ X0) = (g @ X0))) ) | ~spl0_1),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f10])).
% 1.62/1.31 thf(f10,definition,(
% 1.62/1.31 spl0_1 <=> ! [X0 : b] : ((f @ X0) = (g @ X0))),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.62/1.31 thf(f16,plain,(
% 1.62/1.31 ((g @ sK1) != (f @ sK1))),
% 1.62/1.31 inference(negative_extensionality,[status(thm)],[f8])).
% 1.62/1.31 thf(f8,plain,(
% 1.62/1.31 (f != g)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.62/1.31 thf(f6,plain,(
% 1.62/1.31 (f != g) & (! [X0 : b] : ((f @ X0) = (g @ X0)) | ! [X1 : (b > a) > $o] : (((X1 @ g) = $true) | ($true != (X1 @ f))))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.31 thf(f5,plain,(
% 1.62/1.31 ~((! [X0 : b] : ((f @ X0) = (g @ X0)) | ! [X1 : (b > a) > $o] : (($true = (X1 @ f)) => ((X1 @ g) = $true))) => (f = g))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,plain,(
% 1.62/1.31 ~((! [X0 : b] : ((f @ X0) = (g @ X0)) | ! [X1 : (b > a) > $o] : ((X1 @ f) => (X1 @ g))) => (f = g))),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,negated_conjecture,(
% 1.62/1.31 ~((! [X1 : b] : ((f @ X1) = (g @ X1)) | ! [X0 : (b > a) > $o] : ((X0 @ f) => (X0 @ g))) => (f = g))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.31 thf(f1,conjecture,(
% 1.62/1.31 (! [X1 : b] : ((f @ X1) = (g @ X1)) | ! [X0 : (b > a) > $o] : ((X0 @ f) => (X0 @ g))) => (f = g)),
% 1.62/1.31 file('/export/starexec/sandbox2/tmp/tmp.tpNU1h5bjF/DTF2THF_16562.p',cTHM504)).
% 1.62/1.31 thf(f34,plain,(
% 1.62/1.31 ~spl0_2),
% 1.62/1.31 inference(avatar_contradiction_clause,[status(thm)],[f33])).
% 1.62/1.31 thf(f33,plain,(
% 1.62/1.31 $false | ~spl0_2),
% 1.62/1.31 inference(subsumption_resolution,[status(thm)],[f19,f8])).
% 1.62/1.31 thf(f19,plain,(
% 1.62/1.31 (f = g) | ~spl0_2),
% 1.62/1.31 inference(leibniz_equality_elimination,[status(thm)],[f14])).
% 1.62/1.31 thf(f14,plain,(
% 1.62/1.31 ( ! [X1 : (b > a) > $o] : (($true != (X1 @ f)) | ((X1 @ g) = $true)) ) | ~spl0_2),
% 1.62/1.31 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.62/1.31 thf(f13,definition,(
% 1.62/1.31 spl0_2 <=> ! [X1 : (b > a) > $o] : (((X1 @ g) = $true) | ($true != (X1 @ f)))),
% 1.62/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.62/1.31 thf(f15,plain,(
% 1.62/1.31 spl0_1 | spl0_2),
% 1.62/1.31 inference(avatar_split_clause,[status(thm)],[f7,f13,f10])).
% 1.62/1.31 thf(f7,plain,(
% 1.62/1.31 ( ! [X0 : b,X1 : (b > a) > $o] : (((X1 @ g) = $true) | ($true != (X1 @ f)) | ((f @ X0) = (g @ X0))) )),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.62/1.31 % SZS output end Proof for DTF2THF_16562
% 1.62/1.31 % (16731)------------------------------
% 1.62/1.31 % (16731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16731)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (16731)Memory used [KB]: 5500
% 1.62/1.31 % (16731)Time elapsed: 0.003 s
% 1.62/1.31 % (16731)Instructions burned: 2 (million)
% 1.62/1.31 % (16731)------------------------------
% 1.62/1.31 % (16731)------------------------------
% 1.62/1.31 % (16727)Success in time 0.013 s
%------------------------------------------------------------------------------