%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM665^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 09:24:10 AM UTC 2026
% Result : Theorem 1.42s 1.28s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 406 ( 102 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 528 ( 93 ~; 84 |; 0 &; 338 @)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 80 ( 22 ^; 58 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
moreis: nat > nat > $o ).
thf(func_def_6,type,
some: ( nat > $o ) > $o ).
thf(func_def_7,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_8,type,
lessis: nat > nat > $o ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK2: nat ).
thf(func_def_16,type,
sK3: nat > nat > nat ).
thf(func_def_17,type,
sK4: nat > nat ).
thf(f136,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f92,f110,f114,f134]) ).
thf(f134,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f133]) ).
thf(f133,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f132,f104]) ).
thf(f104,plain,
( ( ( lessis @ y @ x )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl0_8
<=> ( ( lessis @ y @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f132,plain,
( ( ( lessis @ y @ x )
!= $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true = $false )
| ( ( lessis @ y @ x )
!= $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(duplicate_literal_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( lessis @ y @ x )
!= $true )
| ( $true = $false )
| ( $true = $false )
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f99,f109]) ).
thf(f109,plain,
( ( ( diffprop @ y @ z @ ( sK4 @ y ) )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl0_9
<=> ( ( diffprop @ y @ z @ ( sK4 @ y ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f99,plain,
( ! [X0: nat] :
( ( ( diffprop @ y @ z @ ( sK4 @ X0 ) )
= $false )
| ( ( lessis @ X0 @ x )
!= $true )
| ( ( diffprop @ X0 @ z @ ( sK4 @ X0 ) )
= $false ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ! [X0: nat] :
( ( ( lessis @ X0 @ x )
!= $true )
| ( ( diffprop @ y @ z @ ( sK4 @ X0 ) )
!= ( diffprop @ X0 @ z @ ( sK4 @ X0 ) ) ) )
| ~ spl0_6 ),
inference(negative_extensionality,[status(thm)],[f95]) ).
thf(f95,plain,
( ! [X0: nat] :
( ( ( diffprop @ y @ z )
!= ( diffprop @ X0 @ z ) )
| ( ( lessis @ X0 @ x )
!= $true ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ! [X0: nat] :
( ( ( diffprop @ y @ z )
!= ( diffprop @ X0 @ z ) )
| ( ( lessis @ X0 @ x )
!= $true )
| ( $true != $true ) )
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f73,f29]) ).
thf(f29,plain,
( ( some @ ( diffprop @ y @ z ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ z @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ z @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( some
@ ^ [X0: nat] : ( diffprop @ y @ z @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ y @ z @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',n) ).
thf(f73,plain,
( ! [X0: nat] :
( ( ( some @ ( diffprop @ X0 @ z ) )
!= $true )
| ( ( lessis @ X0 @ x )
!= $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_6
<=> ! [X0: nat] :
( ( ( some @ ( diffprop @ X0 @ z ) )
!= $true )
| ( ( lessis @ X0 @ x )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f114,plain,
spl0_8,
inference(avatar_contradiction_clause,[status(thm)],[f113]) ).
thf(f113,plain,
( $false
| spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f112,f26]) ).
thf(f26,plain,
( ( moreis @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( moreis @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
moreis @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
moreis @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',m) ).
thf(f112,plain,
( ( ( moreis @ x @ y )
!= $true )
| spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $true != $true )
| ( ( moreis @ x @ y )
!= $true )
| spl0_8 ),
inference(superposition,[status(thm)],[f105,f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
=> ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X1 @ X0 )
=> ( lessis @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat,X1: nat] :
( ( moreis @ X1 @ X2 )
=> ( lessis @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz13) ).
thf(f105,plain,
( ( ( lessis @ y @ x )
!= $true )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f110,plain,
( ~ spl0_8
| spl0_9
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f101,f72,f107,f103]) ).
thf(f101,plain,
( ( ( diffprop @ y @ z @ ( sK4 @ y ) )
= $true )
| ( ( lessis @ y @ x )
!= $true )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( diffprop @ y @ z @ ( sK4 @ y ) )
= $true )
| ( ( lessis @ y @ x )
!= $true )
| ( $true != $true )
| ~ spl0_6 ),
inference(equality_factoring,[status(thm)],[f98]) ).
thf(f98,plain,
( ! [X0: nat] :
( ( ( diffprop @ y @ z @ ( sK4 @ X0 ) )
= $true )
| ( ( lessis @ X0 @ x )
!= $true )
| ( ( diffprop @ X0 @ z @ ( sK4 @ X0 ) )
= $true ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f92,plain,
( spl0_6
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f82,f68,f72]) ).
thf(f68,definition,
( spl0_5
<=> ( ( diffprop @ x @ z @ ( sK3 @ z @ x ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f82,plain,
( ! [X0: nat] :
( ( ( lessis @ X0 @ x )
!= $true )
| ( ( some @ ( diffprop @ X0 @ z ) )
!= $true ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ! [X0: nat] :
( ( ( lessis @ X0 @ x )
!= $true )
| ( $true = $false )
| ( ( some @ ( diffprop @ X0 @ z ) )
!= $true ) )
| ~ spl0_5 ),
inference(duplicate_literal_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( ( lessis @ X0 @ x )
!= $true )
| ( ( some @ ( diffprop @ X0 @ z ) )
!= $true )
| ( $true = $false ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f64,f70]) ).
thf(f70,plain,
( ( ( diffprop @ x @ z @ ( sK3 @ z @ x ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f64,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( diffprop @ x @ z @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( lessis @ X2 @ X0 )
!= $true )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true )
| ( ( diffprop @ X0 @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( diffprop @ X0 @ X1 @ ( sK3 @ X1 @ X0 ) )
!= ( diffprop @ x @ z @ ( sK3 @ X1 @ X0 ) ) )
| ( ( lessis @ X2 @ X0 )
!= $true )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true ) ),
inference(negative_extensionality,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( diffprop @ x @ z )
!= ( diffprop @ X0 @ X1 ) )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true )
| ( ( lessis @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( ( lessis @ X2 @ X0 )
!= $true )
| ( ( diffprop @ x @ z )
!= ( diffprop @ X0 @ X1 ) )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true ) ),
inference(constrained_superposition,[status(thm)],[f27,f28]) ).
thf(f28,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some @ ( diffprop @ X1 @ X2 ) )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true )
| ( ( some @ ( diffprop @ X0 @ X2 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
=> ( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( some
@ ^ [Y0: nat] : ( diffprop @ X1 @ X2 @ Y0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X0 @ X2 @ X3 ) )
=> ( ( lessis @ X0 @ X1 )
=> ( some
@ ^ [X4: nat] : ( diffprop @ X1 @ X2 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: nat,X3: nat,X1: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X1 @ X4 ) )
=> ( ( lessis @ X2 @ X3 )
=> ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz16b) ).
thf(f27,plain,
( $true
!= ( some @ ( diffprop @ x @ z ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) )
!= $true ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz16c) ).
thf(f74,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f66,f72,f68]) ).
thf(f66,plain,
! [X0: nat] :
( ( ( some @ ( diffprop @ X0 @ z ) )
!= $true )
| ( ( diffprop @ x @ z @ ( sK3 @ z @ x ) )
= $true )
| ( ( lessis @ X0 @ x )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: nat] :
( ( ( diffprop @ x @ z @ ( sK3 @ z @ x ) )
= $true )
| ( $true != $true )
| ( ( some @ ( diffprop @ X0 @ z ) )
!= $true )
| ( ( lessis @ X0 @ x )
!= $true ) ),
inference(equality_factoring,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
= ( diffprop @ x @ z @ ( sK3 @ X1 @ X0 ) ) )
| ( ( some @ ( diffprop @ X2 @ X1 ) )
!= $true )
| ( ( diffprop @ X0 @ X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
| ( ( lessis @ X2 @ X0 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM665^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:10:16 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : NUM665^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.48 % Domain : Number Theory
% 0.31/0.48 % Problem : Landau theorem 16c
% 0.31/0.48 % Version : Especial.
% 0.31/0.48 % English : some (lambda u.diffprop x z u)
% 0.31/0.48
% 0.31/0.48 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.48 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.48 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Bro09]
% 0.31/0.48 % Names : satz16c [Lan30]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % : Without extensionality : Theorem
% 0.31/0.48 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% 0.31/0.48 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 0.31/0.48 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 5 ( 2 avg)
% 0.31/0.48 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 24 @)
% 0.31/0.48 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 11 ( 6 avg)
% 0.31/0.48 % Number of types : 2 ( 1 usr)
% 0.31/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 7 ( 7 usr; 3 con; 0-3 aty)
% 0.31/0.48 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 0.31/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.48
% 0.31/0.48 % Comments :
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(nat_type,type,
% 0.31/0.48 nat: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(x,type,
% 0.31/0.48 x: nat ).
% 0.31/0.48
% 0.31/0.48 thf(y,type,
% 0.31/0.48 y: nat ).
% 0.31/0.48
% 0.31/0.48 thf(z,type,
% 0.31/0.48 z: nat ).
% 0.31/0.48
% 0.31/0.48 thf(moreis,type,
% 0.31/0.48 moreis: nat > nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(m,axiom,
% 0.31/0.48 moreis @ x @ y ).
% 0.31/0.48
% 0.31/0.48 thf(some,type,
% 0.31/0.48 some: ( nat > $o ) > $o ).
% 0.31/0.48
% 0.31/0.48 thf(diffprop,type,
% 0.31/0.48 diffprop: nat > nat > nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(n,axiom,
% 0.31/0.48 ( some
% 0.31/0.48 @ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(lessis,type,
% 0.31/0.48 lessis: nat > nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(satz16b,axiom,
% 0.31/0.48 ! [Xx: nat,Xy: nat,Xz: nat] :
% 0.31/0.48 ( ( some
% 0.31/0.48 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 0.31/0.48 => ( ( lessis @ Xy @ Xz )
% 0.31/0.48 => ( some
% 0.31/0.48 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(satz13,axiom,
% 0.31/0.48 ! [Xx: nat,Xy: nat] :
% 0.31/0.48 ( ( moreis @ Xx @ Xy )
% 0.31/0.48 => ( lessis @ Xy @ Xx ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(satz16c,conjecture,
% 0.31/0.48 ( some
% 0.31/0.48 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.42/1.25 ---- Embedded in THF ---
% 1.42/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.25 %%% Generated on Tue Feb 24 11:10:17 EST 2026
% 1.42/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.25 %%% Logic specification used:
% 1.42/1.25 %%% thf(spec, logic, $$dhol).
% 1.42/1.25
% 1.42/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2DTF28371.p
% See solution above
% 1.42/1.25 ------------------------
% 1.42/1.26 ---- Cleaned THF ---
% 1.42/1.26 thf(nat_type,type,
% 1.42/1.26 nat: $tType ).
% 1.42/1.26
% 1.42/1.26 thf(x,type,
% 1.42/1.26 x: nat ).
% 1.42/1.26
% 1.42/1.26 thf(y,type,
% 1.42/1.26 y: nat ).
% 1.42/1.26
% 1.42/1.26 thf(z,type,
% 1.42/1.26 z: nat ).
% 1.42/1.26
% 1.42/1.26 thf(moreis,type,
% 1.42/1.26 moreis: nat > nat > $o ).
% 1.42/1.26
% 1.42/1.26 thf(m,axiom,
% 1.42/1.26 moreis @ x @ y ).
% 1.42/1.26
% 1.42/1.26 thf(some,type,
% 1.42/1.26 some: ( nat > $o ) > $o ).
% 1.42/1.26
% 1.42/1.26 thf(diffprop,type,
% 1.42/1.26 diffprop: nat > nat > nat > $o ).
% 1.42/1.26
% 1.42/1.26 thf(n,axiom,
% 1.42/1.26 ( some
% 1.42/1.26 @ ^ [Xu: nat] : ( diffprop @ y @ z @ Xu ) ) ).
% 1.42/1.26
% 1.42/1.26 thf(lessis,type,
% 1.42/1.26 lessis: nat > nat > $o ).
% 1.42/1.26
% 1.42/1.26 thf(satz16b,axiom,
% 1.42/1.26 ! [Xx: nat,Xy: nat,Xz: nat] :
% 1.42/1.26 ( ( some
% 1.42/1.26 @ ^ [Xv: nat] : ( diffprop @ Xy @ Xx @ Xv ) )
% 1.42/1.26 => ( ( lessis @ Xy @ Xz )
% 1.42/1.26 => ( some
% 1.42/1.26 @ ^ [Xv: nat] : ( diffprop @ Xz @ Xx @ Xv ) ) ) ) ).
% 1.42/1.26
% 1.42/1.26 thf(satz13,axiom,
% 1.42/1.26 ! [Xx: nat,Xy: nat] :
% 1.42/1.26 ( ( moreis @ Xx @ Xy )
% 1.42/1.26 => ( lessis @ Xy @ Xx ) ) ).
% 1.42/1.26
% 1.42/1.26 thf(satz16c,conjecture,
% 1.42/1.26 ( some
% 1.42/1.26 @ ^ [Xu: nat] : ( diffprop @ x @ z @ Xu ) ) ).
% 1.42/1.26 ------------------------
% 1.42/1.27 % (28468)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28371 for (2999ds/183Mi)
% 1.42/1.28 % (28468)First to succeed.
% 1.42/1.28 % (28470)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_28371 for (2999ds/27Mi)
% 1.42/1.28 % (28471)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28371 for (2999ds/2Mi)
% 1.42/1.28 % (28473)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_28371 for (2999ds/275Mi)
% 1.42/1.28 % (28474)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28371 for (2999ds/18Mi)
% 1.42/1.28 % (28472)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_28371 for (2999ds/2Mi)
% 1.42/1.28 % (28469)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_28371 for (2999ds/4Mi)
% 1.42/1.28 % (28473)Refutation not found, incomplete strategy
% 1.42/1.28 % (28473)------------------------------
% 1.42/1.28 % (28473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.28 % (28468)Refutation found. Thanks to Tanya!
% 1.42/1.28 % SZS status Theorem for DTF2THF_28371
% 1.42/1.28 % SZS output start Proof for DTF2THF_28371
% 1.42/1.28 thf(type_def_5, type, nat: $tType).
% 1.42/1.28 thf(func_def_0, type, nat: $tType).
% 1.42/1.28 thf(func_def_1, type, x: nat).
% 1.42/1.28 thf(func_def_2, type, y: nat).
% 1.42/1.28 thf(func_def_3, type, z: nat).
% 1.42/1.28 thf(func_def_4, type, moreis: nat > nat > $o).
% 1.42/1.28 thf(func_def_6, type, some: (nat > $o) > $o).
% 1.42/1.28 thf(func_def_7, type, diffprop: nat > nat > nat > $o).
% 1.42/1.28 thf(func_def_8, type, lessis: nat > nat > $o).
% 1.42/1.28 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.42/1.28 thf(func_def_15, type, sK2: nat).
% 1.42/1.28 thf(func_def_16, type, sK3: nat > nat > nat).
% 1.42/1.28 thf(func_def_17, type, sK4: nat > nat).
% 1.42/1.28 thf(f136,plain,(
% 1.42/1.28 $false),
% 1.42/1.28 inference(avatar_sat_refutation,[status(thm)],[f74,f92,f110,f114,f134])).
% 1.42/1.28 thf(f134,plain,(
% 1.42/1.28 ~spl0_6 | ~spl0_8 | ~spl0_9),
% 1.42/1.28 inference(avatar_contradiction_clause,[status(thm)],[f133])).
% 1.42/1.28 thf(f133,plain,(
% 1.42/1.28 $false | (~spl0_6 | ~spl0_8 | ~spl0_9)),
% 1.42/1.28 inference(subsumption_resolution,[status(thm)],[f132,f104])).
% 1.42/1.28 thf(f104,plain,(
% 1.42/1.28 ((lessis @ y @ x) = $true) | ~spl0_8),
% 1.42/1.28 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.42/1.28 thf(f103,definition,(
% 1.42/1.28 spl0_8 <=> ((lessis @ y @ x) = $true)),
% 1.42/1.28 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.42/1.28 thf(f132,plain,(
% 1.42/1.28 ((lessis @ y @ x) != $true) | (~spl0_6 | ~spl0_9)),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.42/1.28 thf(f131,plain,(
% 1.42/1.28 ($true = $false) | ((lessis @ y @ x) != $true) | (~spl0_6 | ~spl0_9)),
% 1.42/1.28 inference(duplicate_literal_removal,[status(thm)],[f121])).
% 1.42/1.28 thf(f121,plain,(
% 1.42/1.28 ((lessis @ y @ x) != $true) | ($true = $false) | ($true = $false) | (~spl0_6 | ~spl0_9)),
% 1.42/1.28 inference(superposition,[status(thm)],[f99,f109])).
% 1.42/1.28 thf(f109,plain,(
% 1.42/1.28 ((diffprop @ y @ z @ (sK4 @ y)) = $true) | ~spl0_9),
% 1.42/1.28 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.42/1.28 thf(f107,definition,(
% 1.42/1.28 spl0_9 <=> ((diffprop @ y @ z @ (sK4 @ y)) = $true)),
% 1.42/1.28 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.42/1.28 thf(f99,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((diffprop @ y @ z @ (sK4 @ X0)) = $false) | ((lessis @ X0 @ x) != $true) | ((diffprop @ X0 @ z @ (sK4 @ X0)) = $false)) ) | ~spl0_6),
% 1.42/1.28 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.42/1.28 thf(f97,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((lessis @ X0 @ x) != $true) | ((diffprop @ y @ z @ (sK4 @ X0)) != (diffprop @ X0 @ z @ (sK4 @ X0)))) ) | ~spl0_6),
% 1.42/1.28 inference(negative_extensionality,[status(thm)],[f95])).
% 1.42/1.28 thf(f95,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((diffprop @ y @ z) != (diffprop @ X0 @ z)) | ((lessis @ X0 @ x) != $true)) ) | ~spl0_6),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.42/1.28 thf(f94,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((diffprop @ y @ z) != (diffprop @ X0 @ z)) | ((lessis @ X0 @ x) != $true) | ($true != $true)) ) | ~spl0_6),
% 1.42/1.28 inference(constrained_superposition,[status(thm)],[f73,f29])).
% 1.42/1.28 thf(f29,plain,(
% 1.42/1.28 ((some @ (diffprop @ y @ z)) = $true)),
% 1.42/1.28 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.42/1.28 thf(f22,plain,(
% 1.42/1.28 ((some @ (^[Y0 : nat]: (diffprop @ y @ z @ Y0))) = $true)),
% 1.42/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.42/1.28 thf(f15,plain,(
% 1.42/1.28 ((some @ (^[Y0 : nat]: (diffprop @ y @ z @ Y0))) = $true)),
% 1.42/1.28 inference(fool_elimination,[status(thm)],[f14])).
% 1.42/1.28 thf(f14,plain,(
% 1.42/1.28 (some @ (^[X0 : nat] : (diffprop @ y @ z @ X0)))),
% 1.42/1.28 inference(rectify,[status(thm)],[f2])).
% 1.42/1.28 thf(f2,axiom,(
% 1.42/1.28 (some @ (^[X0 : nat] : (diffprop @ y @ z @ X0)))),
% 1.42/1.28 file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',n)).
% 1.42/1.28 thf(f73,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((some @ (diffprop @ X0 @ z)) != $true) | ((lessis @ X0 @ x) != $true)) ) | ~spl0_6),
% 1.42/1.28 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.42/1.28 thf(f72,definition,(
% 1.42/1.28 spl0_6 <=> ! [X0 : nat] : (((some @ (diffprop @ X0 @ z)) != $true) | ((lessis @ X0 @ x) != $true))),
% 1.42/1.28 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.42/1.28 thf(f114,plain,(
% 1.42/1.28 spl0_8),
% 1.42/1.28 inference(avatar_contradiction_clause,[status(thm)],[f113])).
% 1.42/1.28 thf(f113,plain,(
% 1.42/1.28 $false | spl0_8),
% 1.42/1.28 inference(subsumption_resolution,[status(thm)],[f112,f26])).
% 1.42/1.28 thf(f26,plain,(
% 1.42/1.28 ((moreis @ x @ y) = $true)),
% 1.42/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.28 thf(f9,plain,(
% 1.42/1.28 ((moreis @ x @ y) = $true)),
% 1.42/1.28 inference(fool_elimination,[status(thm)],[f8])).
% 1.42/1.28 thf(f8,plain,(
% 1.42/1.28 (moreis @ x @ y)),
% 1.42/1.28 inference(rectify,[status(thm)],[f1])).
% 1.42/1.28 thf(f1,axiom,(
% 1.42/1.28 (moreis @ x @ y)),
% 1.42/1.28 file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',m)).
% 1.42/1.28 thf(f112,plain,(
% 1.42/1.28 ((moreis @ x @ y) != $true) | spl0_8),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.42/1.28 thf(f111,plain,(
% 1.42/1.28 ($true != $true) | ((moreis @ x @ y) != $true) | spl0_8),
% 1.42/1.28 inference(superposition,[status(thm)],[f105,f24])).
% 1.42/1.28 thf(f24,plain,(
% 1.42/1.28 ( ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) | ((moreis @ X1 @ X0) != $true)) )),
% 1.42/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.42/1.28 thf(f19,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) | ((moreis @ X1 @ X0) != $true))),
% 1.42/1.28 inference(ennf_transformation,[status(thm)],[f11])).
% 1.42/1.28 thf(f11,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat] : (((moreis @ X1 @ X0) = $true) => ((lessis @ X0 @ X1) = $true))),
% 1.42/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.42/1.28 thf(f10,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat] : ((moreis @ X1 @ X0) => (lessis @ X0 @ X1))),
% 1.42/1.28 inference(rectify,[status(thm)],[f4])).
% 1.42/1.28 thf(f4,axiom,(
% 1.42/1.28 ! [X2 : nat,X1 : nat] : ((moreis @ X1 @ X2) => (lessis @ X2 @ X1))),
% 1.42/1.28 file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz13)).
% 1.42/1.28 thf(f105,plain,(
% 1.42/1.28 ((lessis @ y @ x) != $true) | spl0_8),
% 1.42/1.28 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.42/1.28 thf(f110,plain,(
% 1.42/1.28 ~spl0_8 | spl0_9 | ~spl0_6),
% 1.42/1.28 inference(avatar_split_clause,[status(thm)],[f101,f72,f107,f103])).
% 1.42/1.28 thf(f101,plain,(
% 1.42/1.28 ((diffprop @ y @ z @ (sK4 @ y)) = $true) | ((lessis @ y @ x) != $true) | ~spl0_6),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.42/1.28 thf(f100,plain,(
% 1.42/1.28 ((diffprop @ y @ z @ (sK4 @ y)) = $true) | ((lessis @ y @ x) != $true) | ($true != $true) | ~spl0_6),
% 1.42/1.28 inference(equality_factoring,[status(thm)],[f98])).
% 1.42/1.28 thf(f98,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((diffprop @ y @ z @ (sK4 @ X0)) = $true) | ((lessis @ X0 @ x) != $true) | ((diffprop @ X0 @ z @ (sK4 @ X0)) = $true)) ) | ~spl0_6),
% 1.42/1.28 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.42/1.28 thf(f92,plain,(
% 1.42/1.28 spl0_6 | ~spl0_5),
% 1.42/1.28 inference(avatar_split_clause,[status(thm)],[f82,f68,f72])).
% 1.42/1.28 thf(f68,definition,(
% 1.42/1.28 spl0_5 <=> ((diffprop @ x @ z @ (sK3 @ z @ x)) = $true)),
% 1.42/1.28 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.42/1.28 thf(f82,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((lessis @ X0 @ x) != $true) | ((some @ (diffprop @ X0 @ z)) != $true)) ) | ~spl0_5),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.42/1.28 thf(f81,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((lessis @ X0 @ x) != $true) | ($true = $false) | ((some @ (diffprop @ X0 @ z)) != $true)) ) | ~spl0_5),
% 1.42/1.28 inference(duplicate_literal_removal,[status(thm)],[f76])).
% 1.42/1.28 thf(f76,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (($true = $false) | ((lessis @ X0 @ x) != $true) | ((some @ (diffprop @ X0 @ z)) != $true) | ($true = $false)) ) | ~spl0_5),
% 1.42/1.28 inference(superposition,[status(thm)],[f64,f70])).
% 1.42/1.28 thf(f70,plain,(
% 1.42/1.28 ((diffprop @ x @ z @ (sK3 @ z @ x)) = $true) | ~spl0_5),
% 1.42/1.28 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.42/1.28 thf(f64,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((diffprop @ x @ z @ (sK3 @ X1 @ X0)) = $false) | ((lessis @ X2 @ X0) != $true) | ((some @ (diffprop @ X2 @ X1)) != $true) | ((diffprop @ X0 @ X1 @ (sK3 @ X1 @ X0)) = $false)) )),
% 1.42/1.28 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.42/1.28 thf(f62,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((diffprop @ X0 @ X1 @ (sK3 @ X1 @ X0)) != (diffprop @ x @ z @ (sK3 @ X1 @ X0))) | ((lessis @ X2 @ X0) != $true) | ((some @ (diffprop @ X2 @ X1)) != $true)) )),
% 1.42/1.28 inference(negative_extensionality,[status(thm)],[f61])).
% 1.42/1.28 thf(f61,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((diffprop @ x @ z) != (diffprop @ X0 @ X1)) | ((some @ (diffprop @ X2 @ X1)) != $true) | ((lessis @ X2 @ X0) != $true)) )),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.42/1.28 thf(f60,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ((lessis @ X2 @ X0) != $true) | ((diffprop @ x @ z) != (diffprop @ X0 @ X1)) | ((some @ (diffprop @ X2 @ X1)) != $true)) )),
% 1.42/1.28 inference(constrained_superposition,[status(thm)],[f27,f28])).
% 1.42/1.28 thf(f28,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (diffprop @ X1 @ X2)) = $true) | ((lessis @ X0 @ X1) != $true) | ((some @ (diffprop @ X0 @ X2)) != $true)) )),
% 1.42/1.28 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.42/1.28 thf(f23,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X1 @ X2 @ Y0))) = $true) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0)))) | ((lessis @ X0 @ X1) != $true)) )),
% 1.42/1.28 inference(cnf_transformation,[status(thm)],[f21])).
% 1.42/1.28 thf(f21,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat,X2 : nat] : (((some @ (^[Y0 : nat]: (diffprop @ X1 @ X2 @ Y0))) = $true) | ((lessis @ X0 @ X1) != $true) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0)))))),
% 1.42/1.28 inference(flattening,[status(thm)],[f20])).
% 1.42/1.28 thf(f20,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((((some @ (^[Y0 : nat]: (diffprop @ X1 @ X2 @ Y0))) = $true) | ((lessis @ X0 @ X1) != $true)) | ($true != (some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0)))))),
% 1.42/1.28 inference(ennf_transformation,[status(thm)],[f13])).
% 1.42/1.28 thf(f13,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (some @ (^[Y0 : nat]: (diffprop @ X0 @ X2 @ Y0)))) => (((lessis @ X0 @ X1) = $true) => ((some @ (^[Y0 : nat]: (diffprop @ X1 @ X2 @ Y0))) = $true)))),
% 1.42/1.28 inference(fool_elimination,[status(thm)],[f12])).
% 1.42/1.28 thf(f12,plain,(
% 1.42/1.28 ! [X0 : nat,X1 : nat,X2 : nat] : ((some @ (^[X3 : nat] : (diffprop @ X0 @ X2 @ X3))) => ((lessis @ X0 @ X1) => (some @ (^[X4 : nat] : (diffprop @ X1 @ X2 @ X4)))))),
% 1.42/1.28 inference(rectify,[status(thm)],[f3])).
% 1.42/1.28 thf(f3,axiom,(
% 1.42/1.28 ! [X2 : nat,X3 : nat,X1 : nat] : ((some @ (^[X4 : nat] : (diffprop @ X2 @ X1 @ X4))) => ((lessis @ X2 @ X3) => (some @ (^[X4 : nat] : (diffprop @ X3 @ X1 @ X4)))))),
% 1.42/1.28 file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz16b)).
% 1.42/1.28 thf(f27,plain,(
% 1.42/1.28 ($true != (some @ (diffprop @ x @ z)))),
% 1.42/1.28 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.42/1.28 thf(f25,plain,(
% 1.42/1.28 ((some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))) != $true)),
% 1.42/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.42/1.28 thf(f18,plain,(
% 1.42/1.28 ((some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))) != $true)),
% 1.42/1.28 inference(flattening,[status(thm)],[f17])).
% 1.42/1.28 thf(f17,plain,(
% 1.42/1.28 ~((some @ (^[Y0 : nat]: (diffprop @ x @ z @ Y0))) = $true)),
% 1.42/1.28 inference(fool_elimination,[status(thm)],[f16])).
% 1.42/1.28 thf(f16,plain,(
% 1.42/1.28 ~(some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.42/1.28 inference(rectify,[status(thm)],[f6])).
% 1.42/1.28 thf(f6,negated_conjecture,(
% 1.42/1.28 ~(some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.42/1.28 inference(negated_conjecture,[status(cth)],[f5])).
% 1.42/1.28 thf(f5,conjecture,(
% 1.42/1.28 (some @ (^[X0 : nat] : (diffprop @ x @ z @ X0)))),
% 1.42/1.28 file('/export/starexec/sandbox/tmp/tmp.iAEcGuHtlh/DTF2THF_28371.p',satz16c)).
% 1.42/1.28 thf(f74,plain,(
% 1.42/1.28 spl0_5 | spl0_6),
% 1.42/1.28 inference(avatar_split_clause,[status(thm)],[f66,f72,f68])).
% 1.42/1.28 thf(f66,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((some @ (diffprop @ X0 @ z)) != $true) | ((diffprop @ x @ z @ (sK3 @ z @ x)) = $true) | ((lessis @ X0 @ x) != $true)) )),
% 1.42/1.28 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.42/1.28 thf(f65,plain,(
% 1.42/1.28 ( ! [X0 : nat] : (((diffprop @ x @ z @ (sK3 @ z @ x)) = $true) | ($true != $true) | ((some @ (diffprop @ X0 @ z)) != $true) | ((lessis @ X0 @ x) != $true)) )),
% 1.42/1.28 inference(equality_factoring,[status(thm)],[f63])).
% 1.42/1.28 thf(f63,plain,(
% 1.42/1.28 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (diffprop @ x @ z @ (sK3 @ X1 @ X0))) | ((some @ (diffprop @ X2 @ X1)) != $true) | ((diffprop @ X0 @ X1 @ (sK3 @ X1 @ X0)) = $true) | ((lessis @ X2 @ X0) != $true)) )),
% 1.42/1.28 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.42/1.28 % SZS output end Proof for DTF2THF_28371
% 1.42/1.28 % (28468)------------------------------
% 1.42/1.28 % (28468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.28 % (28468)Termination reason: Refutation
% 1.42/1.28
% 1.42/1.28 % (28468)Memory used [KB]: 5628
% 1.42/1.28 % (28468)Time elapsed: 0.008 s
% 1.42/1.28 % (28468)Instructions burned: 15 (million)
% 1.42/1.28 % (28468)------------------------------
% 1.42/1.28 % (28468)------------------------------
% 1.42/1.28 % (28467)Success in time 0.006 s
%------------------------------------------------------------------------------