%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO373^5 : 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 : n012.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 0.81s 0.89s
% Output : Refutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 182 ( 44 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 134 ( 30 ~; 27 |; 6 &; 55 @)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 13 !; 2 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
g: b > $o ).
thf(func_def_2,type,
f: b > $o ).
thf(func_def_6,type,
sK0: ( b > $o ) > $o ).
thf(func_def_8,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
sK3: b ).
thf(f68,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f36,f42,f48,f67]) ).
thf(f67,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f62,f25]) ).
thf(f25,plain,
( ( $true
!= ( g @ sK3 ) )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl1_2
<=> ( $true
= ( g @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f62,plain,
( ( $true
= ( g @ sK3 ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true
= ( g @ sK3 ) )
| ( $true = $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f13,f22]) ).
thf(f22,plain,
( ( $true
= ( f @ sK3 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl1_1
<=> ( $true
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f13,plain,
! [X0: b] :
( ( ( f @ X0 )
= $false )
| ( ( g @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( $true
= ( sK0 @ f ) )
& ( ( sK0 @ g )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
& ( ( X1 @ g )
!= $true ) )
=> ( ( $true
= ( sK0 @ f ) )
& ( ( sK0 @ g )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ? [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
& ( ( X1 @ g )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ f )
= $true )
=> ( ( X1 @ g )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: b] :
( ( f @ X0 )
<=> ( g @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a8IpO3r3K5/DTF2THF_28926.p',cEXT_SET) ).
thf(f48,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f26,f35]) ).
thf(f35,plain,
( ( ( g @ sK3 )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl1_4
<=> ( ( g @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( g @ sK3 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f42,plain,
( spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f39,f29,f33]) ).
thf(f29,definition,
( spl1_3
<=> ( $false
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f39,plain,
( ( ( g @ sK3 )
= $false )
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( g @ sK3 )
= $false )
| ( $true = $false )
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f12,f31]) ).
thf(f31,plain,
( ( $false
= ( f @ sK3 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f12,plain,
! [X0: b] :
( ( ( f @ X0 )
= $true )
| ( ( g @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f36,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f29]) ).
thf(f18,plain,
( ( ( g @ sK3 )
= $false )
| ( $false
= ( f @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( g @ sK3 )
!= ( f @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
f != g,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( f != g )
| ( $true != $true ) ),
inference(constrained_superposition,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( $true
= ( sK0 @ f ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f9,plain,
( ( sK0 @ g )
!= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f27,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f24,f20]) ).
thf(f17,plain,
( ( $true
= ( g @ sK3 ) )
| ( $true
= ( f @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO373^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 14:29:00 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SYO373^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Syntactic
% 0.07/0.32 % Problem : TPS problem from EXTENSIONALITY
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0708 [Bro09]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 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, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.07/0.32 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 4 ( 4 avg)
% 0.07/0.32 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.07/0.32 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 5 ( 5 avg)
% 0.07/0.32 % Number of types : 2 ( 1 usr)
% 0.07/0.32 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.07/0.32 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.07/0.32 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(b_type,type,
% 0.07/0.32 b: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(g,type,
% 0.07/0.32 g: b > $o ).
% 0.07/0.32
% 0.07/0.32 thf(f,type,
% 0.07/0.32 f: b > $o ).
% 0.07/0.32
% 0.07/0.32 thf(cEXT_SET,conjecture,
% 0.07/0.32 ( ! [Xx: b] :
% 0.07/0.32 ( ( f @ Xx )
% 0.07/0.32 <=> ( g @ Xx ) )
% 0.07/0.32 => ! [Xq: ( b > $o ) > $o] :
% 0.07/0.32 ( ( Xq @ f )
% 0.07/0.32 => ( Xq @ g ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.81/0.87 ---- Embedded in THF ---
% 0.81/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.81/0.87 %%% Generated on Tue Feb 24 14:29:01 EST 2026
% 0.81/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.81/0.87 %%% Logic specification used:
% 0.81/0.87 %%% thf(spec, logic, $$dhol).
% 0.81/0.87
% 0.81/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a8IpO3r3K5/DTF2DTF28926.p
% See solution above
% 0.81/0.87 ------------------------
% 0.81/0.88 ---- Cleaned THF ---
% 0.81/0.88 thf(b_type,type,
% 0.81/0.88 b: $tType ).
% 0.81/0.88
% 0.81/0.88 thf(g,type,
% 0.81/0.88 g: b > $o ).
% 0.81/0.88
% 0.81/0.88 thf(f,type,
% 0.81/0.88 f: b > $o ).
% 0.81/0.88
% 0.81/0.88 thf(cEXT_SET,conjecture,
% 0.81/0.88 ( ! [Xx: b] :
% 0.81/0.88 ( ( f @ Xx )
% 0.81/0.88 <=> ( g @ Xx ) )
% 0.81/0.88 => ! [Xq: ( b > $o ) > $o] :
% 0.81/0.88 ( ( Xq @ f )
% 0.81/0.88 => ( Xq @ g ) ) ) ).
% 0.81/0.88 ------------------------
% 0.81/0.89 % (29188)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_28926 for (3000ds/4Mi)
% 0.81/0.89 % (29187)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28926 for (3000ds/183Mi)
% 0.81/0.89 % (29189)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_28926 for (3000ds/27Mi)
% 0.81/0.89 % (29190)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28926 for (3000ds/2Mi)
% 0.81/0.89 % (29191)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_28926 for (3000ds/2Mi)
% 0.81/0.89 % (29193)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28926 for (3000ds/18Mi)
% 0.81/0.89 % (29192)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_28926 for (3000ds/275Mi)
% 0.81/0.89 % (29190)Instruction limit reached!
% 0.81/0.89 % (29190)------------------------------
% 0.81/0.89 % (29190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29190)Termination reason: Unknown
% 0.81/0.89 % (29190)Termination phase: Saturation
% 0.81/0.89
% 0.81/0.89 % (29190)Memory used [KB]: 5500
% 0.81/0.89 % (29190)Time elapsed: 0.002 s
% 0.81/0.89 % (29190)Instructions burned: 2 (million)
% 0.81/0.89 % (29190)------------------------------
% 0.81/0.89 % (29190)------------------------------
% 0.81/0.89 % (29191)Instruction limit reached!
% 0.81/0.89 % (29191)------------------------------
% 0.81/0.89 % (29191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29191)Termination reason: Unknown
% 0.81/0.89 % (29191)Termination phase: Saturation
% 0.81/0.89
% 0.81/0.89 % (29191)Memory used [KB]: 5500
% 0.81/0.89 % (29191)Time elapsed: 0.002 s
% 0.81/0.89 % (29191)Instructions burned: 2 (million)
% 0.81/0.89 % (29191)------------------------------
% 0.81/0.89 % (29191)------------------------------
% 0.81/0.89 % (29189)Refutation not found, incomplete strategy
% 0.81/0.89 % (29189)------------------------------
% 0.81/0.89 % (29189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29189)Termination reason: Refutation not found, incomplete strategy
% 0.81/0.89
% 0.81/0.89
% 0.81/0.89 % (29189)Memory used [KB]: 5500
% 0.81/0.89 % (29189)Time elapsed: 0.002 s
% 0.81/0.89 % (29189)Instructions burned: 2 (million)
% 0.81/0.89 % (29189)------------------------------
% 0.81/0.89 % (29189)------------------------------
% 0.81/0.89 % (29192)Refutation not found, incomplete strategy
% 0.81/0.89 % (29192)------------------------------
% 0.81/0.89 % (29192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29192)Termination reason: Refutation not found, incomplete strategy
% 0.81/0.89
% 0.81/0.89
% 0.81/0.89 % (29192)Memory used [KB]: 5500
% 0.81/0.89 % (29192)Time elapsed: 0.002 s
% 0.81/0.89 % (29192)Instructions burned: 2 (million)
% 0.81/0.89 % (29192)------------------------------
% 0.81/0.89 % (29192)------------------------------
% 0.81/0.89 % (29188)Refutation not found, incomplete strategy
% 0.81/0.89 % (29188)------------------------------
% 0.81/0.89 % (29188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29188)Termination reason: Refutation not found, incomplete strategy
% 0.81/0.89
% 0.81/0.89
% 0.81/0.89 % (29188)Memory used [KB]: 5500
% 0.81/0.89 % (29188)Time elapsed: 0.002 s
% 0.81/0.89 % (29188)Instructions burned: 2 (million)
% 0.81/0.89 % (29188)------------------------------
% 0.81/0.89 % (29188)------------------------------
% 0.81/0.89 % (29187)First to succeed.
% 0.81/0.89 % (29193)Also succeeded, but the first one will report.
% 0.81/0.89 % (29187)Refutation found. Thanks to Tanya!
% 0.81/0.89 % SZS status Theorem for DTF2THF_28926
% 0.81/0.89 % SZS output start Proof for DTF2THF_28926
% 0.81/0.89 thf(type_def_5, type, b: $tType).
% 0.81/0.89 thf(func_def_0, type, b: $tType).
% 0.81/0.89 thf(func_def_1, type, g: b > $o).
% 0.81/0.89 thf(func_def_2, type, f: b > $o).
% 0.81/0.89 thf(func_def_6, type, sK0: (b > $o) > $o).
% 0.81/0.89 thf(func_def_8, type, ph2: !>[X0: $tType]:(X0)).
% 0.81/0.89 thf(func_def_9, type, sK3: b).
% 0.81/0.89 thf(f68,plain,(
% 0.81/0.89 $false),
% 0.81/0.89 inference(avatar_sat_refutation,[status(thm)],[f27,f36,f42,f48,f67])).
% 0.81/0.89 thf(f67,plain,(
% 0.81/0.89 ~spl1_1 | spl1_2),
% 0.81/0.89 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 0.81/0.89 thf(f66,plain,(
% 0.81/0.89 $false | (~spl1_1 | spl1_2)),
% 0.81/0.89 inference(subsumption_resolution,[status(thm)],[f62,f25])).
% 0.81/0.89 thf(f25,plain,(
% 0.81/0.89 ($true != (g @ sK3)) | spl1_2),
% 0.81/0.89 inference(avatar_component_clause,[status(thm)],[f24])).
% 0.81/0.89 thf(f24,definition,(
% 0.81/0.89 spl1_2 <=> ($true = (g @ sK3))),
% 0.81/0.89 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 0.81/0.89 thf(f62,plain,(
% 0.81/0.89 ($true = (g @ sK3)) | ~spl1_1),
% 0.81/0.89 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 0.81/0.89 thf(f56,plain,(
% 0.81/0.89 ($true = (g @ sK3)) | ($true = $false) | ~spl1_1),
% 0.81/0.89 inference(superposition,[status(thm)],[f13,f22])).
% 0.81/0.89 thf(f22,plain,(
% 0.81/0.89 ($true = (f @ sK3)) | ~spl1_1),
% 0.81/0.89 inference(avatar_component_clause,[status(thm)],[f20])).
% 0.81/0.89 thf(f20,definition,(
% 0.81/0.89 spl1_1 <=> ($true = (f @ sK3))),
% 0.81/0.89 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 0.81/0.89 thf(f13,plain,(
% 0.81/0.89 ( ! [X0 : b] : (((f @ X0) = $false) | ((g @ X0) = $true)) )),
% 0.81/0.89 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.81/0.89 thf(f11,plain,(
% 0.81/0.89 ( ! [X0 : b] : (((f @ X0) = (g @ X0))) )),
% 0.81/0.89 inference(cnf_transformation,[status(thm)],[f8])).
% 0.81/0.89 thf(f8,plain,(
% 0.81/0.89 ! [X0 : b] : ((f @ X0) = (g @ X0)) & (($true = (sK0 @ f)) & ((sK0 @ g) != $true))),
% 0.81/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 0.81/0.89 thf(f7,plain,(
% 0.81/0.89 ? [X1 : (b > $o) > $o] : (((X1 @ f) = $true) & ((X1 @ g) != $true)) => (($true = (sK0 @ f)) & ((sK0 @ g) != $true))),
% 0.81/0.89 introduced(definition,[],[choice_axiom])).
% 0.81/0.89 thf(f6,plain,(
% 0.81/0.89 ! [X0 : b] : ((f @ X0) = (g @ X0)) & ? [X1 : (b > $o) > $o] : (((X1 @ f) = $true) & ((X1 @ g) != $true))),
% 0.81/0.89 inference(ennf_transformation,[status(thm)],[f5])).
% 0.81/0.89 thf(f5,plain,(
% 0.81/0.89 ~(! [X0 : b] : ((f @ X0) = (g @ X0)) => ! [X1 : (b > $o) > $o] : (((X1 @ f) = $true) => ((X1 @ g) = $true)))),
% 0.81/0.89 inference(fool_elimination,[status(thm)],[f4])).
% 0.81/0.89 thf(f4,plain,(
% 0.81/0.89 ~(! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g)))),
% 0.81/0.89 inference(rectify,[status(thm)],[f2])).
% 0.81/0.89 thf(f2,negated_conjecture,(
% 0.81/0.89 ~(! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g)))),
% 0.81/0.89 inference(negated_conjecture,[status(cth)],[f1])).
% 0.81/0.89 thf(f1,conjecture,(
% 0.81/0.89 ! [X0 : b] : ((f @ X0) <=> (g @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g))),
% 0.81/0.89 file('/export/starexec/sandbox/tmp/tmp.a8IpO3r3K5/DTF2THF_28926.p',cEXT_SET)).
% 0.81/0.89 thf(f48,plain,(
% 0.81/0.89 ~spl1_2 | ~spl1_4),
% 0.81/0.89 inference(avatar_contradiction_clause,[status(thm)],[f47])).
% 0.81/0.89 thf(f47,plain,(
% 0.81/0.89 $false | (~spl1_2 | ~spl1_4)),
% 0.81/0.89 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 0.81/0.89 thf(f44,plain,(
% 0.81/0.89 ($true = $false) | (~spl1_2 | ~spl1_4)),
% 0.81/0.89 inference(superposition,[status(thm)],[f26,f35])).
% 0.81/0.89 thf(f35,plain,(
% 0.81/0.89 ((g @ sK3) = $false) | ~spl1_4),
% 0.81/0.89 inference(avatar_component_clause,[status(thm)],[f33])).
% 0.81/0.89 thf(f33,definition,(
% 0.81/0.89 spl1_4 <=> ((g @ sK3) = $false)),
% 0.81/0.89 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 0.81/0.89 thf(f26,plain,(
% 0.81/0.89 ($true = (g @ sK3)) | ~spl1_2),
% 0.81/0.89 inference(avatar_component_clause,[status(thm)],[f24])).
% 0.81/0.89 thf(f42,plain,(
% 0.81/0.89 spl1_4 | ~spl1_3),
% 0.81/0.89 inference(avatar_split_clause,[status(thm)],[f39,f29,f33])).
% 0.81/0.89 thf(f29,definition,(
% 0.81/0.89 spl1_3 <=> ($false = (f @ sK3))),
% 0.81/0.89 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 0.81/0.89 thf(f39,plain,(
% 0.81/0.89 ((g @ sK3) = $false) | ~spl1_3),
% 0.81/0.89 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 0.81/0.89 thf(f37,plain,(
% 0.81/0.89 ((g @ sK3) = $false) | ($true = $false) | ~spl1_3),
% 0.81/0.89 inference(superposition,[status(thm)],[f12,f31])).
% 0.81/0.89 thf(f31,plain,(
% 0.81/0.89 ($false = (f @ sK3)) | ~spl1_3),
% 0.81/0.89 inference(avatar_component_clause,[status(thm)],[f29])).
% 0.81/0.89 thf(f12,plain,(
% 0.81/0.89 ( ! [X0 : b] : (((f @ X0) = $true) | ((g @ X0) = $false)) )),
% 0.81/0.89 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.81/0.89 thf(f36,plain,(
% 0.81/0.89 spl1_3 | spl1_4),
% 0.81/0.89 inference(avatar_split_clause,[status(thm)],[f18,f33,f29])).
% 0.81/0.89 thf(f18,plain,(
% 0.81/0.89 ((g @ sK3) = $false) | ($false = (f @ sK3))),
% 0.81/0.89 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.81/0.89 thf(f16,plain,(
% 0.81/0.89 ((g @ sK3) != (f @ sK3))),
% 0.81/0.89 inference(negative_extensionality,[status(thm)],[f15])).
% 0.81/0.89 thf(f15,plain,(
% 0.81/0.89 (f != g)),
% 0.81/0.89 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 0.81/0.89 thf(f14,plain,(
% 0.81/0.89 (f != g) | ($true != $true)),
% 0.81/0.89 inference(constrained_superposition,[status(thm)],[f9,f10])).
% 0.81/0.89 thf(f10,plain,(
% 0.81/0.89 ($true = (sK0 @ f))),
% 0.81/0.89 inference(cnf_transformation,[status(thm)],[f8])).
% 0.81/0.89 thf(f9,plain,(
% 0.81/0.89 ((sK0 @ g) != $true)),
% 0.81/0.89 inference(cnf_transformation,[status(thm)],[f8])).
% 0.81/0.89 thf(f27,plain,(
% 0.81/0.89 spl1_1 | spl1_2),
% 0.81/0.89 inference(avatar_split_clause,[status(thm)],[f17,f24,f20])).
% 0.81/0.89 thf(f17,plain,(
% 0.81/0.89 ($true = (g @ sK3)) | ($true = (f @ sK3))),
% 0.81/0.89 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 0.81/0.89 % SZS output end Proof for DTF2THF_28926
% 0.81/0.89 % (29187)------------------------------
% 0.81/0.89 % (29187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.81/0.89 % (29187)Termination reason: Refutation
% 0.81/0.89
% 0.81/0.89 % (29187)Memory used [KB]: 5500
% 0.81/0.89 % (29187)Time elapsed: 0.003 s
% 0.81/0.89 % (29187)Instructions burned: 4 (million)
% 0.81/0.89 % (29187)------------------------------
% 0.81/0.89 % (29187)------------------------------
% 0.81/0.89 % (29186)Success in time 0.011 s
%------------------------------------------------------------------------------