%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV433^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.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 09:41:14 AM UTC 2026
% Result : Theorem 1.63s 1.37s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 4 unt; 0 typ; 9 def)
% Number of atoms : 492 ( 179 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 370 ( 110 ~; 169 |; 10 &; 70 @)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 14 con; 0-2 aty)
% Number of variables : 125 ( 0 ^; 116 !; 9 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $o ).
thf(f347,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f79,f100,f101,f102,f139,f235,f278,f282,f283,f311,f346]) ).
thf(f346,plain,
( spl3_9
| ~ spl3_11 ),
inference(avatar_split_clause,[status(thm)],[f345,f233,f224]) ).
thf(f224,definition,
( spl3_9
<=> ! [X2: $i] :
( ( f @ X2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition]) ).
thf(f233,definition,
( spl3_11
<=> ! [X2: $i] :
( ( f @ X2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_11])],[avatar_definition]) ).
thf(f345,plain,
( ! [X0: $i] :
( ( f @ X0 )
= $false )
| ~ spl3_11 ),
inference(subsumption_resolution,[status(thm)],[f334,f340]) ).
thf(f340,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl3_11 ),
inference(trivial_inequality_removal,[status(thm)],[f330]) ).
thf(f330,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( X0 = X1 ) )
| ~ spl3_11 ),
inference(superposition,[status(thm)],[f327,f234]) ).
thf(f234,plain,
( ! [X2: $i] :
( ( f @ X2 )
= $true )
| ~ spl3_11 ),
inference(avatar_component_clause,[status(thm)],[f233]) ).
thf(f327,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( f @ X1 )
= $false ) )
| ~ spl3_11 ),
inference(trivial_inequality_removal,[status(thm)],[f322]) ).
thf(f322,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( X0 = X1 )
| ( ( f @ X1 )
= $false ) )
| ~ spl3_11 ),
inference(superposition,[status(thm)],[f16,f234]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( f @ X0 )
= $false )
| ( ( f @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHVTjW422/DTF2THF_7345.p',finj) ).
thf(f334,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $false )
| ( sK0 != X0 ) )
| ~ spl3_11 ),
inference(superposition,[status(thm)],[f12,f327]) ).
thf(f12,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK2 != sK1 )
& ( sK1 != sK0 )
& ( sK2 != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 != X1 )
& ( X0 != X2 ) )
=> ( ( sK2 != sK1 )
& ( sK1 != sK0 )
& ( sK2 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 != X1 )
& ( X0 != X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i,X2: $i,X0: $i] :
( ( X0 != X2 )
& ( X1 != X2 )
& ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X2: $i,X1: $i] :
( ( X0 = X1 )
| ( X1 = X2 )
| ( X0 = X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( X1 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHVTjW422/DTF2THF_7345.p',less3) ).
thf(f311,plain,
( ~ spl3_8
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f310]) ).
thf(f310,plain,
( $false
| ~ spl3_8
| ~ spl3_9 ),
inference(subsumption_resolution,[status(thm)],[f297,f309]) ).
thf(f309,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f308]) ).
thf(f308,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( X0 = X1 ) )
| ~ spl3_9 ),
inference(forward_demodulation,[status(thm)],[f299,f225]) ).
thf(f225,plain,
( ! [X2: $i] :
( ( f @ X2 )
= $false )
| ~ spl3_9 ),
inference(avatar_component_clause,[status(thm)],[f224]) ).
thf(f299,plain,
( ! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $true )
| ( X0 = X1 ) )
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f284]) ).
thf(f284,plain,
( ! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $true )
| ( $true = $false )
| ( X0 = X1 ) )
| ~ spl3_9 ),
inference(backward_demodulation,[status(thm)],[f15,f225]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= $true )
| ( ( f @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f297,plain,
( ! [X0: $i] : ( sK0 != X0 )
| ~ spl3_8
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f293]) ).
thf(f293,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( sK0 != X0 ) )
| ~ spl3_8
| ~ spl3_9 ),
inference(backward_demodulation,[status(thm)],[f99,f225]) ).
thf(f99,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $true )
| ( sK0 != X0 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl3_8
<=> ! [X0: $i] :
( ( sK0 != X0 )
| ( ( f @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f283,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f182,f84,f81]) ).
thf(f81,definition,
( spl3_3
<=> ! [X1: $i] :
( ( ( f @ X1 )
= $true )
| ( sK1 = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f84,definition,
( spl3_4
<=> ! [X0: $i] :
( ( sK0 != X0 )
| ( ( f @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f182,plain,
! [X0: $i,X1: $i] :
( ( sK1 = X1 )
| ( ( f @ X1 )
= $true )
| ( sK0 != X0 )
| ( ( f @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f12,f36]) ).
thf(f36,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( X0 = X2 )
| ( ( f @ X1 )
= $true )
| ( ( f @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( f @ X2 )
= $false )
| ( X0 = X1 )
| ( ( f @ X1 )
= $true )
| ( X0 = X2 ) ),
inference(superposition,[status(thm)],[f15,f16]) ).
thf(f282,plain,
( spl3_11
| spl3_6
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f281,f81,f91,f233]) ).
thf(f91,definition,
( spl3_6
<=> ! [X1: $i] :
( ( ( f @ X1 )
= $false )
| ( sK2 = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f281,plain,
( ! [X0: $i,X1: $i] :
( ( sK2 = X1 )
| ( ( f @ X0 )
= $true )
| ( ( f @ X1 )
= $false ) )
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f177,f245]) ).
thf(f245,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( sK1 = X0 )
| ( X1 = X2 )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f241]) ).
thf(f241,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( X1 = X2 )
| ( X0 = X1 )
| ( sK1 = X0 )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f36,f82]) ).
thf(f82,plain,
( ! [X1: $i] :
( ( ( f @ X1 )
= $true )
| ( sK1 = X1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f177,plain,
! [X0: $i,X1: $i] :
( ( sK2 = X1 )
| ( sK1 != X0 )
| ( ( f @ X0 )
= $true )
| ( ( f @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f13,f36]) ).
thf(f13,plain,
sK2 != sK1,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f278,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f277]) ).
thf(f277,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(subsumption_resolution,[status(thm)],[f273,f270]) ).
thf(f270,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl3_1
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f268,f268]) ).
thf(f268,plain,
( ! [X0: $i] : ( sK2 = X0 )
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f267]) ).
thf(f267,plain,
( ! [X0: $i] :
( ( sK2 = X0 )
| ( $true = $false ) )
| ~ spl3_1
| ~ spl3_6 ),
inference(duplicate_literal_removal,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X0: $i] :
( ( sK2 = X0 )
| ( $true = $false )
| ( sK2 = X0 ) )
| ~ spl3_1
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f75,f92]) ).
thf(f92,plain,
( ! [X1: $i] :
( ( ( f @ X1 )
= $false )
| ( sK2 = X1 ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f75,plain,
( ! [X1: $i] :
( ( ( f @ X1 )
= $true )
| ( sK2 = X1 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl3_1
<=> ! [X1: $i] :
( ( sK2 = X1 )
| ( ( f @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f273,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl3_1
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f13,f268]) ).
thf(f235,plain,
( spl3_9
| spl3_11
| spl3_9
| ~ spl3_4
| ~ spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f231,f98,f84,f224,f233,f224]) ).
thf(f231,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( f @ X0 )
= $false )
| ( ( f @ X1 )
= $false )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_4
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f230,f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X3 )
| ( ( f @ X3 )
= $false )
| ( X0 = X1 )
| ( X1 = X2 )
| ( ( f @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( f @ X3 )
= $false )
| ( X0 = X1 )
| ( X0 = X3 )
| ( ( f @ X2 )
= $false )
| ( $true = $false )
| ( X1 = X2 ) ),
inference(superposition,[status(thm)],[f36,f16]) ).
thf(f230,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( f @ X0 )
= $false )
| ( ( f @ X1 )
= $false )
| ( ( f @ X2 )
= $true )
| ( X0 != X1 ) )
| ~ spl3_4
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f220,f99]) ).
thf(f220,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( sK0 = X2 )
| ( X0 != X1 )
| ( ( f @ X1 )
= $false )
| ( ( f @ X0 )
= $false )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f85,f36]) ).
thf(f85,plain,
( ! [X0: $i] :
( ( sK0 != X0 )
| ( ( f @ X0 )
= $false ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f139,plain,
( ~ spl3_2
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl3_2
| ~ spl3_7 ),
inference(subsumption_resolution,[status(thm)],[f122,f121]) ).
thf(f121,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl3_2
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true = $false ) )
| ~ spl3_2
| ~ spl3_7 ),
inference(forward_demodulation,[status(thm)],[f111,f103]) ).
thf(f103,plain,
( ! [X0: $i] :
( ( f @ X0 )
= $false )
| ~ spl3_2
| ~ spl3_7 ),
inference(subsumption_resolution,[status(thm)],[f78,f96]) ).
thf(f96,plain,
( ! [X1: $i] :
( ( ( f @ X1 )
= $false )
| ( sK1 = X1 ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl3_7
<=> ! [X1: $i] :
( ( ( f @ X1 )
= $false )
| ( sK1 = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f78,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( ( f @ X0 )
= $false ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl3_2
<=> ! [X0: $i] :
( ( ( f @ X0 )
= $false )
| ( sK1 != X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f111,plain,
( ! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $true )
| ( X0 = X1 ) )
| ~ spl3_2
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $true )
| ( $true = $false )
| ( X0 = X1 ) )
| ~ spl3_2
| ~ spl3_7 ),
inference(backward_demodulation,[status(thm)],[f15,f103]) ).
thf(f122,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl3_2
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f13,f121]) ).
thf(f102,plain,
( spl3_6
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f47,f98,f91]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( sK0 != X0 )
| ( ( f @ X0 )
= $true )
| ( sK2 = X1 )
| ( ( f @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f11,f36]) ).
thf(f11,plain,
sK2 != sK0,
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f101,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f44,f84,f74]) ).
thf(f44,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= $false )
| ( ( f @ X1 )
= $true )
| ( sK2 = X1 )
| ( sK0 != X0 ) ),
inference(superposition,[status(thm)],[f11,f36]) ).
thf(f100,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f48,f98,f95]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $false )
| ( sK1 = X1 )
| ( sK0 != X0 )
| ( ( f @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f12,f36]) ).
thf(f79,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f43,f77,f74]) ).
thf(f43,plain,
! [X0: $i,X1: $i] :
( ( sK2 = X1 )
| ( ( f @ X0 )
= $false )
| ( sK1 != X0 )
| ( ( f @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f13,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV433^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n028.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:46:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV433^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : There are at most 2 individuals if there is an injection into o
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro11]
% 0.19/0.46 % Names : INJO [Bro11]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 7 ( 5 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.46 % Number of connectives : 5 ( 0 ~; 2 |; 0 &; 2 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.19/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(f,type,
% 0.19/0.46 f: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(finj,axiom,
% 0.19/0.46 ! [X: $i,Y: $i] :
% 0.19/0.46 ( ( ( f @ X )
% 0.19/0.46 = ( f @ Y ) )
% 0.19/0.46 => ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(less3,conjecture,
% 0.19/0.46 ! [X: $i,Y: $i,Z: $i] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 | ( X = Z )
% 0.19/0.46 | ( Y = Z ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 12:46:42 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WVHVTjW422/DTF2DTF7345.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(f,type,
% 1.47/1.29 f: $i > $o ).
% 1.47/1.29
% 1.47/1.29 thf(finj,axiom,
% 1.47/1.29 ! [X: $i,Y: $i] :
% 1.47/1.29 ( ( ( f @ X )
% 1.47/1.29 = ( f @ Y ) )
% 1.47/1.29 => ( X = Y ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(less3,conjecture,
% 1.47/1.29 ! [X: $i,Y: $i,Z: $i] :
% 1.47/1.29 ( ( X = Y )
% 1.47/1.29 | ( X = Z )
% 1.47/1.29 | ( Y = Z ) ) ).
% 1.47/1.29 ------------------------
% 1.63/1.31 % (7535)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_7345 for (3000ds/4Mi)
% 1.63/1.31 % (7540)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7345 for (3000ds/18Mi)
% 1.63/1.31 % (7537)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7345 for (3000ds/2Mi)
% 1.63/1.31 % (7535)Instruction limit reached!
% 1.63/1.31 % (7535)------------------------------
% 1.63/1.31 % (7535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7535)Termination reason: Unknown
% 1.63/1.31 % (7535)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7535)Memory used [KB]: 5500
% 1.63/1.31 % (7535)Time elapsed: 0.003 s
% 1.63/1.31 % (7535)Instructions burned: 4 (million)
% 1.63/1.31 % (7535)------------------------------
% 1.63/1.31 % (7535)------------------------------
% 1.63/1.31 % (7537)Instruction limit reached!
% 1.63/1.31 % (7537)------------------------------
% 1.63/1.31 % (7537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7537)Termination reason: Unknown
% 1.63/1.31 % (7537)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7537)Memory used [KB]: 5500
% 1.63/1.31 % (7537)Time elapsed: 0.002 s
% 1.63/1.31 % (7537)Instructions burned: 3 (million)
% 1.63/1.31 % (7537)------------------------------
% 1.63/1.31 % (7537)------------------------------
% 1.63/1.31 % (7540)Instruction limit reached!
% 1.63/1.31 % (7540)------------------------------
% 1.63/1.31 % (7540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7540)Termination reason: Unknown
% 1.63/1.31 % (7540)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7540)Memory used [KB]: 5500
% 1.63/1.31 % (7540)Time elapsed: 0.007 s
% 1.63/1.31 % (7540)Instructions burned: 18 (million)
% 1.63/1.31 % (7540)------------------------------
% 1.63/1.31 % (7540)------------------------------
% 1.63/1.31 % (7539)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_7345 for (3000ds/275Mi)
% 1.63/1.31 % (7539)Refutation not found, incomplete strategy
% 1.63/1.31 % (7539)------------------------------
% 1.63/1.31 % (7539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7539)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.31
% 1.63/1.31
% 1.63/1.31 % (7539)Memory used [KB]: 5373
% 1.63/1.31 % (7539)Time elapsed: 0.001 s
% 1.63/1.31 % (7539)------------------------------
% 1.63/1.31 % (7539)------------------------------
% 1.63/1.31 % (7534)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7345 for (3000ds/183Mi)
% 1.63/1.31 % (7536)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_7345 for (3000ds/27Mi)
% 1.63/1.31 % (7538)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_7345 for (3000ds/2Mi)
% 1.63/1.32 % (7538)Instruction limit reached!
% 1.63/1.32 % (7538)------------------------------
% 1.63/1.32 % (7538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7538)Termination reason: Unknown
% 1.63/1.32 % (7538)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (7538)Memory used [KB]: 5500
% 1.63/1.32 % (7538)Time elapsed: 0.003 s
% 1.63/1.32 % (7538)Instructions burned: 2 (million)
% 1.63/1.32 % (7538)------------------------------
% 1.63/1.32 % (7538)------------------------------
% 1.63/1.32 % (7542)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/37Mi)
% 1.63/1.32 % (7541)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/3Mi)
% 1.63/1.32 % (7541)Refutation not found, incomplete strategy
% 1.63/1.32 % (7541)------------------------------
% 1.63/1.32 % (7541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7541)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (7541)Memory used [KB]: 5500
% 1.63/1.32 % (7541)Time elapsed: 0.002 s
% 1.63/1.32 % (7541)Instructions burned: 1 (million)
% 1.63/1.32 % (7541)------------------------------
% 1.63/1.32 % (7541)------------------------------
% 1.63/1.32 % (7543)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/15Mi)
% 1.63/1.32 % (7543)Refutation not found, incomplete strategy
% 1.63/1.32 % (7543)------------------------------
% 1.63/1.32 % (7543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7543)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (7543)Memory used [KB]: 5500
% 1.63/1.32 % (7543)Time elapsed: 0.001 s
% 1.63/1.32 % (7543)Instructions burned: 1 (million)
% 1.63/1.32 % (7543)------------------------------
% 1.63/1.32 % (7543)------------------------------
% 1.63/1.33 % (7546)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/7Mi)
% 1.63/1.33 % (7544)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/3Mi)
% 1.63/1.33 % (7542)Instruction limit reached!
% 1.63/1.33 % (7542)------------------------------
% 1.63/1.33 % (7542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7542)Termination reason: Unknown
% 1.63/1.33 % (7542)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (7542)Memory used [KB]: 5628
% 1.63/1.33 % (7542)Time elapsed: 0.014 s
% 1.63/1.33 % (7542)Instructions burned: 39 (million)
% 1.63/1.33 % (7542)------------------------------
% 1.63/1.33 % (7542)------------------------------
% 1.63/1.33 % (7544)Instruction limit reached!
% 1.63/1.33 % (7544)------------------------------
% 1.63/1.33 % (7544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7547)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/16Mi)
% 1.63/1.33 % (7544)Termination reason: Unknown
% 1.63/1.33 % (7544)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (7544)Memory used [KB]: 5500
% 1.63/1.33 % (7544)Time elapsed: 0.004 s
% 1.63/1.33 % (7544)Instructions burned: 4 (million)
% 1.63/1.33 % (7544)------------------------------
% 1.63/1.33 % (7544)------------------------------
% 1.63/1.33 % (7536)Instruction limit reached!
% 1.63/1.33 % (7536)------------------------------
% 1.63/1.33 % (7536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7536)Termination reason: Unknown
% 1.63/1.33 % (7536)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (7536)Memory used [KB]: 5500
% 1.63/1.33 % (7536)Time elapsed: 0.020 s
% 1.63/1.33 % (7536)Instructions burned: 28 (million)
% 1.63/1.33 % (7536)------------------------------
% 1.63/1.33 % (7536)------------------------------
% 1.63/1.33 % (7546)Instruction limit reached!
% 1.63/1.33 % (7546)------------------------------
% 1.63/1.33 % (7546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (7546)Termination reason: Unknown
% 1.63/1.33 % (7546)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (7546)Memory used [KB]: 1023
% 1.63/1.33 % (7546)Time elapsed: 0.005 s
% 1.63/1.33 % (7546)Instructions burned: 9 (million)
% 1.63/1.33 % (7546)------------------------------
% 1.63/1.33 % (7546)------------------------------
% 1.63/1.33 % (7545)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/1041Mi)
% 1.63/1.34 % (7547)Instruction limit reached!
% 1.63/1.34 % (7547)------------------------------
% 1.63/1.34 % (7547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (7547)Termination reason: Unknown
% 1.63/1.34 % (7547)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (7547)Memory used [KB]: 5500
% 1.63/1.34 % (7547)Time elapsed: 0.007 s
% 1.63/1.34 % (7547)Instructions burned: 18 (million)
% 1.63/1.34 % (7547)------------------------------
% 1.63/1.34 % (7547)------------------------------
% 1.63/1.34 % (7548)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/3Mi)
% 1.63/1.34 % (7548)Refutation not found, incomplete strategy
% 1.63/1.34 % (7548)------------------------------
% 1.63/1.34 % (7548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (7548)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (7548)Memory used [KB]: 5500
% 1.63/1.34 % (7548)Time elapsed: 0.001 s
% 1.63/1.34 % (7548)Instructions burned: 1 (million)
% 1.63/1.34 % (7548)------------------------------
% 1.63/1.34 % (7548)------------------------------
% 1.63/1.34 % (7551)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/3Mi)
% 1.63/1.34 % (7551)Instruction limit reached!
% 1.63/1.34 % (7551)------------------------------
% 1.63/1.34 % (7551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (7551)Termination reason: Unknown
% 1.63/1.34 % (7551)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (7551)Memory used [KB]: 5500
% 1.63/1.34 % (7551)Time elapsed: 0.003 s
% 1.63/1.34 % (7551)Instructions burned: 4 (million)
% 1.63/1.34 % (7551)------------------------------
% 1.63/1.34 % (7551)------------------------------
% 1.63/1.35 % (7552)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/4Mi)
% 1.63/1.35 % (7552)Instruction limit reached!
% 1.63/1.35 % (7552)------------------------------
% 1.63/1.35 % (7552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (7552)Termination reason: Unknown
% 1.63/1.35 % (7552)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (7552)Memory used [KB]: 5500
% 1.63/1.35 % (7552)Time elapsed: 0.003 s
% 1.63/1.35 % (7552)Instructions burned: 6 (million)
% 1.63/1.35 % (7552)------------------------------
% 1.63/1.35 % (7552)------------------------------
% 1.63/1.35 % (7550)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/7Mi)
% 1.63/1.35 % (7549)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/3Mi)
% 1.63/1.35 % (7553)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/18Mi)
% 1.63/1.35 % (7550)Refutation not found, incomplete strategy
% 1.63/1.35 % (7550)------------------------------
% 1.63/1.35 % (7550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (7550)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (7550)Memory used [KB]: 5373
% 1.63/1.35 % (7550)Time elapsed: 0.003 s
% 1.63/1.35 % (7550)Instructions burned: 1 (million)
% 1.63/1.35 % (7550)------------------------------
% 1.63/1.35 % (7550)------------------------------
% 1.63/1.35 % (7549)Refutation not found, incomplete strategy
% 1.63/1.35 % (7549)------------------------------
% 1.63/1.35 % (7549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (7549)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (7549)Memory used [KB]: 5500
% 1.63/1.35 % (7549)Time elapsed: 0.003 s
% 1.63/1.35 % (7549)Instructions burned: 2 (million)
% 1.63/1.35 % (7549)------------------------------
% 1.63/1.35 % (7549)------------------------------
% 1.63/1.35 % (7554)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/710Mi)
% 1.63/1.36 % (7553)Instruction limit reached!
% 1.63/1.36 % (7553)------------------------------
% 1.63/1.36 % (7553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (7553)Termination reason: Unknown
% 1.63/1.36 % (7553)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (7553)Memory used [KB]: 5500
% 1.63/1.36 % (7553)Time elapsed: 0.007 s
% 1.63/1.36 % (7553)Instructions burned: 18 (million)
% 1.63/1.36 % (7553)------------------------------
% 1.63/1.36 % (7553)------------------------------
% 1.63/1.36 % (7555)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/6Mi)
% 1.63/1.36 % (7555)Instruction limit reached!
% 1.63/1.36 % (7555)------------------------------
% 1.63/1.36 % (7555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (7555)Termination reason: Unknown
% 1.63/1.36 % (7555)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (7555)Memory used [KB]: 5500
% 1.63/1.36 % (7555)Time elapsed: 0.003 s
% 1.63/1.36 % (7555)Instructions burned: 6 (million)
% 1.63/1.36 % (7555)------------------------------
% 1.63/1.36 % (7555)------------------------------
% 1.63/1.36 % (7557)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/21Mi)
% 1.63/1.36 % (7558)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7345 for (2999ds/5Mi)
% 1.63/1.37 % (7554)First to succeed.
% 1.63/1.37 % (7558)Instruction limit reached!
% 1.63/1.37 % (7558)------------------------------
% 1.63/1.37 % (7558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (7558)Termination reason: Unknown
% 1.63/1.37 % (7558)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (7558)Memory used [KB]: 5500
% 1.63/1.37 % (7558)Time elapsed: 0.003 s
% 1.63/1.37 % (7558)Instructions burned: 6 (million)
% 1.63/1.37 % (7558)------------------------------
% 1.63/1.37 % (7558)------------------------------
% 1.63/1.37 % (7554)Refutation found. Thanks to Tanya!
% 1.63/1.37 % SZS status Theorem for DTF2THF_7345
% 1.63/1.37 % SZS output start Proof for DTF2THF_7345
% 1.63/1.37 thf(func_def_0, type, f: $i > $o).
% 1.63/1.37 thf(f347,plain,(
% 1.63/1.37 $false),
% 1.63/1.37 inference(avatar_sat_refutation,[status(thm)],[f79,f100,f101,f102,f139,f235,f278,f282,f283,f311,f346])).
% 1.63/1.37 thf(f346,plain,(
% 1.63/1.37 spl3_9 | ~spl3_11),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f345,f233,f224])).
% 1.63/1.37 thf(f224,definition,(
% 1.63/1.37 spl3_9 <=> ! [X2 : $i] : ((f @ X2) = $false)),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition])).
% 1.63/1.37 thf(f233,definition,(
% 1.63/1.37 spl3_11 <=> ! [X2 : $i] : ((f @ X2) = $true)),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_11])],[avatar_definition])).
% 1.63/1.37 thf(f345,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((f @ X0) = $false)) ) | ~spl3_11),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f334,f340])).
% 1.63/1.37 thf(f340,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl3_11),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f330])).
% 1.63/1.37 thf(f330,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (X0 = X1)) ) | ~spl3_11),
% 1.63/1.37 inference(superposition,[status(thm)],[f327,f234])).
% 1.63/1.37 thf(f234,plain,(
% 1.63/1.37 ( ! [X2 : $i] : (((f @ X2) = $true)) ) | ~spl3_11),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f233])).
% 1.63/1.37 thf(f327,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((f @ X1) = $false)) ) | ~spl3_11),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f322])).
% 1.63/1.37 thf(f322,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (X0 = X1) | ((f @ X1) = $false)) ) | ~spl3_11),
% 1.63/1.37 inference(superposition,[status(thm)],[f16,f234])).
% 1.63/1.37 thf(f16,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((f @ X0) = $false) | ((f @ X1) = $false)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.63/1.37 thf(f14,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X0) != (f @ X1)) | (X0 = X1)) )),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.37 thf(f7,plain,(
% 1.63/1.37 ! [X0 : $i,X1 : $i] : (((f @ X0) != (f @ X1)) | (X0 = X1))),
% 1.63/1.37 inference(ennf_transformation,[status(thm)],[f1])).
% 1.63/1.37 thf(f1,axiom,(
% 1.63/1.37 ! [X0 : $i,X1 : $i] : (((f @ X0) = (f @ X1)) => (X0 = X1))),
% 1.63/1.37 file('/export/starexec/sandbox/tmp/tmp.WVHVTjW422/DTF2THF_7345.p',finj)).
% 1.63/1.37 thf(f334,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((f @ X0) = $false) | (sK0 != X0)) ) | ~spl3_11),
% 1.63/1.37 inference(superposition,[status(thm)],[f12,f327])).
% 1.63/1.37 thf(f12,plain,(
% 1.63/1.37 (sK1 != sK0)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.37 thf(f10,plain,(
% 1.63/1.37 (sK2 != sK1) & (sK1 != sK0) & (sK2 != sK0)),
% 1.63/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.63/1.37 thf(f9,plain,(
% 1.63/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : ((X1 != X2) & (X0 != X1) & (X0 != X2)) => ((sK2 != sK1) & (sK1 != sK0) & (sK2 != sK0))),
% 1.63/1.37 introduced(definition,[],[choice_axiom])).
% 1.63/1.37 thf(f8,plain,(
% 1.63/1.37 ? [X0 : $i,X1 : $i,X2 : $i] : ((X1 != X2) & (X0 != X1) & (X0 != X2))),
% 1.63/1.37 inference(rectify,[status(thm)],[f6])).
% 1.63/1.37 thf(f6,plain,(
% 1.63/1.37 ? [X1 : $i,X2 : $i,X0 : $i] : ((X0 != X2) & (X1 != X2) & (X0 != X1))),
% 1.63/1.37 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.37 thf(f5,plain,(
% 1.63/1.37 ~! [X0 : $i,X2 : $i,X1 : $i] : ((X0 = X1) | (X1 = X2) | (X0 = X2))),
% 1.63/1.37 inference(rectify,[status(thm)],[f3])).
% 1.63/1.37 thf(f3,negated_conjecture,(
% 1.63/1.37 ~! [X1 : $i,X0 : $i,X2 : $i] : ((X0 = X2) | (X0 = X1) | (X1 = X2))),
% 1.63/1.37 inference(negated_conjecture,[status(cth)],[f2])).
% 1.63/1.37 thf(f2,conjecture,(
% 1.63/1.37 ! [X1 : $i,X0 : $i,X2 : $i] : ((X0 = X2) | (X0 = X1) | (X1 = X2))),
% 1.63/1.37 file('/export/starexec/sandbox/tmp/tmp.WVHVTjW422/DTF2THF_7345.p',less3)).
% 1.63/1.37 thf(f311,plain,(
% 1.63/1.37 ~spl3_8 | ~spl3_9),
% 1.63/1.37 inference(avatar_contradiction_clause,[status(thm)],[f310])).
% 1.63/1.37 thf(f310,plain,(
% 1.63/1.37 $false | (~spl3_8 | ~spl3_9)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f297,f309])).
% 1.63/1.37 thf(f309,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl3_9),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f308])).
% 1.63/1.37 thf(f308,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (X0 = X1)) ) | ~spl3_9),
% 1.63/1.37 inference(forward_demodulation,[status(thm)],[f299,f225])).
% 1.63/1.37 thf(f225,plain,(
% 1.63/1.37 ( ! [X2 : $i] : (((f @ X2) = $false)) ) | ~spl3_9),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f224])).
% 1.63/1.37 thf(f299,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X1) = $true) | (X0 = X1)) ) | ~spl3_9),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f284])).
% 1.63/1.37 thf(f284,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X1) = $true) | ($true = $false) | (X0 = X1)) ) | ~spl3_9),
% 1.63/1.37 inference(backward_demodulation,[status(thm)],[f15,f225])).
% 1.63/1.37 thf(f15,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X0) = $true) | ((f @ X1) = $true) | (X0 = X1)) )),
% 1.63/1.37 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.63/1.37 thf(f297,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK0 != X0)) ) | (~spl3_8 | ~spl3_9)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f293])).
% 1.63/1.37 thf(f293,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (($true = $false) | (sK0 != X0)) ) | (~spl3_8 | ~spl3_9)),
% 1.63/1.37 inference(backward_demodulation,[status(thm)],[f99,f225])).
% 1.63/1.37 thf(f99,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((f @ X0) = $true) | (sK0 != X0)) ) | ~spl3_8),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.63/1.37 thf(f98,definition,(
% 1.63/1.37 spl3_8 <=> ! [X0 : $i] : ((sK0 != X0) | ((f @ X0) = $true))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.63/1.37 thf(f283,plain,(
% 1.63/1.37 spl3_3 | spl3_4),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f182,f84,f81])).
% 1.63/1.37 thf(f81,definition,(
% 1.63/1.37 spl3_3 <=> ! [X1 : $i] : (((f @ X1) = $true) | (sK1 = X1))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.63/1.37 thf(f84,definition,(
% 1.63/1.37 spl3_4 <=> ! [X0 : $i] : ((sK0 != X0) | ((f @ X0) = $false))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.63/1.37 thf(f182,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((sK1 = X1) | ((f @ X1) = $true) | (sK0 != X0) | ((f @ X0) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f12,f36])).
% 1.63/1.37 thf(f36,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | (X0 = X2) | ((f @ X1) = $true) | ((f @ X2) = $false)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f24])).
% 1.63/1.37 thf(f24,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((f @ X2) = $false) | (X0 = X1) | ((f @ X1) = $true) | (X0 = X2)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f15,f16])).
% 1.63/1.37 thf(f282,plain,(
% 1.63/1.37 spl3_11 | spl3_6 | ~spl3_3),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f281,f81,f91,f233])).
% 1.63/1.37 thf(f91,definition,(
% 1.63/1.37 spl3_6 <=> ! [X1 : $i] : (((f @ X1) = $false) | (sK2 = X1))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.63/1.37 thf(f281,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((sK2 = X1) | ((f @ X0) = $true) | ((f @ X1) = $false)) ) | ~spl3_3),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f177,f245])).
% 1.63/1.37 thf(f245,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | (sK1 = X0) | (X1 = X2) | ((f @ X2) = $true)) ) | ~spl3_3),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f241])).
% 1.63/1.37 thf(f241,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (X1 = X2) | (X0 = X1) | (sK1 = X0) | ((f @ X2) = $true)) ) | ~spl3_3),
% 1.63/1.37 inference(superposition,[status(thm)],[f36,f82])).
% 1.63/1.37 thf(f82,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (((f @ X1) = $true) | (sK1 = X1)) ) | ~spl3_3),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.63/1.37 thf(f177,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((sK2 = X1) | (sK1 != X0) | ((f @ X0) = $true) | ((f @ X1) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f13,f36])).
% 1.63/1.37 thf(f13,plain,(
% 1.63/1.37 (sK2 != sK1)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.37 thf(f278,plain,(
% 1.63/1.37 ~spl3_1 | ~spl3_6),
% 1.63/1.37 inference(avatar_contradiction_clause,[status(thm)],[f277])).
% 1.63/1.37 thf(f277,plain,(
% 1.63/1.37 $false | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f273,f270])).
% 1.63/1.37 thf(f270,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(superposition,[status(thm)],[f268,f268])).
% 1.63/1.37 thf(f268,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK2 = X0)) ) | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f267])).
% 1.63/1.37 thf(f267,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK2 = X0) | ($true = $false)) ) | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(duplicate_literal_removal,[status(thm)],[f256])).
% 1.63/1.37 thf(f256,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK2 = X0) | ($true = $false) | (sK2 = X0)) ) | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(superposition,[status(thm)],[f75,f92])).
% 1.63/1.37 thf(f92,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (((f @ X1) = $false) | (sK2 = X1)) ) | ~spl3_6),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.63/1.37 thf(f75,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (((f @ X1) = $true) | (sK2 = X1)) ) | ~spl3_1),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.63/1.37 thf(f74,definition,(
% 1.63/1.37 spl3_1 <=> ! [X1 : $i] : ((sK2 = X1) | ((f @ X1) = $true))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.63/1.37 thf(f273,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK1 != X0)) ) | (~spl3_1 | ~spl3_6)),
% 1.63/1.37 inference(superposition,[status(thm)],[f13,f268])).
% 1.63/1.37 thf(f235,plain,(
% 1.63/1.37 spl3_9 | spl3_11 | spl3_9 | ~spl3_4 | ~spl3_8),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f231,f98,f84,f224,f233,f224])).
% 1.63/1.37 thf(f231,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((f @ X0) = $false) | ((f @ X1) = $false) | ((f @ X2) = $true)) ) | (~spl3_4 | ~spl3_8)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f230,f70])).
% 1.63/1.37 thf(f70,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X3) | ((f @ X3) = $false) | (X0 = X1) | (X1 = X2) | ((f @ X2) = $false)) )),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.63/1.37 thf(f38,plain,(
% 1.63/1.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((f @ X3) = $false) | (X0 = X1) | (X0 = X3) | ((f @ X2) = $false) | ($true = $false) | (X1 = X2)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f36,f16])).
% 1.63/1.37 thf(f230,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((f @ X0) = $false) | ((f @ X1) = $false) | ((f @ X2) = $true) | (X0 != X1)) ) | (~spl3_4 | ~spl3_8)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f220,f99])).
% 1.63/1.37 thf(f220,plain,(
% 1.63/1.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((sK0 = X2) | (X0 != X1) | ((f @ X1) = $false) | ((f @ X0) = $false) | ((f @ X2) = $true)) ) | ~spl3_4),
% 1.63/1.37 inference(superposition,[status(thm)],[f85,f36])).
% 1.63/1.37 thf(f85,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK0 != X0) | ((f @ X0) = $false)) ) | ~spl3_4),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.63/1.37 thf(f139,plain,(
% 1.63/1.37 ~spl3_2 | ~spl3_7),
% 1.63/1.37 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.63/1.37 thf(f138,plain,(
% 1.63/1.37 $false | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f122,f121])).
% 1.63/1.37 thf(f121,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.63/1.37 thf(f120,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true = $false)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(forward_demodulation,[status(thm)],[f111,f103])).
% 1.63/1.37 thf(f103,plain,(
% 1.63/1.37 ( ! [X0 : $i] : (((f @ X0) = $false)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(subsumption_resolution,[status(thm)],[f78,f96])).
% 1.63/1.37 thf(f96,plain,(
% 1.63/1.37 ( ! [X1 : $i] : (((f @ X1) = $false) | (sK1 = X1)) ) | ~spl3_7),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.63/1.37 thf(f95,definition,(
% 1.63/1.37 spl3_7 <=> ! [X1 : $i] : (((f @ X1) = $false) | (sK1 = X1))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.63/1.37 thf(f78,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK1 != X0) | ((f @ X0) = $false)) ) | ~spl3_2),
% 1.63/1.37 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.63/1.37 thf(f77,definition,(
% 1.63/1.37 spl3_2 <=> ! [X0 : $i] : (((f @ X0) = $false) | (sK1 != X0))),
% 1.63/1.37 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.63/1.37 thf(f111,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X1) = $true) | (X0 = X1)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.63/1.37 thf(f104,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X1) = $true) | ($true = $false) | (X0 = X1)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(backward_demodulation,[status(thm)],[f15,f103])).
% 1.63/1.37 thf(f122,plain,(
% 1.63/1.37 ( ! [X0 : $i] : ((sK1 != X0)) ) | (~spl3_2 | ~spl3_7)),
% 1.63/1.37 inference(superposition,[status(thm)],[f13,f121])).
% 1.63/1.37 thf(f102,plain,(
% 1.63/1.37 spl3_6 | spl3_8),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f47,f98,f91])).
% 1.63/1.37 thf(f47,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((sK0 != X0) | ((f @ X0) = $true) | (sK2 = X1) | ((f @ X1) = $false)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f11,f36])).
% 1.63/1.37 thf(f11,plain,(
% 1.63/1.37 (sK2 != sK0)),
% 1.63/1.37 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.37 thf(f101,plain,(
% 1.63/1.37 spl3_1 | spl3_4),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f44,f84,f74])).
% 1.63/1.37 thf(f44,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X0) = $false) | ((f @ X1) = $true) | (sK2 = X1) | (sK0 != X0)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f11,f36])).
% 1.63/1.37 thf(f100,plain,(
% 1.63/1.37 spl3_7 | spl3_8),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f48,f98,f95])).
% 1.63/1.37 thf(f48,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : (((f @ X1) = $false) | (sK1 = X1) | (sK0 != X0) | ((f @ X0) = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f12,f36])).
% 1.63/1.37 thf(f79,plain,(
% 1.63/1.37 spl3_1 | spl3_2),
% 1.63/1.37 inference(avatar_split_clause,[status(thm)],[f43,f77,f74])).
% 1.63/1.37 thf(f43,plain,(
% 1.63/1.37 ( ! [X0 : $i,X1 : $i] : ((sK2 = X1) | ((f @ X0) = $false) | (sK1 != X0) | ((f @ X1) = $true)) )),
% 1.63/1.37 inference(superposition,[status(thm)],[f13,f36])).
% 1.63/1.37 % SZS output end Proof for DTF2THF_7345
% 1.63/1.37 % (7554)------------------------------
% 1.63/1.37 % (7554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (7554)Termination reason: Refutation
% 1.63/1.37
% 1.63/1.37 % (7554)Memory used [KB]: 5628
% 1.63/1.37 % (7554)Time elapsed: 0.015 s
% 1.63/1.37 % (7554)Instructions burned: 35 (million)
% 1.63/1.37 % (7554)------------------------------
% 1.63/1.37 % (7554)------------------------------
% 1.63/1.37 % (7533)Success in time 0.063 s
%------------------------------------------------------------------------------