%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO359^5 : 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 : n026.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 1.62s 1.48s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 224 ( 58 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 202 ( 38 ~; 34 |; 8 &; 95 @)
% ( 10 <=>; 17 =>; 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 : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 23 !; 4 ?; 27 :)
% 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_8,type,
sK0: b ).
thf(func_def_11,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK3: b ).
thf(f95,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f60,f76,f82,f94]) ).
thf(f94,plain,
( ~ spl1_6
| spl1_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f93]) ).
thf(f93,plain,
( $false
| ~ spl1_6
| spl1_7 ),
inference(subsumption_resolution,[status(thm)],[f87,f49]) ).
thf(f49,plain,
( ( $true
!= ( g @ sK3 ) )
| spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl1_7
<=> ( $true
= ( g @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f87,plain,
( ( $true
= ( g @ sK3 ) )
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( $true
= ( g @ sK3 ) )
| ( $true = $false )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f46,f15]) ).
thf(f15,plain,
! [X0: b] :
( ( ( f @ X0 )
= $false )
| ( ( g @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ( h @ f )
!= ( h @ g ) )
& ( ( ( g @ sK0 )
!= ( f @ sK0 ) )
| ! [X2: ( b > $o ) > $o] :
( ( $true
= ( X2 @ g ) )
| ( $true
!= ( X2 @ f ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X1: b] :
( ( f @ X1 )
!= ( g @ X1 ) )
=> ( ( g @ sK0 )
!= ( f @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ( h @ f )
!= ( h @ g ) )
& ( ? [X1: b] :
( ( f @ X1 )
!= ( g @ X1 ) )
| ! [X2: ( b > $o ) > $o] :
( ( $true
= ( X2 @ g ) )
| ( $true
!= ( X2 @ f ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) )
& ( ( h @ f )
!= ( h @ g ) )
& ( ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) )
| ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( h @ f )
!= ( h @ g ) )
& ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) )
& ( ? [X0: b] :
( ( f @ X0 )
!= ( g @ X0 ) )
| ! [X1: ( b > $o ) > $o] :
( ( ( X1 @ g )
= $true )
| ( ( X1 @ f )
!= $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 ) ) )
=> ( ! [X2: b] :
( ( g @ X2 )
= ( f @ X2 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X2: b] :
( ( g @ X2 )
<=> ( f @ X2 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ! [X1: ( b > $o ) > $o] :
( ( X1 @ f )
=> ( X1 @ g ) ) )
=> ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xccpM9MQmm/DTF2THF_29618.p',cEXT1) ).
thf(f46,plain,
( ( $true
= ( f @ sK3 ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl1_6
<=> ( $true
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f82,plain,
( ~ spl1_7
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl1_7
| ~ spl1_9 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true = $false )
| ~ spl1_7
| ~ spl1_9 ),
inference(superposition,[status(thm)],[f50,f59]) ).
thf(f59,plain,
( ( ( g @ sK3 )
= $false )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f57,definition,
( spl1_9
<=> ( ( g @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( g @ sK3 ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f76,plain,
( spl1_9
| ~ spl1_8 ),
inference(avatar_split_clause,[status(thm)],[f71,f53,f57]) ).
thf(f53,definition,
( spl1_8
<=> ( $false
= ( f @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f71,plain,
( ( ( g @ sK3 )
= $false )
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true = $false )
| ( ( g @ sK3 )
= $false )
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f55,f14]) ).
thf(f14,plain,
! [X0: b] :
( ( ( f @ X0 )
= $true )
| ( ( g @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f55,plain,
( ( $false
= ( f @ sK3 ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f60,plain,
( spl1_8
| spl1_9 ),
inference(avatar_split_clause,[status(thm)],[f42,f57,f53]) ).
thf(f42,plain,
( ( ( g @ sK3 )
= $false )
| ( $false
= ( f @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( g @ sK3 )
!= ( f @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f39]) ).
thf(f39,plain,
f != g,
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f51,plain,
( spl1_6
| spl1_7 ),
inference(avatar_split_clause,[status(thm)],[f41,f48,f44]) ).
thf(f41,plain,
( ( $true
= ( g @ sK3 ) )
| ( $true
= ( f @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO359^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:28:55 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : SYO359^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.49 % Domain : Syntactic
% 0.27/0.49 % Problem : TPS problem EXT1
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : Theorem about extensionality.
% 0.27/0.49
% 0.27/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : tps_0243 [Bro09]
% 0.27/0.49 % : EXT1 [TPS]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.00 v8.1.0, 0.09 v7.5.0, 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, 0.20 v5.2.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.27/0.49 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.27/0.49 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 7 ( 9 avg)
% 0.27/0.49 % Number of connectives : 14 ( 0 ~; 0 |; 0 &; 8 @)
% 0.27/0.49 % ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 6 ( 6 avg)
% 0.27/0.49 % Number of types : 3 ( 2 usr)
% 0.27/0.49 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.27/0.49 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(b_type,type,
% 0.27/0.49 b: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(g_type,type,
% 0.27/0.49 gtype: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(g,type,
% 0.27/0.49 g: b > $o ).
% 0.27/0.49
% 0.27/0.49 thf(h,type,
% 0.27/0.49 h: ( b > $o ) > gtype ).
% 0.27/0.49
% 0.27/0.49 thf(f,type,
% 0.27/0.49 f: b > $o ).
% 0.27/0.49
% 0.27/0.49 thf(cEXT1,conjecture,
% 0.27/0.49 ( ( ! [Xx: b] :
% 0.27/0.49 ( ( f @ Xx )
% 0.27/0.49 <=> ( g @ Xx ) )
% 0.27/0.49 => ! [Xq: ( b > $o ) > $o] :
% 0.27/0.49 ( ( Xq @ f )
% 0.27/0.49 => ( Xq @ g ) ) )
% 0.27/0.49 => ( ! [Xx: b] :
% 0.27/0.49 ( ( f @ Xx )
% 0.27/0.49 <=> ( g @ Xx ) )
% 0.27/0.49 => ( ( h @ f )
% 0.27/0.49 = ( h @ g ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.62/1.44 ---- Embedded in THF ---
% 1.62/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.45 %%% Generated on Tue Feb 24 14:28:56 EST 2026
% 1.62/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.45 %%% Logic specification used:
% 1.62/1.45 %%% thf(spec, logic, $$dhol).
% 1.62/1.45
% 1.62/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xccpM9MQmm/DTF2DTF29618.p
% See solution above
% 1.62/1.45 ------------------------
% 1.62/1.45 ---- Cleaned THF ---
% 1.62/1.45 thf(b_type,type,
% 1.62/1.45 b: $tType ).
% 1.62/1.45
% 1.62/1.45 thf(g_type,type,
% 1.62/1.45 gtype: $tType ).
% 1.62/1.45
% 1.62/1.45 thf(g,type,
% 1.62/1.45 g: b > $o ).
% 1.62/1.45
% 1.62/1.45 thf(h,type,
% 1.62/1.45 h: ( b > $o ) > gtype ).
% 1.62/1.45
% 1.62/1.45 thf(f,type,
% 1.62/1.45 f: b > $o ).
% 1.62/1.45
% 1.62/1.45 thf(cEXT1,conjecture,
% 1.62/1.45 ( ( ! [Xx: b] :
% 1.62/1.45 ( ( f @ Xx )
% 1.62/1.45 <=> ( g @ Xx ) )
% 1.62/1.45 => ! [Xq: ( b > $o ) > $o] :
% 1.62/1.45 ( ( Xq @ f )
% 1.62/1.45 => ( Xq @ g ) ) )
% 1.62/1.45 => ( ! [Xx: b] :
% 1.62/1.45 ( ( f @ Xx )
% 1.62/1.45 <=> ( g @ Xx ) )
% 1.62/1.45 => ( ( h @ f )
% 1.62/1.45 = ( h @ g ) ) ) ) ).
% 1.62/1.45 ------------------------
% 1.62/1.47 % (29778)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29618 for (3000ds/183Mi)
% 1.62/1.47 % (29779)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_29618 for (3000ds/4Mi)
% 1.62/1.47 % (29781)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29618 for (3000ds/2Mi)
% 1.62/1.47 % (29780)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_29618 for (3000ds/27Mi)
% 1.62/1.47 % (29782)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_29618 for (3000ds/2Mi)
% 1.62/1.47 % (29783)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_29618 for (3000ds/275Mi)
% 1.62/1.47 % (29784)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29618 for (3000ds/18Mi)
% 1.62/1.48 % (29782)Instruction limit reached!
% 1.62/1.48 % (29782)------------------------------
% 1.62/1.48 % (29782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (29782)Termination reason: Unknown
% 1.62/1.48 % (29782)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (29782)Memory used [KB]: 5500
% 1.62/1.48 % (29782)Time elapsed: 0.003 s
% 1.62/1.48 % (29782)Instructions burned: 2 (million)
% 1.62/1.48 % (29782)------------------------------
% 1.62/1.48 % (29782)------------------------------
% 1.62/1.48 % (29780)Refutation not found, incomplete strategy
% 1.62/1.48 % (29780)------------------------------
% 1.62/1.48 % (29780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (29780)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.48
% 1.62/1.48
% 1.62/1.48 % (29780)Memory used [KB]: 5500
% 1.62/1.48 % (29780)Time elapsed: 0.003 s
% 1.62/1.48 % (29780)Instructions burned: 2 (million)
% 1.62/1.48 % (29780)------------------------------
% 1.62/1.48 % (29780)------------------------------
% 1.62/1.48 % (29781)Instruction limit reached!
% 1.62/1.48 % (29781)------------------------------
% 1.62/1.48 % (29781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (29781)Termination reason: Unknown
% 1.62/1.48 % (29781)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (29781)Memory used [KB]: 5500
% 1.62/1.48 % (29781)Time elapsed: 0.004 s
% 1.62/1.48 % (29781)Instructions burned: 2 (million)
% 1.62/1.48 % (29781)------------------------------
% 1.62/1.48 % (29781)------------------------------
% 1.62/1.48 % (29778)First to succeed.
% 1.62/1.48 % (29779)Instruction limit reached!
% 1.62/1.48 % (29779)------------------------------
% 1.62/1.48 % (29779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (29779)Termination reason: Unknown
% 1.62/1.48 % (29779)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (29779)Memory used [KB]: 5500
% 1.62/1.48 % (29779)Time elapsed: 0.005 s
% 1.62/1.48 % (29779)Instructions burned: 5 (million)
% 1.62/1.48 % (29779)------------------------------
% 1.62/1.48 % (29779)------------------------------
% 1.62/1.48 % (29783)Also succeeded, but the first one will report.
% 1.62/1.48 % (29778)Refutation found. Thanks to Tanya!
% 1.62/1.48 % SZS status Theorem for DTF2THF_29618
% 1.62/1.48 % SZS output start Proof for DTF2THF_29618
% 1.62/1.48 thf(type_def_5, type, b: $tType).
% 1.62/1.48 thf(type_def_7, type, gtype: $tType).
% 1.62/1.48 thf(func_def_0, type, b: $tType).
% 1.62/1.48 thf(func_def_1, type, gtype: $tType).
% 1.62/1.48 thf(func_def_2, type, g: b > $o).
% 1.62/1.48 thf(func_def_3, type, h: (b > $o) > gtype).
% 1.62/1.48 thf(func_def_4, type, f: b > $o).
% 1.62/1.48 thf(func_def_8, type, sK0: b).
% 1.62/1.48 thf(func_def_11, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.48 thf(func_def_12, type, sK3: b).
% 1.62/1.48 thf(f95,plain,(
% 1.62/1.48 $false),
% 1.62/1.48 inference(avatar_sat_refutation,[status(thm)],[f51,f60,f76,f82,f94])).
% 1.62/1.48 thf(f94,plain,(
% 1.62/1.48 ~spl1_6 | spl1_7),
% 1.62/1.48 inference(avatar_contradiction_clause,[status(thm)],[f93])).
% 1.62/1.48 thf(f93,plain,(
% 1.62/1.48 $false | (~spl1_6 | spl1_7)),
% 1.62/1.48 inference(subsumption_resolution,[status(thm)],[f87,f49])).
% 1.62/1.48 thf(f49,plain,(
% 1.62/1.48 ($true != (g @ sK3)) | spl1_7),
% 1.62/1.48 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.62/1.48 thf(f48,definition,(
% 1.62/1.48 spl1_7 <=> ($true = (g @ sK3))),
% 1.62/1.48 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.62/1.48 thf(f87,plain,(
% 1.62/1.48 ($true = (g @ sK3)) | ~spl1_6),
% 1.62/1.48 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.62/1.48 thf(f85,plain,(
% 1.62/1.48 ($true = (g @ sK3)) | ($true = $false) | ~spl1_6),
% 1.62/1.48 inference(superposition,[status(thm)],[f46,f15])).
% 1.62/1.48 thf(f15,plain,(
% 1.62/1.48 ( ! [X0 : b] : (((f @ X0) = $false) | ((g @ X0) = $true)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.62/1.48 thf(f13,plain,(
% 1.62/1.48 ( ! [X0 : b] : (((f @ X0) = (g @ X0))) )),
% 1.62/1.48 inference(cnf_transformation,[status(thm)],[f10])).
% 1.62/1.48 thf(f10,plain,(
% 1.62/1.48 ! [X0 : b] : ((f @ X0) = (g @ X0)) & ((h @ f) != (h @ g)) & (((g @ sK0) != (f @ sK0)) | ! [X2 : (b > $o) > $o] : (($true = (X2 @ g)) | ($true != (X2 @ f))))),
% 1.62/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.62/1.48 thf(f9,plain,(
% 1.62/1.48 ? [X1 : b] : ((f @ X1) != (g @ X1)) => ((g @ sK0) != (f @ sK0))),
% 1.62/1.48 introduced(definition,[],[choice_axiom])).
% 1.62/1.48 thf(f8,plain,(
% 1.62/1.48 ! [X0 : b] : ((f @ X0) = (g @ X0)) & ((h @ f) != (h @ g)) & (? [X1 : b] : ((f @ X1) != (g @ X1)) | ! [X2 : (b > $o) > $o] : (($true = (X2 @ g)) | ($true != (X2 @ f))))),
% 1.62/1.48 inference(rectify,[status(thm)],[f7])).
% 1.62/1.48 thf(f7,plain,(
% 1.62/1.48 ! [X2 : b] : ((g @ X2) = (f @ X2)) & ((h @ f) != (h @ g)) & (? [X0 : b] : ((f @ X0) != (g @ X0)) | ! [X1 : (b > $o) > $o] : (((X1 @ g) = $true) | ((X1 @ f) != $true)))),
% 1.62/1.48 inference(flattening,[status(thm)],[f6])).
% 1.62/1.48 thf(f6,plain,(
% 1.62/1.48 (((h @ f) != (h @ g)) & ! [X2 : b] : ((g @ X2) = (f @ X2))) & (? [X0 : b] : ((f @ X0) != (g @ X0)) | ! [X1 : (b > $o) > $o] : (((X1 @ g) = $true) | ((X1 @ f) != $true)))),
% 1.62/1.48 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.48 thf(f5,plain,(
% 1.62/1.48 ~((! [X0 : b] : ((f @ X0) = (g @ X0)) => ! [X1 : (b > $o) > $o] : (((X1 @ f) = $true) => ((X1 @ g) = $true))) => (! [X2 : b] : ((g @ X2) = (f @ X2)) => ((h @ f) = (h @ g))))),
% 1.62/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.48 thf(f4,plain,(
% 1.62/1.48 ~((! [X0 : b] : ((g @ X0) <=> (f @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g))) => (! [X2 : b] : ((g @ X2) <=> (f @ X2)) => ((h @ f) = (h @ g))))),
% 1.62/1.48 inference(rectify,[status(thm)],[f2])).
% 1.62/1.48 thf(f2,negated_conjecture,(
% 1.62/1.48 ~((! [X0 : b] : ((g @ X0) <=> (f @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g))) => (! [X0 : b] : ((g @ X0) <=> (f @ X0)) => ((h @ f) = (h @ g))))),
% 1.62/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.48 thf(f1,conjecture,(
% 1.62/1.48 (! [X0 : b] : ((g @ X0) <=> (f @ X0)) => ! [X1 : (b > $o) > $o] : ((X1 @ f) => (X1 @ g))) => (! [X0 : b] : ((g @ X0) <=> (f @ X0)) => ((h @ f) = (h @ g)))),
% 1.62/1.48 file('/export/starexec/sandbox/tmp/tmp.xccpM9MQmm/DTF2THF_29618.p',cEXT1)).
% 1.62/1.48 thf(f46,plain,(
% 1.62/1.48 ($true = (f @ sK3)) | ~spl1_6),
% 1.62/1.48 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.62/1.48 thf(f44,definition,(
% 1.62/1.48 spl1_6 <=> ($true = (f @ sK3))),
% 1.62/1.48 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.62/1.48 thf(f82,plain,(
% 1.62/1.48 ~spl1_7 | ~spl1_9),
% 1.62/1.48 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.62/1.48 thf(f81,plain,(
% 1.62/1.48 $false | (~spl1_7 | ~spl1_9)),
% 1.62/1.48 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.62/1.48 thf(f78,plain,(
% 1.62/1.48 ($true = $false) | (~spl1_7 | ~spl1_9)),
% 1.62/1.48 inference(superposition,[status(thm)],[f50,f59])).
% 1.62/1.48 thf(f59,plain,(
% 1.62/1.48 ((g @ sK3) = $false) | ~spl1_9),
% 1.62/1.48 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.62/1.48 thf(f57,definition,(
% 1.62/1.48 spl1_9 <=> ((g @ sK3) = $false)),
% 1.62/1.48 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.62/1.48 thf(f50,plain,(
% 1.62/1.48 ($true = (g @ sK3)) | ~spl1_7),
% 1.62/1.48 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.62/1.48 thf(f76,plain,(
% 1.62/1.48 spl1_9 | ~spl1_8),
% 1.62/1.48 inference(avatar_split_clause,[status(thm)],[f71,f53,f57])).
% 1.62/1.48 thf(f53,definition,(
% 1.62/1.48 spl1_8 <=> ($false = (f @ sK3))),
% 1.62/1.48 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.62/1.48 thf(f71,plain,(
% 1.62/1.48 ((g @ sK3) = $false) | ~spl1_8),
% 1.62/1.48 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.62/1.48 thf(f70,plain,(
% 1.62/1.48 ($true = $false) | ((g @ sK3) = $false) | ~spl1_8),
% 1.62/1.48 inference(superposition,[status(thm)],[f55,f14])).
% 1.62/1.48 thf(f14,plain,(
% 1.62/1.48 ( ! [X0 : b] : (((f @ X0) = $true) | ((g @ X0) = $false)) )),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.62/1.48 thf(f55,plain,(
% 1.62/1.48 ($false = (f @ sK3)) | ~spl1_8),
% 1.62/1.48 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.62/1.48 thf(f60,plain,(
% 1.62/1.48 spl1_8 | spl1_9),
% 1.62/1.48 inference(avatar_split_clause,[status(thm)],[f42,f57,f53])).
% 1.62/1.48 thf(f42,plain,(
% 1.62/1.48 ((g @ sK3) = $false) | ($false = (f @ sK3))),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.48 thf(f40,plain,(
% 1.62/1.48 ((g @ sK3) != (f @ sK3))),
% 1.62/1.48 inference(negative_extensionality,[status(thm)],[f39])).
% 1.62/1.48 thf(f39,plain,(
% 1.62/1.48 (f != g)),
% 1.62/1.48 inference(equality_resolution,[status(thm)],[f12])).
% 1.62/1.48 thf(f12,plain,(
% 1.62/1.48 ((h @ f) != (h @ g))),
% 1.62/1.48 inference(cnf_transformation,[status(thm)],[f10])).
% 1.62/1.48 thf(f51,plain,(
% 1.62/1.48 spl1_6 | spl1_7),
% 1.62/1.48 inference(avatar_split_clause,[status(thm)],[f41,f48,f44])).
% 1.62/1.48 thf(f41,plain,(
% 1.62/1.48 ($true = (g @ sK3)) | ($true = (f @ sK3))),
% 1.62/1.48 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.48 % SZS output end Proof for DTF2THF_29618
% 1.62/1.48 % (29778)------------------------------
% 1.62/1.48 % (29778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (29778)Termination reason: Refutation
% 1.62/1.48
% 1.62/1.48 % (29778)Memory used [KB]: 5500
% 1.62/1.48 % (29778)Time elapsed: 0.005 s
% 1.62/1.48 % (29778)Instructions burned: 3 (million)
% 1.62/1.48 % (29778)------------------------------
% 1.62/1.48 % (29778)------------------------------
% 1.62/1.48 % (29777)Success in time 0.017 s
%------------------------------------------------------------------------------