%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM705^1 : 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 : n002.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 09:24:22 AM UTC 2026
% Result : Theorem 1.71s 1.42s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 5 unt; 0 typ; 6 def)
% Number of atoms : 532 ( 136 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 714 ( 168 ~; 81 |; 20 &; 327 @)
% ( 6 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 13 con; 0-2 aty)
% ( 17 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 117 ( 39 ^; 72 !; 6 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
p: nat > $o ).
thf(func_def_2,type,
some: ( nat > $o ) > $o ).
thf(func_def_4,type,
lessis: nat > nat > $o ).
thf(func_def_5,type,
more: nat > nat > $o ).
thf(func_def_14,type,
sK0: nat ).
thf(func_def_15,type,
sK1: nat ).
thf(func_def_17,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK4: nat ).
thf(func_def_19,type,
sK5: nat ).
thf(f129,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f57,f61,f66,f71,f103,f128]) ).
thf(f128,plain,
( spl2_1
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f127]) ).
thf(f127,plain,
( $false
| spl2_1
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_6 ),
inference(subsumption_resolution,[status(thm)],[f122,f112]) ).
thf(f112,plain,
( ( ( more @ sK0 @ sK1 )
= $true )
| spl2_1
| ~ spl2_3
| ~ spl2_6 ),
inference(subsumption_resolution,[status(thm)],[f110,f48]) ).
thf(f48,plain,
( ( sK0 != sK1 )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f110,plain,
( ( sK0 = sK1 )
| ( ( more @ sK0 @ sK1 )
= $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( more @ sK0 @ sK1 )
= $true )
| ( sK0 = sK1 )
| ( $true != $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f39,f106]) ).
thf(f106,plain,
( ( ( lessis @ sK1 @ sK0 )
= $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( lessis @ sK1 @ sK0 )
= $true )
| ( $true != $true )
| ~ spl2_3
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f56,f70]) ).
thf(f70,plain,
( ( ( p @ sK0 )
= $true )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl2_6
<=> ( ( p @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f56,plain,
( ! [X2: nat] :
( ( ( p @ X2 )
!= $true )
| ( $true
= ( lessis @ sK1 @ X2 ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl2_3
<=> ! [X2: nat] :
( ( $true
= ( lessis @ sK1 @ X2 ) )
| ( ( p @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f39,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( more @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
= $true )
| ( X0 = X1 )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( more @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( ( more @ X1 @ X0 )
!= $true )
=> ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( ( more @ X1 @ X0 )
!= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz14) ).
thf(f122,plain,
( ( ( more @ sK0 @ sK1 )
!= $true )
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( more @ sK0 @ sK1 )
!= $true )
| ( $true != $true )
| ~ spl2_4
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f41,f118]) ).
thf(f118,plain,
( ( $true
= ( lessis @ sK0 @ sK1 ) )
| ~ spl2_4
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ( $true != $true )
| ( $true
= ( lessis @ sK0 @ sK1 ) )
| ~ spl2_4
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f60,f65]) ).
thf(f65,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl2_5
<=> ( ( p @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f60,plain,
( ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ sK0 @ X3 )
= $true ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl2_4
<=> ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ sK0 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( lessis @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( lessis @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X1 @ X0 )
=> ~ ( more @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( lessis @ X0 @ X1 )
=> ~ ( more @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz10d) ).
thf(f103,plain,
spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f101,f52]) ).
thf(f52,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl2_2
<=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f101,plain,
( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f43,f42]) ).
thf(f42,plain,
( ( some @ p )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( some @ p )
= $true ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
some @ p,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
some @ p,
file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',s) ).
thf(f43,plain,
! [X0: nat > $o] :
( ( ( some @ X0 )
!= $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat > $o] :
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) )
= $true )
| ( ( some @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat > $o] :
( ( ( some @ X0 )
= $true )
=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( X0 @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( X0 @ Y0 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat > $o] :
( ( some @ X0 )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( X0 @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: nat > $o] :
( ( some @ X3 )
=> ( some
@ ^ [X0: nat] :
~ ( ! [X4: nat] :
( ( X3 @ X4 )
=> ( lessis @ X0 @ X4 ) )
=> ~ ( X3 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz27) ).
thf(f71,plain,
( ~ spl2_2
| spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f37,f68,f50]) ).
thf(f37,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( ( p @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( ! [X2: nat] :
( ( $true
= ( lessis @ sK1 @ X2 ) )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ sK0 )
= $true )
& ( ( p @ sK1 )
= $true )
& ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ sK0 @ X3 )
= $true ) )
& ( sK0 != sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f29,f32]) ).
thf(f32,plain,
( ? [X0: nat,X1: nat] :
( ! [X2: nat] :
( ( ( lessis @ X1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ X0 )
= $true )
& ( ( p @ X1 )
= $true )
& ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ X0 @ X3 )
= $true ) )
& ( X0 != X1 ) )
=> ( ! [X2: nat] :
( ( $true
= ( lessis @ sK1 @ X2 ) )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ sK0 )
= $true )
& ( ( p @ sK1 )
= $true )
& ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ sK0 @ X3 )
= $true ) )
& ( sK0 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ? [X0: nat,X1: nat] :
( ! [X2: nat] :
( ( ( lessis @ X1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) )
& ( ( p @ X0 )
= $true )
& ( ( p @ X1 )
= $true )
& ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ X0 @ X3 )
= $true ) )
& ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ? [X0: nat,X1: nat] :
( ( X0 != X1 )
& ( ( p @ X0 )
= $true )
& ! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ X0 @ X3 )
= $true ) )
& ( ( p @ X1 )
= $true )
& ! [X2: nat] :
( ( ( lessis @ X1 @ X2 )
= $true )
| ( ( p @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( ( p @ X2 )
= $true )
=> ( ( lessis @ X1 @ X2 )
= $true ) )
=> ( ( p @ X1 )
!= $true ) )
=> ( ~ ( ! [X3: nat] :
( ( $true
= ( p @ X3 ) )
=> ( ( lessis @ X0 @ X3 )
= $true ) )
=> ( ( p @ X0 )
!= $true ) )
=> ( X0 = X1 ) ) )
=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( ( p @ X2 )
= $true )
=> ( ( lessis @ X1 @ X2 )
= $true ) )
=> ( ( p @ X1 )
!= $true ) )
=> ( ~ ( ! [X3: nat] :
( ( $true
= ( p @ X3 ) )
=> ( ( lessis @ X0 @ X3 )
= $true ) )
=> ( ( p @ X0 )
!= $true ) )
=> ( X0 = X1 ) ) )
=> ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ~ ( ! [X0: nat,X1: nat] :
( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X0 @ X3 ) )
=> ~ ( p @ X0 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X4: nat] :
~ ( ! [X5: nat] :
( ( p @ X5 )
=> ( lessis @ X4 @ X5 ) )
=> ~ ( p @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ~ ( ! [X1: nat,X0: nat] :
( ~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X0 @ X4 ) )
=> ~ ( p @ X0 ) )
=> ( ~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X1 @ X4 ) )
=> ~ ( p @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X0: nat] :
~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X0 @ X4 ) )
=> ~ ( p @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
~ ( ! [X1: nat,X0: nat] :
( ~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X0 @ X4 ) )
=> ~ ( p @ X0 ) )
=> ( ~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X1 @ X4 ) )
=> ~ ( p @ X1 ) )
=> ( X0 = X1 ) ) )
=> ~ ( some
@ ^ [X0: nat] :
~ ( ! [X4: nat] :
( ( p @ X4 )
=> ( lessis @ X0 @ X4 ) )
=> ~ ( p @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz27a) ).
thf(f66,plain,
( spl2_5
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f50,f63]) ).
thf(f36,plain,
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( ( p @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f61,plain,
( spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f35,f50,f59]) ).
thf(f35,plain,
! [X3: nat] :
( ( $true
!= ( p @ X3 ) )
| ( ( lessis @ sK0 @ X3 )
= $true )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f57,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f38,f55,f50]) ).
thf(f38,plain,
! [X2: nat] :
( ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true )
| ( $true
= ( lessis @ sK1 @ X2 ) )
| ( ( p @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f53,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f50,f46]) ).
thf(f34,plain,
( ( sK0 != sK1 )
| ( ( some
@ ^ [Y0: nat] :
~ ( ( !! @ nat
@ ^ [Y1: nat] :
( ( p @ Y1 )
=> ( lessis @ Y0 @ Y1 ) ) )
=> ~ ( p @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM705^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n002.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 11:12:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : NUM705^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.44 % Domain : Number Theory
% 0.19/0.44 % Problem : Landau theorem 27a
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English : ~((forall x:nat.forall y:nat.~((forall x_0:nat.p x_0 ->
% 0.19/0.44 % lessis x x_0) -> ~(p x)) -> ~((forall x_0:nat.p x_0 ->
% 0.19/0.44 % lessis y x_0) -> ~(p y)) -> x = y) -> ~(some (lambda x.
% 0.19/0.44 % ~((forall x_0:nat.p x_0 -> lessis x x_0) -> ~(p x)))))
% 0.19/0.44
% 0.19/0.44 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.19/0.44 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.19/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [Bro09]
% 0.19/0.44 % Names : satz27a [Lan30]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % : Without extensionality : Theorem
% 0.19/0.44 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.19/0.44 % Syntax : Number of formulae : 11 ( 0 unt; 5 typ; 0 def)
% 0.19/0.44 % Number of atoms : 21 ( 2 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 11 ( 3 avg)
% 0.19/0.44 % Number of connectives : 58 ( 14 ~; 0 |; 0 &; 28 @)
% 0.19/0.44 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 13 ( 8 avg)
% 0.19/0.44 % Number of types : 2 ( 1 usr)
% 0.19/0.44 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.19/0.44 % Number of variables : 14 ( 2 ^; 12 !; 0 ?; 14 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments :
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(nat_type,type,
% 0.19/0.44 nat: $tType ).
% 0.19/0.44
% 0.19/0.44 thf(p,type,
% 0.19/0.44 p: nat > $o ).
% 0.19/0.44
% 0.19/0.44 thf(some,type,
% 0.19/0.44 some: ( nat > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(s,axiom,
% 0.19/0.44 some @ p ).
% 0.19/0.44
% 0.19/0.44 thf(lessis,type,
% 0.19/0.44 lessis: nat > nat > $o ).
% 0.19/0.44
% 0.19/0.44 thf(more,type,
% 0.19/0.44 more: nat > nat > $o ).
% 0.19/0.44
% 0.19/0.44 thf(satz14,axiom,
% 0.19/0.44 ! [Xx: nat,Xy: nat] :
% 0.19/0.44 ( ( lessis @ Xx @ Xy )
% 0.19/0.44 => ( ~ ( more @ Xy @ Xx )
% 0.19/0.44 => ( Xy = Xx ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(et,axiom,
% 0.19/0.44 ! [Xa: $o] :
% 0.19/0.44 ( ~ ~ Xa
% 0.19/0.44 => Xa ) ).
% 0.19/0.44
% 0.19/0.44 thf(satz10d,axiom,
% 0.19/0.44 ! [Xx: nat,Xy: nat] :
% 0.19/0.44 ( ( lessis @ Xx @ Xy )
% 0.19/0.44 => ~ ( more @ Xx @ Xy ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(satz27,axiom,
% 0.19/0.44 ! [Xp: nat > $o] :
% 0.19/0.44 ( ( some @ Xp )
% 0.19/0.44 => ( some
% 0.19/0.44 @ ^ [Xx: nat] :
% 0.19/0.44 ~ ( ! [Xx_0: nat] :
% 0.19/0.44 ( ( Xp @ Xx_0 )
% 0.19/0.44 => ( lessis @ Xx @ Xx_0 ) )
% 0.19/0.44 => ~ ( Xp @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(satz27a,conjecture,
% 0.19/0.44 ~ ( ! [Xx: nat,Xy: nat] :
% 0.19/0.44 ( ~ ( ! [Xx_0: nat] :
% 0.19/0.44 ( ( p @ Xx_0 )
% 0.19/0.44 => ( lessis @ Xx @ Xx_0 ) )
% 0.19/0.44 => ~ ( p @ Xx ) )
% 0.19/0.44 => ( ~ ( ! [Xx_0: nat] :
% 0.19/0.44 ( ( p @ Xx_0 )
% 0.19/0.44 => ( lessis @ Xy @ Xx_0 ) )
% 0.19/0.44 => ~ ( p @ Xy ) )
% 0.19/0.44 => ( Xx = Xy ) ) )
% 0.19/0.44 => ~ ( some
% 0.19/0.44 @ ^ [Xx: nat] :
% 0.19/0.44 ~ ( ! [Xx_0: nat] :
% 0.19/0.44 ( ( p @ Xx_0 )
% 0.19/0.44 => ( lessis @ Xx @ Xx_0 ) )
% 0.19/0.44 => ~ ( p @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.53/1.38 ---- Embedded in THF ---
% 1.53/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.38 %%% Generated on Tue Feb 24 11:12:04 EST 2026
% 1.53/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.38 %%% Logic specification used:
% 1.53/1.38 %%% thf(spec, logic, $$dhol).
% 1.53/1.38
% 1.53/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2DTF11058.p
% See solution above
% 1.53/1.38 ------------------------
% 1.53/1.39 ---- Cleaned THF ---
% 1.53/1.39 thf(nat_type,type,
% 1.53/1.39 nat: $tType ).
% 1.53/1.39
% 1.53/1.39 thf(p,type,
% 1.53/1.39 p: nat > $o ).
% 1.53/1.39
% 1.53/1.39 thf(some,type,
% 1.53/1.39 some: ( nat > $o ) > $o ).
% 1.53/1.39
% 1.53/1.39 thf(s,axiom,
% 1.53/1.39 some @ p ).
% 1.53/1.39
% 1.53/1.39 thf(lessis,type,
% 1.53/1.39 lessis: nat > nat > $o ).
% 1.53/1.39
% 1.53/1.39 thf(more,type,
% 1.53/1.39 more: nat > nat > $o ).
% 1.53/1.39
% 1.53/1.39 thf(satz14,axiom,
% 1.53/1.39 ! [Xx: nat,Xy: nat] :
% 1.53/1.39 ( ( lessis @ Xx @ Xy )
% 1.53/1.39 => ( ~ ( more @ Xy @ Xx )
% 1.53/1.39 => ( Xy = Xx ) ) ) ).
% 1.53/1.39
% 1.53/1.39 thf(et,axiom,
% 1.53/1.39 ! [Xa: $o] :
% 1.53/1.39 ( ~ ~ Xa
% 1.53/1.39 => Xa ) ).
% 1.53/1.39
% 1.53/1.39 thf(satz10d,axiom,
% 1.53/1.39 ! [Xx: nat,Xy: nat] :
% 1.53/1.39 ( ( lessis @ Xx @ Xy )
% 1.53/1.39 => ~ ( more @ Xx @ Xy ) ) ).
% 1.53/1.39
% 1.53/1.39 thf(satz27,axiom,
% 1.53/1.39 ! [Xp: nat > $o] :
% 1.53/1.39 ( ( some @ Xp )
% 1.53/1.39 => ( some
% 1.53/1.39 @ ^ [Xx: nat] :
% 1.53/1.39 ~ ( ! [Xx_0: nat] :
% 1.53/1.39 ( ( Xp @ Xx_0 )
% 1.53/1.39 => ( lessis @ Xx @ Xx_0 ) )
% 1.53/1.39 => ~ ( Xp @ Xx ) ) ) ) ).
% 1.53/1.39
% 1.53/1.39 thf(satz27a,conjecture,
% 1.53/1.39 ~ ( ! [Xx: nat,Xy: nat] :
% 1.53/1.39 ( ~ ( ! [Xx_0: nat] :
% 1.53/1.39 ( ( p @ Xx_0 )
% 1.53/1.39 => ( lessis @ Xx @ Xx_0 ) )
% 1.53/1.39 => ~ ( p @ Xx ) )
% 1.53/1.39 => ( ~ ( ! [Xx_0: nat] :
% 1.53/1.39 ( ( p @ Xx_0 )
% 1.53/1.39 => ( lessis @ Xy @ Xx_0 ) )
% 1.53/1.39 => ~ ( p @ Xy ) )
% 1.53/1.39 => ( Xx = Xy ) ) )
% 1.53/1.39 => ~ ( some
% 1.53/1.39 @ ^ [Xx: nat] :
% 1.53/1.39 ~ ( ! [Xx_0: nat] :
% 1.53/1.39 ( ( p @ Xx_0 )
% 1.53/1.39 => ( lessis @ Xx @ Xx_0 ) )
% 1.53/1.39 => ~ ( p @ Xx ) ) ) ) ).
% 1.53/1.39 ------------------------
% 1.71/1.41 % (11159)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11058 for (2999ds/2Mi)
% 1.71/1.41 % (11160)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_11058 for (2999ds/2Mi)
% 1.71/1.41 % (11158)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_11058 for (2999ds/27Mi)
% 1.71/1.41 % (11161)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_11058 for (2999ds/275Mi)
% 1.71/1.41 % (11157)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_11058 for (2999ds/4Mi)
% 1.71/1.41 % (11162)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11058 for (2999ds/18Mi)
% 1.71/1.41 % (11156)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11058 for (2999ds/183Mi)
% 1.71/1.41 % (11159)Instruction limit reached!
% 1.71/1.41 % (11159)------------------------------
% 1.71/1.41 % (11159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (11159)Termination reason: Unknown
% 1.71/1.41 % (11160)Instruction limit reached!
% 1.71/1.41 % (11160)------------------------------
% 1.71/1.41 % (11160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.41 % (11159)Termination phase: Property scanning
% 1.71/1.41
% 1.71/1.41 % (11159)Memory used [KB]: 1023
% 1.71/1.41 % (11159)Time elapsed: 0.003 s
% 1.71/1.41 % (11159)Instructions burned: 2 (million)
% 1.71/1.41 % (11159)------------------------------
% 1.71/1.41 % (11159)------------------------------
% 1.71/1.41 % (11160)Termination reason: Unknown
% 1.71/1.41 % (11160)Termination phase: Property scanning
% 1.71/1.41
% 1.71/1.41 % (11160)Memory used [KB]: 1023
% 1.71/1.41 % (11160)Time elapsed: 0.003 s
% 1.71/1.41 % (11160)Instructions burned: 3 (million)
% 1.71/1.41 % (11160)------------------------------
% 1.71/1.41 % (11160)------------------------------
% 1.71/1.42 % (11157)Instruction limit reached!
% 1.71/1.42 % (11157)------------------------------
% 1.71/1.42 % (11157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (11157)Termination reason: Unknown
% 1.71/1.42 % (11157)Termination phase: Saturation
% 1.71/1.42
% 1.71/1.42 % (11157)Memory used [KB]: 5500
% 1.71/1.42 % (11157)Time elapsed: 0.004 s
% 1.71/1.42 % (11157)Instructions burned: 4 (million)
% 1.71/1.42 % (11157)------------------------------
% 1.71/1.42 % (11157)------------------------------
% 1.71/1.42 % (11161)Refutation not found, incomplete strategy
% 1.71/1.42 % (11161)------------------------------
% 1.71/1.42 % (11161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (11161)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.42
% 1.71/1.42
% 1.71/1.42 % (11161)Memory used [KB]: 5500
% 1.71/1.42 % (11161)Time elapsed: 0.005 s
% 1.71/1.42 % (11161)Instructions burned: 6 (million)
% 1.71/1.42 % (11161)------------------------------
% 1.71/1.42 % (11161)------------------------------
% 1.71/1.42 % (11162)First to succeed.
% 1.71/1.42 % (11158)Also succeeded, but the first one will report.
% 1.71/1.42 % (11162)Refutation found. Thanks to Tanya!
% 1.71/1.42 % SZS status Theorem for DTF2THF_11058
% 1.71/1.42 % SZS output start Proof for DTF2THF_11058
% 1.71/1.42 thf(type_def_5, type, nat: $tType).
% 1.71/1.42 thf(func_def_0, type, nat: $tType).
% 1.71/1.42 thf(func_def_1, type, p: nat > $o).
% 1.71/1.42 thf(func_def_2, type, some: (nat > $o) > $o).
% 1.71/1.42 thf(func_def_4, type, lessis: nat > nat > $o).
% 1.71/1.42 thf(func_def_5, type, more: nat > nat > $o).
% 1.71/1.42 thf(func_def_14, type, sK0: nat).
% 1.71/1.42 thf(func_def_15, type, sK1: nat).
% 1.71/1.42 thf(func_def_17, type, ph3: !>[X0: $tType]:(X0)).
% 1.71/1.42 thf(func_def_18, type, sK4: nat).
% 1.71/1.42 thf(func_def_19, type, sK5: nat).
% 1.71/1.42 thf(f129,plain,(
% 1.71/1.42 $false),
% 1.71/1.42 inference(avatar_sat_refutation,[status(thm)],[f53,f57,f61,f66,f71,f103,f128])).
% 1.71/1.42 thf(f128,plain,(
% 1.71/1.42 spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6),
% 1.71/1.42 inference(avatar_contradiction_clause,[status(thm)],[f127])).
% 1.71/1.42 thf(f127,plain,(
% 1.71/1.42 $false | (spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f122,f112])).
% 1.71/1.42 thf(f112,plain,(
% 1.71/1.42 ((more @ sK0 @ sK1) = $true) | (spl2_1 | ~spl2_3 | ~spl2_6)),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f110,f48])).
% 1.71/1.42 thf(f48,plain,(
% 1.71/1.42 (sK0 != sK1) | spl2_1),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.71/1.42 thf(f46,definition,(
% 1.71/1.42 spl2_1 <=> (sK0 = sK1)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.71/1.42 thf(f110,plain,(
% 1.71/1.42 (sK0 = sK1) | ((more @ sK0 @ sK1) = $true) | (~spl2_3 | ~spl2_6)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.71/1.42 thf(f108,plain,(
% 1.71/1.42 ((more @ sK0 @ sK1) = $true) | (sK0 = sK1) | ($true != $true) | (~spl2_3 | ~spl2_6)),
% 1.71/1.42 inference(superposition,[status(thm)],[f39,f106])).
% 1.71/1.42 thf(f106,plain,(
% 1.71/1.42 ((lessis @ sK1 @ sK0) = $true) | (~spl2_3 | ~spl2_6)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.71/1.42 thf(f105,plain,(
% 1.71/1.42 ((lessis @ sK1 @ sK0) = $true) | ($true != $true) | (~spl2_3 | ~spl2_6)),
% 1.71/1.42 inference(superposition,[status(thm)],[f56,f70])).
% 1.71/1.42 thf(f70,plain,(
% 1.71/1.42 ((p @ sK0) = $true) | ~spl2_6),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.71/1.42 thf(f68,definition,(
% 1.71/1.42 spl2_6 <=> ((p @ sK0) = $true)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 1.71/1.42 thf(f56,plain,(
% 1.71/1.42 ( ! [X2 : nat] : (((p @ X2) != $true) | ($true = (lessis @ sK1 @ X2))) ) | ~spl2_3),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.71/1.42 thf(f55,definition,(
% 1.71/1.42 spl2_3 <=> ! [X2 : nat] : (($true = (lessis @ sK1 @ X2)) | ((p @ X2) != $true))),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.71/1.42 thf(f39,plain,(
% 1.71/1.42 ( ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) != $true) | (X0 = X1) | ((more @ X1 @ X0) = $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f31])).
% 1.71/1.42 thf(f31,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (((more @ X1 @ X0) = $true) | (X0 = X1) | ((lessis @ X0 @ X1) != $true))),
% 1.71/1.42 inference(flattening,[status(thm)],[f30])).
% 1.71/1.42 thf(f30,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ((more @ X1 @ X0) = $true)) | ((lessis @ X0 @ X1) != $true))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f22])).
% 1.71/1.42 thf(f22,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) => (((more @ X1 @ X0) != $true) => (X0 = X1)))),
% 1.71/1.42 inference(flattening,[status(thm)],[f12])).
% 1.71/1.42 thf(f12,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (((lessis @ X0 @ X1) = $true) => (~((more @ X1 @ X0) = $true) => (X0 = X1)))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.71/1.42 thf(f11,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (~(more @ X1 @ X0) => (X0 = X1)))),
% 1.71/1.42 inference(rectify,[status(thm)],[f2])).
% 1.71/1.42 thf(f2,axiom,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (~(more @ X1 @ X0) => (X0 = X1)))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz14)).
% 1.71/1.42 thf(f122,plain,(
% 1.71/1.42 ((more @ sK0 @ sK1) != $true) | (~spl2_4 | ~spl2_5)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.71/1.42 thf(f121,plain,(
% 1.71/1.42 ((more @ sK0 @ sK1) != $true) | ($true != $true) | (~spl2_4 | ~spl2_5)),
% 1.71/1.42 inference(superposition,[status(thm)],[f41,f118])).
% 1.71/1.42 thf(f118,plain,(
% 1.71/1.42 ($true = (lessis @ sK0 @ sK1)) | (~spl2_4 | ~spl2_5)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.71/1.42 thf(f116,plain,(
% 1.71/1.42 ($true != $true) | ($true = (lessis @ sK0 @ sK1)) | (~spl2_4 | ~spl2_5)),
% 1.71/1.42 inference(superposition,[status(thm)],[f60,f65])).
% 1.71/1.42 thf(f65,plain,(
% 1.71/1.42 ((p @ sK1) = $true) | ~spl2_5),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.71/1.42 thf(f63,definition,(
% 1.71/1.42 spl2_5 <=> ((p @ sK1) = $true)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.71/1.42 thf(f60,plain,(
% 1.71/1.42 ( ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ sK0 @ X3) = $true)) ) | ~spl2_4),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.71/1.42 thf(f59,definition,(
% 1.71/1.42 spl2_4 <=> ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ sK0 @ X3) = $true))),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.71/1.42 thf(f41,plain,(
% 1.71/1.42 ( ! [X0 : nat,X1 : nat] : (($true != (lessis @ X1 @ X0)) | ((more @ X1 @ X0) != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f27])).
% 1.71/1.42 thf(f27,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (($true != (lessis @ X1 @ X0)) | ((more @ X1 @ X0) != $true))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f24])).
% 1.71/1.42 thf(f24,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (($true = (lessis @ X1 @ X0)) => ((more @ X1 @ X0) != $true))),
% 1.71/1.42 inference(flattening,[status(thm)],[f16])).
% 1.71/1.42 thf(f16,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (($true = (lessis @ X1 @ X0)) => ~((more @ X1 @ X0) = $true))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f15])).
% 1.71/1.42 thf(f15,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : ((lessis @ X1 @ X0) => ~(more @ X1 @ X0))),
% 1.71/1.42 inference(rectify,[status(thm)],[f4])).
% 1.71/1.42 thf(f4,axiom,(
% 1.71/1.42 ! [X1 : nat,X0 : nat] : ((lessis @ X0 @ X1) => ~(more @ X0 @ X1))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz10d)).
% 1.71/1.42 thf(f103,plain,(
% 1.71/1.42 spl2_2),
% 1.71/1.42 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.71/1.42 thf(f102,plain,(
% 1.71/1.42 $false | spl2_2),
% 1.71/1.42 inference(subsumption_resolution,[status(thm)],[f101,f52])).
% 1.71/1.42 thf(f52,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | spl2_2),
% 1.71/1.42 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.71/1.42 thf(f50,definition,(
% 1.71/1.42 spl2_2 <=> ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) = $true)),
% 1.71/1.42 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.71/1.42 thf(f101,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) = $true)),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.71/1.42 thf(f100,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) = $true) | ($true != $true)),
% 1.71/1.42 inference(superposition,[status(thm)],[f43,f42])).
% 1.71/1.42 thf(f42,plain,(
% 1.71/1.42 ((some @ p) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f20])).
% 1.71/1.42 thf(f20,plain,(
% 1.71/1.42 ((some @ p) = $true)),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f19])).
% 1.71/1.42 thf(f19,plain,(
% 1.71/1.42 (some @ p)),
% 1.71/1.42 inference(rectify,[status(thm)],[f1])).
% 1.71/1.42 thf(f1,axiom,(
% 1.71/1.42 (some @ p)),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',s)).
% 1.71/1.42 thf(f43,plain,(
% 1.71/1.42 ( ! [X0 : nat > $o] : (((some @ X0) != $true) | ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))) = $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f25])).
% 1.71/1.42 thf(f25,plain,(
% 1.71/1.42 ! [X0 : nat > $o] : (((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))) = $true) | ((some @ X0) != $true))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f18])).
% 1.71/1.42 thf(f18,plain,(
% 1.71/1.42 ! [X0 : nat > $o] : (((some @ X0) = $true) => ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))) = $true))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f17])).
% 1.71/1.42 thf(f17,plain,(
% 1.71/1.42 ! [X0 : nat > $o] : ((some @ X0) => (some @ (^[X1 : nat] : (~(! [X2 : nat] : ((X0 @ X2) => (lessis @ X1 @ X2)) => ~(X0 @ X1))))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f5])).
% 1.71/1.42 thf(f5,axiom,(
% 1.71/1.42 ! [X3 : nat > $o] : ((some @ X3) => (some @ (^[X0 : nat] : (~(! [X4 : nat] : ((X3 @ X4) => (lessis @ X0 @ X4)) => ~(X3 @ X0))))))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz27)).
% 1.71/1.42 thf(f71,plain,(
% 1.71/1.42 ~spl2_2 | spl2_6),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f37,f68,f50])).
% 1.71/1.42 thf(f37,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | ((p @ sK0) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.42 thf(f33,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | (! [X2 : nat] : (($true = (lessis @ sK1 @ X2)) | ((p @ X2) != $true)) & ((p @ sK0) = $true) & ((p @ sK1) = $true) & ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ sK0 @ X3) = $true)) & (sK0 != sK1))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f29,f32])).
% 1.71/1.42 thf(f32,plain,(
% 1.71/1.42 ? [X0 : nat,X1 : nat] : (! [X2 : nat] : (((lessis @ X1 @ X2) = $true) | ((p @ X2) != $true)) & ((p @ X0) = $true) & ((p @ X1) = $true) & ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ X0 @ X3) = $true)) & (X0 != X1)) => (! [X2 : nat] : (($true = (lessis @ sK1 @ X2)) | ((p @ X2) != $true)) & ((p @ sK0) = $true) & ((p @ sK1) = $true) & ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ sK0 @ X3) = $true)) & (sK0 != sK1))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f29,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | ? [X0 : nat,X1 : nat] : (! [X2 : nat] : (((lessis @ X1 @ X2) = $true) | ((p @ X2) != $true)) & ((p @ X0) = $true) & ((p @ X1) = $true) & ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ X0 @ X3) = $true)) & (X0 != X1))),
% 1.71/1.42 inference(flattening,[status(thm)],[f28])).
% 1.71/1.42 thf(f28,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | ? [X0 : nat,X1 : nat] : (((X0 != X1) & (((p @ X0) = $true) & ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ X0 @ X3) = $true)))) & (((p @ X1) = $true) & ! [X2 : nat] : (((lessis @ X1 @ X2) = $true) | ((p @ X2) != $true))))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f23])).
% 1.71/1.42 thf(f23,plain,(
% 1.71/1.42 ! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : (((p @ X2) = $true) => ((lessis @ X1 @ X2) = $true)) => ((p @ X1) != $true)) => (~(! [X3 : nat] : (($true = (p @ X3)) => ((lessis @ X0 @ X3) = $true)) => ((p @ X0) != $true)) => (X0 = X1))) => ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true)),
% 1.71/1.42 inference(flattening,[status(thm)],[f14])).
% 1.71/1.42 thf(f14,plain,(
% 1.71/1.42 ~~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : (((p @ X2) = $true) => ((lessis @ X1 @ X2) = $true)) => ~((p @ X1) = $true)) => (~(! [X3 : nat] : (($true = (p @ X3)) => ((lessis @ X0 @ X3) = $true)) => ~((p @ X0) = $true)) => (X0 = X1))) => ~((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) = $true))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f13])).
% 1.71/1.42 thf(f13,plain,(
% 1.71/1.42 ~~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X1 @ X2)) => ~(p @ X1)) => (~(! [X3 : nat] : ((p @ X3) => (lessis @ X0 @ X3)) => ~(p @ X0)) => (X0 = X1))) => ~(some @ (^[X4 : nat] : (~(! [X5 : nat] : ((p @ X5) => (lessis @ X4 @ X5)) => ~(p @ X4))))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f7])).
% 1.71/1.42 thf(f7,negated_conjecture,(
% 1.71/1.42 ~~(! [X1 : nat,X0 : nat] : (~(! [X4 : nat] : ((p @ X4) => (lessis @ X0 @ X4)) => ~(p @ X0)) => (~(! [X4 : nat] : ((p @ X4) => (lessis @ X1 @ X4)) => ~(p @ X1)) => (X0 = X1))) => ~(some @ (^[X0 : nat] : (~(! [X4 : nat] : ((p @ X4) => (lessis @ X0 @ X4)) => ~(p @ X0))))))),
% 1.71/1.42 inference(negated_conjecture,[status(cth)],[f6])).
% 1.71/1.42 thf(f6,conjecture,(
% 1.71/1.42 ~(! [X1 : nat,X0 : nat] : (~(! [X4 : nat] : ((p @ X4) => (lessis @ X0 @ X4)) => ~(p @ X0)) => (~(! [X4 : nat] : ((p @ X4) => (lessis @ X1 @ X4)) => ~(p @ X1)) => (X0 = X1))) => ~(some @ (^[X0 : nat] : (~(! [X4 : nat] : ((p @ X4) => (lessis @ X0 @ X4)) => ~(p @ X0))))))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.AaY8JdmMyy/DTF2THF_11058.p',satz27a)).
% 1.71/1.42 thf(f66,plain,(
% 1.71/1.42 spl2_5 | ~spl2_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f36,f50,f63])).
% 1.71/1.42 thf(f36,plain,(
% 1.71/1.42 ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | ((p @ sK1) = $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.42 thf(f61,plain,(
% 1.71/1.42 spl2_4 | ~spl2_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f35,f50,f59])).
% 1.71/1.42 thf(f35,plain,(
% 1.71/1.42 ( ! [X3 : nat] : (($true != (p @ X3)) | ((lessis @ sK0 @ X3) = $true) | ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.42 thf(f57,plain,(
% 1.71/1.42 ~spl2_2 | spl2_3),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f38,f55,f50])).
% 1.71/1.42 thf(f38,plain,(
% 1.71/1.42 ( ! [X2 : nat] : (((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true) | ($true = (lessis @ sK1 @ X2)) | ((p @ X2) != $true)) )),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.42 thf(f53,plain,(
% 1.71/1.42 ~spl2_1 | ~spl2_2),
% 1.71/1.42 inference(avatar_split_clause,[status(thm)],[f34,f50,f46])).
% 1.71/1.42 thf(f34,plain,(
% 1.71/1.42 (sK0 != sK1) | ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))) != $true)),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 1.71/1.42 % SZS output end Proof for DTF2THF_11058
% 1.71/1.42 % (11162)------------------------------
% 1.71/1.42 % (11162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (11162)Termination reason: Refutation
% 1.71/1.42
% 1.71/1.42 % (11162)Memory used [KB]: 5628
% 1.71/1.42 % (11162)Time elapsed: 0.010 s
% 1.71/1.42 % (11162)Instructions burned: 11 (million)
% 1.71/1.42 % (11162)------------------------------
% 1.71/1.42 % (11162)------------------------------
% 1.71/1.42 % (11155)Success in time 0.023 s
%------------------------------------------------------------------------------