%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO372^5 : 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 : n029.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 09:54:04 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 151 ( 36 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 119 ( 30 ~; 30 |; 1 &; 47 @)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
gtype: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
gtype: $tType ).
thf(func_def_2,type,
g: b > $o ).
thf(func_def_3,type,
h: ( b > $o ) > gtype ).
thf(func_def_4,type,
f: b > $o ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK2: b ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f23,f32,f35,f50,f59]) ).
thf(f59,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f54,f26]) ).
thf(f26,plain,
( ( $false
!= ( g @ sK2 ) )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl0_3
<=> ( $false
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f54,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false
= ( g @ sK2 ) )
| ( $false = $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f9,f31]) ).
thf(f31,plain,
( ( $false
= ( f @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_4
<=> ( $false
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f9,plain,
! [X0: b] :
( ( ( f @ X0 )
= $true )
| ( ( g @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ( h @ f )
!= ( h @ g ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rptOSaiuRm/DTF2THF_9096.p',cEXT_SET2) ).
thf(f50,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f42,f27]) ).
thf(f27,plain,
( ( $false
= ( g @ sK2 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f42,plain,
( ( $true
= ( g @ sK2 ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
= ( g @ sK2 ) )
| ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f18,f10]) ).
thf(f10,plain,
! [X0: b] :
( ( ( f @ X0 )
= $false )
| ( ( g @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f18,plain,
( ( $true
= ( f @ sK2 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl0_1
<=> ( $true
= ( f @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f22,f27]) ).
thf(f22,plain,
( ( $true
= ( g @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl0_2
<=> ( $true
= ( g @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f32,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f14,f29,f25]) ).
thf(f14,plain,
( ( $false
= ( f @ sK2 ) )
| ( $false
= ( g @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( g @ sK2 )
!= ( f @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f11]) ).
thf(f11,plain,
f != g,
inference(equality_resolution,[status(thm)],[f7]) ).
thf(f7,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f23,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f20,f16]) ).
thf(f13,plain,
( ( $true
= ( g @ sK2 ) )
| ( $true
= ( f @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO372^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.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 14:29:14 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
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO372^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : TPS problem from EXTENSIONALITY
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0687 [Bro09]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 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 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.20/0.47 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 3 ( 5 avg)
% 0.20/0.47 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.20/0.47 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.20/0.47 % Number of types : 3 ( 2 usr)
% 0.20/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.20/0.47 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(b_type,type,
% 0.20/0.47 b: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(g_type,type,
% 0.20/0.47 gtype: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(g,type,
% 0.20/0.47 g: b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(h,type,
% 0.20/0.47 h: ( b > $o ) > gtype ).
% 0.20/0.47
% 0.20/0.47 thf(f,type,
% 0.20/0.47 f: b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cEXT_SET2,conjecture,
% 0.20/0.47 ( ! [Xx: b] :
% 0.20/0.47 ( ( f @ Xx )
% 0.20/0.47 <=> ( g @ Xx ) )
% 0.20/0.47 => ( ( h @ f )
% 0.20/0.47 = ( h @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.50/1.24 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 14:29:15 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rptOSaiuRm/DTF2DTF9096.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(b_type,type,
% 1.50/1.26 b: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(g_type,type,
% 1.50/1.26 gtype: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(g,type,
% 1.50/1.26 g: b > $o ).
% 1.50/1.26
% 1.50/1.26 thf(h,type,
% 1.50/1.26 h: ( b > $o ) > gtype ).
% 1.50/1.26
% 1.50/1.26 thf(f,type,
% 1.50/1.26 f: b > $o ).
% 1.50/1.26
% 1.50/1.26 thf(cEXT_SET2,conjecture,
% 1.50/1.26 ( ! [Xx: b] :
% 1.50/1.26 ( ( f @ Xx )
% 1.50/1.26 <=> ( g @ Xx ) )
% 1.50/1.26 => ( ( h @ f )
% 1.50/1.26 = ( h @ g ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (9286)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_9096 for (3000ds/4Mi)
% 1.50/1.27 % (9291)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9096 for (3000ds/18Mi)
% 1.50/1.27 % (9286)Refutation not found, incomplete strategy
% 1.50/1.27 % (9286)------------------------------
% 1.50/1.27 % (9286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (9286)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.27
% 1.50/1.27
% 1.50/1.27 % (9286)Memory used [KB]: 5500
% 1.50/1.27 % (9286)Time elapsed: 0.002 s
% 1.50/1.27 % (9286)Instructions burned: 1 (million)
% 1.50/1.27 % (9286)------------------------------
% 1.50/1.27 % (9286)------------------------------
% 1.50/1.27 % (9291)First to succeed.
% 1.50/1.27 % (9291)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_9096
% 1.50/1.27 % SZS output start Proof for DTF2THF_9096
% 1.50/1.27 thf(type_def_5, type, b: $tType).
% 1.50/1.27 thf(type_def_7, type, gtype: $tType).
% 1.50/1.27 thf(func_def_0, type, b: $tType).
% 1.50/1.27 thf(func_def_1, type, gtype: $tType).
% 1.50/1.27 thf(func_def_2, type, g: b > $o).
% 1.50/1.27 thf(func_def_3, type, h: (b > $o) > gtype).
% 1.50/1.27 thf(func_def_4, type, f: b > $o).
% 1.50/1.27 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.50/1.27 thf(func_def_10, type, sK2: b).
% 1.50/1.27 thf(f60,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(avatar_sat_refutation,[status(thm)],[f23,f32,f35,f50,f59])).
% 1.50/1.27 thf(f59,plain,(
% 1.50/1.27 spl0_3 | ~spl0_4),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.50/1.27 thf(f58,plain,(
% 1.50/1.27 $false | (spl0_3 | ~spl0_4)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f54,f26])).
% 1.50/1.27 thf(f26,plain,(
% 1.50/1.27 ($false != (g @ sK2)) | spl0_3),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.50/1.27 thf(f25,definition,(
% 1.50/1.27 spl0_3 <=> ($false = (g @ sK2))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.50/1.27 thf(f54,plain,(
% 1.50/1.27 ($false = (g @ sK2)) | ~spl0_4),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.50/1.27 thf(f53,plain,(
% 1.50/1.27 ($false = (g @ sK2)) | ($false = $true) | ~spl0_4),
% 1.50/1.27 inference(superposition,[status(thm)],[f9,f31])).
% 1.50/1.27 thf(f31,plain,(
% 1.50/1.27 ($false = (f @ sK2)) | ~spl0_4),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.50/1.27 thf(f29,definition,(
% 1.50/1.27 spl0_4 <=> ($false = (f @ sK2))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ( ! [X0 : b] : (((f @ X0) = $true) | ((g @ X0) = $false)) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.50/1.27 thf(f8,plain,(
% 1.50/1.27 ( ! [X0 : b] : (((f @ X0) = (g @ X0))) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 ! [X0 : b] : ((f @ X0) = (g @ X0)) & ((h @ f) != (h @ g))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,plain,(
% 1.50/1.27 ~(! [X0 : b] : ((f @ X0) = (g @ X0)) => ((h @ f) = (h @ g)))),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,plain,(
% 1.50/1.27 ~(! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ((h @ f) = (h @ g)))),
% 1.50/1.27 inference(rectify,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,negated_conjecture,(
% 1.50/1.27 ~(! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ((h @ f) = (h @ g)))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.27 thf(f1,conjecture,(
% 1.50/1.27 ! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ((h @ f) = (h @ g))),
% 1.50/1.27 file('/export/starexec/sandbox/tmp/tmp.rptOSaiuRm/DTF2THF_9096.p',cEXT_SET2)).
% 1.50/1.27 thf(f50,plain,(
% 1.50/1.27 ~spl0_1 | ~spl0_3),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.50/1.27 thf(f49,plain,(
% 1.50/1.27 $false | (~spl0_1 | ~spl0_3)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.50/1.27 thf(f48,plain,(
% 1.50/1.27 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.50/1.27 inference(forward_demodulation,[status(thm)],[f42,f27])).
% 1.50/1.27 thf(f27,plain,(
% 1.50/1.27 ($false = (g @ sK2)) | ~spl0_3),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.50/1.27 thf(f42,plain,(
% 1.50/1.27 ($true = (g @ sK2)) | ~spl0_1),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.50/1.27 thf(f39,plain,(
% 1.50/1.27 ($true = (g @ sK2)) | ($false = $true) | ~spl0_1),
% 1.50/1.27 inference(superposition,[status(thm)],[f18,f10])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 ( ! [X0 : b] : (((f @ X0) = $false) | ((g @ X0) = $true)) )),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.50/1.27 thf(f18,plain,(
% 1.50/1.27 ($true = (f @ sK2)) | ~spl0_1),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f16])).
% 1.50/1.27 thf(f16,definition,(
% 1.50/1.27 spl0_1 <=> ($true = (f @ sK2))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.50/1.27 thf(f35,plain,(
% 1.50/1.27 ~spl0_2 | ~spl0_3),
% 1.50/1.27 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.50/1.27 thf(f34,plain,(
% 1.50/1.27 $false | (~spl0_2 | ~spl0_3)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.50/1.27 thf(f33,plain,(
% 1.50/1.27 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.50/1.27 inference(forward_demodulation,[status(thm)],[f22,f27])).
% 1.50/1.27 thf(f22,plain,(
% 1.50/1.27 ($true = (g @ sK2)) | ~spl0_2),
% 1.50/1.27 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.50/1.27 thf(f20,definition,(
% 1.50/1.27 spl0_2 <=> ($true = (g @ sK2))),
% 1.50/1.27 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.50/1.27 thf(f32,plain,(
% 1.50/1.27 spl0_3 | spl0_4),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f14,f29,f25])).
% 1.50/1.27 thf(f14,plain,(
% 1.50/1.27 ($false = (f @ sK2)) | ($false = (g @ sK2))),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.50/1.27 thf(f12,plain,(
% 1.50/1.27 ((g @ sK2) != (f @ sK2))),
% 1.50/1.27 inference(negative_extensionality,[status(thm)],[f11])).
% 1.50/1.27 thf(f11,plain,(
% 1.50/1.27 (f != g)),
% 1.50/1.27 inference(equality_resolution,[status(thm)],[f7])).
% 1.50/1.27 thf(f7,plain,(
% 1.50/1.27 ((h @ f) != (h @ g))),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 1.50/1.27 thf(f23,plain,(
% 1.50/1.27 spl0_1 | spl0_2),
% 1.50/1.27 inference(avatar_split_clause,[status(thm)],[f13,f20,f16])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 ($true = (g @ sK2)) | ($true = (f @ sK2))),
% 1.50/1.27 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.50/1.27 % SZS output end Proof for DTF2THF_9096
% 1.50/1.27 % (9291)------------------------------
% 1.50/1.27 % (9291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (9291)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (9291)Memory used [KB]: 5500
% 1.50/1.27 % (9291)Time elapsed: 0.003 s
% 1.50/1.27 % (9291)Instructions burned: 2 (million)
% 1.50/1.27 % (9291)------------------------------
% 1.50/1.27 % (9291)------------------------------
% 1.50/1.27 % (9284)Success in time 0.009 s
%------------------------------------------------------------------------------