%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM643^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 09:24:03 AM UTC 2026
% Result : Theorem 1.70s 1.49s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 48 unt; 0 typ; 4 def)
% Number of atoms : 471 ( 201 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1394 ( 40 ~; 66 |; 0 &;1205 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 11 con; 0-2 aty)
% ( 36 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 181 ( 101 ^; 80 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
set: $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,
pl: nat > nat > nat ).
thf(func_def_5,type,
set: $tType ).
thf(func_def_6,type,
esti: nat > set > $o ).
thf(func_def_7,type,
setof: ( nat > $o ) > set ).
thf(func_def_9,type,
n_1: nat ).
thf(func_def_10,type,
suc: nat > nat ).
thf(func_def_20,type,
sK1: set > nat ).
thf(func_def_21,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f473,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f354,f367,f373,f403,f466]) ).
thf(f466,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[status(thm)],[f465]) ).
thf(f465,plain,
( $false
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f462]) ).
thf(f462,plain,
( ( ( pl @ x @ ( pl @ y @ z ) )
!= ( pl @ x @ ( pl @ y @ z ) ) )
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f28,f446]) ).
thf(f446,plain,
( ! [X0: nat] :
( ( pl @ x @ ( pl @ y @ X0 ) )
= ( pl @ ( pl @ x @ y ) @ X0 ) )
| ~ spl0_16 ),
inference(equality_proxy_clausification,[status(thm)],[f441]) ).
thf(f441,plain,
( ! [X0: nat] :
( $true
= ( ( pl @ ( pl @ x @ y ) @ X0 )
= ( pl @ x @ ( pl @ y @ X0 ) ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f440]) ).
thf(f440,plain,
( ! [X0: nat] :
( ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ X0 )
= $true )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f427]) ).
thf(f427,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ X0 )
= $true ) )
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f61,f350]) ).
thf(f350,plain,
( ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f349]) ).
thf(f349,definition,
( spl0_16
<=> ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f61,plain,
! [X2: nat,X1: nat > $o] :
( ( $false
= ( esti @ X2 @ ( setof @ X1 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: nat,X1: nat > $o] :
( ( ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X1 ) )
=> ( X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: nat > $o] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X1 ) )
=> ( X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: nat > $o] :
( ( ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat > $o] :
( ( esti @ X0 @ ( setof @ X1 ) )
=> ( X1 @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat > $o] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',estie) ).
thf(f28,plain,
( ( pl @ ( pl @ x @ y ) @ z )
!= ( pl @ x @ ( pl @ y @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( pl @ ( pl @ x @ y ) @ z )
!= ( pl @ x @ ( pl @ y @ z ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
( ( pl @ ( pl @ x @ y ) @ z )
!= ( pl @ x @ ( pl @ y @ z ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ( pl @ ( pl @ x @ y ) @ z )
= ( pl @ x @ ( pl @ y @ z ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz5) ).
thf(f403,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[status(thm)],[f402]) ).
thf(f402,plain,
( $false
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f401]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( ( ( suc @ ( pl @ x @ y ) )
= ( suc @ ( pl @ x @ y ) ) )
= $false )
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f399,f70]) ).
thf(f70,plain,
! [X2: nat,X1: nat] :
( ( suc @ ( pl @ X2 @ X1 ) )
= ( pl @ X2 @ ( suc @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: nat,X1: nat] :
( ( ( suc @ ( pl @ X2 @ X1 ) )
= ( pl @ X2 @ ( suc @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( suc @ ( pl @ Y0 @ X1 ) )
= ( pl @ Y0 @ ( suc @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ ( pl @ Y0 @ X1 ) )
= ( pl @ Y0 @ ( suc @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ Y1 @ ( suc @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ Y1 @ ( suc @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ Y1 @ ( suc @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( suc @ ( pl @ X0 @ X1 ) )
= ( pl @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: nat,X3: nat] :
( ( suc @ ( pl @ X2 @ X3 ) )
= ( pl @ X2 @ ( suc @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz4f) ).
thf(f399,plain,
( ( ( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( suc @ y ) ) )
= $false )
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f398,f36]) ).
thf(f36,plain,
! [X1: nat] :
( ( suc @ X1 )
= ( pl @ X1 @ n_1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: nat] :
( $true
= ( ( pl @ X1 @ n_1 )
= ( suc @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( pl @ Y0 @ n_1 )
= ( suc @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ Y0 @ n_1 )
= ( suc @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ Y0 @ n_1 )
= ( suc @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ X2 @ n_1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz4a) ).
thf(f398,plain,
( ( ( ( suc @ ( pl @ x @ y ) )
= ( pl @ x @ ( pl @ y @ n_1 ) ) )
= $false )
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f379,f36]) ).
thf(f379,plain,
( ( $false
= ( ( pl @ ( pl @ x @ y ) @ n_1 )
= ( pl @ x @ ( pl @ y @ n_1 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f378]) ).
thf(f378,plain,
( ( ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ n_1 )
= $false )
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f376]) ).
thf(f376,plain,
( ( ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ n_1 )
= $false )
| ( $true = $false )
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f94,f263]) ).
thf(f263,plain,
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f261]) ).
thf(f261,definition,
( spl0_10
<=> ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f94,plain,
! [X2: nat > $o,X1: nat] :
( ( $true
= ( esti @ X1 @ ( setof @ X2 ) ) )
| ( ( X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: nat > $o,X1: nat] :
( ( ( X2 @ X1 )
=> ( esti @ X1 @ ( setof @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( Y0 @ X1 )
=> ( esti @ X1 @ ( setof @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: nat] :
( ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( Y0 @ X1 )
=> ( esti @ X1 @ ( setof @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat > $o,X1: nat] :
( ( X0 @ X1 )
=> ( esti @ X1 @ ( setof @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: nat > $o,X1: nat] :
( ( X0 @ X1 )
=> ( esti @ X1 @ ( setof @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',estii) ).
thf(f373,plain,
spl0_9,
inference(avatar_split_clause,[status(thm)],[f372,f257]) ).
thf(f257,definition,
( spl0_9
<=> ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f372,plain,
( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f361]) ).
thf(f361,plain,
( ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f360,f36]) ).
thf(f360,plain,
( ( ( pl @ ( pl @ x @ y ) @ n_1 )
!= ( suc @ ( pl @ x @ y ) ) )
| ( ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f359,f70]) ).
thf(f359,plain,
( ( ( pl @ ( pl @ x @ y ) @ n_1 )
!= ( pl @ x @ ( suc @ y ) ) )
| ( ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f332,f36]) ).
thf(f332,plain,
( ( ( pl @ ( pl @ x @ y ) @ n_1 )
!= ( pl @ x @ ( pl @ y @ n_1 ) ) )
| ( ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f331]) ).
thf(f331,plain,
( ( $true
= ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
| ( ( pl @ ( pl @ x @ y ) @ n_1 )
!= ( pl @ x @ ( pl @ y @ n_1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f326]) ).
thf(f326,plain,
( ( ( pl @ ( pl @ x @ y ) @ n_1 )
!= ( pl @ x @ ( pl @ y @ n_1 ) ) )
| ( $true = $false )
| ( $true
= ( ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f98,f121]) ).
thf(f121,plain,
! [X0: nat > $o] :
( ( $false
= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( $true
= ( X0 @ ( sK1 @ ( setof @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
! [X0: nat > $o] :
( ( $true
= ( X0 @ ( sK1 @ ( setof @ X0 ) ) ) )
| ( $false
= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f61,f81]) ).
thf(f81,plain,
! [X0: set] :
( ( $true
= ( esti @ ( sK1 @ X0 ) @ X0 ) )
| ( ( esti @ n_1 @ X0 )
= $false ) ),
inference(condensation,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: nat,X1: set] :
( ( ( esti @ ( sK1 @ X1 ) @ X1 )
= $true )
| ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( ( esti @ ( sK1 @ X1 ) @ X1 )
=> ( esti @ ( suc @ ( sK1 @ X1 ) ) @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) )
@ ( sK1 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: nat,X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false )
| ( ( esti @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: nat,X1: set] :
( ( $true
= ( ^ [Y0: nat] : ( esti @ Y0 @ X1 )
@ X2 ) )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: set] :
( ( ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) )
= $true )
| ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: set] :
( ( ( esti @ n_1 @ X1 )
=> ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: set] :
( $true
= ( ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ set
@ ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ set
@ ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: set] :
( ( esti @ n_1 @ X0 )
=> ( ! [X1: nat] :
( ( esti @ X1 @ X0 )
=> ( esti @ ( suc @ X1 ) @ X0 ) )
=> ! [X2: nat] : ( esti @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: set] :
( ( esti @ n_1 @ X1 )
=> ( ! [X2: nat] :
( ( esti @ X2 @ X1 )
=> ( esti @ ( suc @ X2 ) @ X1 ) )
=> ! [X2: nat] : ( esti @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',ax5) ).
thf(f98,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ( ( pl @ x @ ( pl @ y @ X0 ) )
!= ( pl @ ( pl @ x @ y ) @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ( ( ( pl @ ( pl @ x @ y ) @ X0 )
= ( pl @ x @ ( pl @ y @ X0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: nat] :
( $true
= ( ( ( pl @ ( pl @ x @ y ) @ X0 )
= ( pl @ x @ ( pl @ y @ X0 ) ) )
=> ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( Y0 @ X0 )
=> ( esti @ X0 @ ( setof @ Y0 ) ) )
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ),
inference(heuristic_instantiation,[status(thm)],[f83]) ).
thf(f367,plain,
( ~ spl0_9
| spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f366]) ).
thf(f366,plain,
( $false
| ~ spl0_9
| spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f365]) ).
thf(f365,plain,
( ( ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
!= ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| ~ spl0_9
| spl0_15 ),
inference(forward_demodulation,[status(thm)],[f364,f259]) ).
thf(f259,plain,
( ( ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
= ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f257]) ).
thf(f364,plain,
( ( ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
!= ( suc
@ ( pl @ ( pl @ x @ y )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) )
| spl0_15 ),
inference(superposition,[status(thm)],[f347,f70]) ).
thf(f347,plain,
( ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
!= ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f345]) ).
thf(f345,definition,
( spl0_15
<=> ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
= ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f354,plain,
( spl0_10
| ~ spl0_15
| spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f353,f349,f345,f261]) ).
thf(f353,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
!= ( suc
@ ( pl @ x
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f352,f70]) ).
thf(f352,plain,
! [X0: nat] :
( ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
!= ( pl @ x
@ ( suc
@ ( pl @ y
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f337,f70]) ).
thf(f337,plain,
! [X0: nat] :
( ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
!= ( pl @ x
@ ( pl @ y
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f330]) ).
thf(f330,plain,
! [X0: nat] :
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) )
= $false )
| ( ( pl @ ( pl @ x @ y )
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) )
!= ( pl @ x
@ ( pl @ y
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) ) ) ) )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ ( pl @ x @ y ) @ Y0 )
= ( pl @ x @ ( pl @ y @ Y0 ) ) ) ) ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f79,f98]) ).
thf(f79,plain,
! [X2: nat,X1: set] :
( ( ( esti @ ( suc @ ( sK1 @ X1 ) ) @ X1 )
= $false )
| ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM643^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.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 11:08:57 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : NUM643^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 5
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : pl (pl x y) z = pl x (pl y z)
% 0.20/0.46
% 0.20/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.20/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.20/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : satz5 [Lan30]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without extensionality : Theorem
% 0.20/0.46 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.80 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 1.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 18 ( 7 unt; 10 typ; 0 def)
% 0.20/0.46 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.46 % Number of connectives : 48 ( 0 ~; 0 |; 0 &; 43 @)
% 0.20/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 9 ( 4 avg)
% 0.20/0.46 % Number of types : 3 ( 2 usr)
% 0.20/0.46 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(nat_type,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(x,type,
% 0.20/0.46 x: nat ).
% 0.20/0.46
% 0.20/0.46 thf(y,type,
% 0.20/0.46 y: nat ).
% 0.20/0.46
% 0.20/0.46 thf(z,type,
% 0.20/0.46 z: nat ).
% 0.20/0.46
% 0.20/0.46 thf(pl,type,
% 0.20/0.46 pl: nat > nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(set_type,type,
% 0.20/0.46 set: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(esti,type,
% 0.20/0.46 esti: nat > set > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setof,type,
% 0.20/0.46 setof: ( nat > $o ) > set ).
% 0.20/0.46
% 0.20/0.46 thf(estie,axiom,
% 0.20/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.20/0.46 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.20/0.46 => ( Xp @ Xs ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(n_1,type,
% 0.20/0.46 n_1: nat ).
% 0.20/0.46
% 0.20/0.46 thf(suc,type,
% 0.20/0.46 suc: nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(ax5,axiom,
% 0.20/0.46 ! [Xs: set] :
% 0.20/0.46 ( ( esti @ n_1 @ Xs )
% 0.20/0.46 => ( ! [Xx: nat] :
% 0.20/0.46 ( ( esti @ Xx @ Xs )
% 0.20/0.46 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.20/0.46 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(estii,axiom,
% 0.20/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.20/0.46 ( ( Xp @ Xs )
% 0.20/0.46 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4e,axiom,
% 0.20/0.46 ! [Xx: nat] :
% 0.20/0.46 ( ( suc @ Xx )
% 0.20/0.46 = ( pl @ Xx @ n_1 ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4f,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] :
% 0.20/0.46 ( ( suc @ ( pl @ Xx @ Xy ) )
% 0.20/0.46 = ( pl @ Xx @ ( suc @ Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4a,axiom,
% 0.20/0.46 ! [Xx: nat] :
% 0.20/0.46 ( ( pl @ Xx @ n_1 )
% 0.20/0.46 = ( suc @ Xx ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz4b,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] :
% 0.20/0.46 ( ( pl @ Xx @ ( suc @ Xy ) )
% 0.20/0.46 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz5,conjecture,
% 0.20/0.46 ( ( pl @ ( pl @ x @ y ) @ z )
% 0.20/0.46 = ( pl @ x @ ( pl @ y @ z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.66/1.31 ---- Embedded in THF ---
% 1.66/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.31 %%% Generated on Tue Feb 24 11:08:58 EST 2026
% 1.66/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.31 %%% Logic specification used:
% 1.66/1.31 %%% thf(spec, logic, $$dhol).
% 1.66/1.31
% 1.66/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2DTF8829.p
% See solution above
% 1.66/1.31 ------------------------
% 1.66/1.32 ---- Cleaned THF ---
% 1.66/1.32 thf(nat_type,type,
% 1.66/1.32 nat: $tType ).
% 1.66/1.32
% 1.66/1.32 thf(x,type,
% 1.66/1.32 x: nat ).
% 1.66/1.32
% 1.66/1.32 thf(y,type,
% 1.66/1.32 y: nat ).
% 1.66/1.32
% 1.66/1.32 thf(z,type,
% 1.66/1.32 z: nat ).
% 1.66/1.32
% 1.66/1.32 thf(pl,type,
% 1.66/1.32 pl: nat > nat > nat ).
% 1.66/1.32
% 1.66/1.32 thf(set_type,type,
% 1.66/1.32 set: $tType ).
% 1.66/1.32
% 1.66/1.32 thf(esti,type,
% 1.66/1.32 esti: nat > set > $o ).
% 1.66/1.32
% 1.66/1.32 thf(setof,type,
% 1.66/1.32 setof: ( nat > $o ) > set ).
% 1.66/1.32
% 1.66/1.32 thf(estie,axiom,
% 1.66/1.32 ! [Xp: nat > $o,Xs: nat] :
% 1.66/1.32 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.66/1.32 => ( Xp @ Xs ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(n_1,type,
% 1.66/1.32 n_1: nat ).
% 1.66/1.32
% 1.66/1.32 thf(suc,type,
% 1.66/1.32 suc: nat > nat ).
% 1.66/1.32
% 1.66/1.32 thf(ax5,axiom,
% 1.66/1.32 ! [Xs: set] :
% 1.66/1.32 ( ( esti @ n_1 @ Xs )
% 1.66/1.32 => ( ! [Xx: nat] :
% 1.66/1.32 ( ( esti @ Xx @ Xs )
% 1.66/1.32 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.66/1.32 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(estii,axiom,
% 1.66/1.32 ! [Xp: nat > $o,Xs: nat] :
% 1.66/1.32 ( ( Xp @ Xs )
% 1.66/1.32 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(satz4e,axiom,
% 1.66/1.32 ! [Xx: nat] :
% 1.66/1.32 ( ( suc @ Xx )
% 1.66/1.32 = ( pl @ Xx @ n_1 ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(satz4f,axiom,
% 1.66/1.32 ! [Xx: nat,Xy: nat] :
% 1.66/1.32 ( ( suc @ ( pl @ Xx @ Xy ) )
% 1.66/1.32 = ( pl @ Xx @ ( suc @ Xy ) ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(satz4a,axiom,
% 1.66/1.32 ! [Xx: nat] :
% 1.66/1.32 ( ( pl @ Xx @ n_1 )
% 1.66/1.32 = ( suc @ Xx ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(satz4b,axiom,
% 1.66/1.32 ! [Xx: nat,Xy: nat] :
% 1.66/1.32 ( ( pl @ Xx @ ( suc @ Xy ) )
% 1.66/1.32 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 1.66/1.32
% 1.66/1.32 thf(satz5,conjecture,
% 1.66/1.32 ( ( pl @ ( pl @ x @ y ) @ z )
% 1.66/1.32 = ( pl @ x @ ( pl @ y @ z ) ) ) ).
% 1.66/1.32 ------------------------
% 1.66/1.34 % (9016)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_8829 for (2999ds/27Mi)
% 1.66/1.34 % (9019)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_8829 for (2999ds/275Mi)
% 1.66/1.34 % (9019)Refutation not found, incomplete strategy
% 1.66/1.34 % (9019)------------------------------
% 1.66/1.34 % (9019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (9019)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.34
% 1.66/1.34
% 1.66/1.34 % (9019)Memory used [KB]: 5500
% 1.66/1.34 % (9019)Time elapsed: 0.001 s
% 1.66/1.34 % (9019)Instructions burned: 1 (million)
% 1.66/1.34 % (9019)------------------------------
% 1.66/1.34 % (9019)------------------------------
% 1.66/1.34 % (9016)Refutation not found, incomplete strategy
% 1.66/1.34 % (9016)------------------------------
% 1.66/1.34 % (9016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (9016)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.34
% 1.66/1.34
% 1.66/1.34 % (9016)Memory used [KB]: 5500
% 1.66/1.34 % (9016)Time elapsed: 0.003 s
% 1.66/1.34 % (9016)Instructions burned: 2 (million)
% 1.66/1.34 % (9016)------------------------------
% 1.66/1.34 % (9016)------------------------------
% 1.66/1.34 % (9015)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_8829 for (2999ds/4Mi)
% 1.66/1.35 % (9015)Instruction limit reached!
% 1.66/1.35 % (9015)------------------------------
% 1.66/1.35 % (9015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (9015)Termination reason: Unknown
% 1.66/1.35 % (9015)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (9015)Memory used [KB]: 5500
% 1.66/1.35 % (9015)Time elapsed: 0.004 s
% 1.66/1.35 % (9015)Instructions burned: 4 (million)
% 1.66/1.35 % (9015)------------------------------
% 1.66/1.35 % (9015)------------------------------
% 1.66/1.35 % (9014)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/183Mi)
% 1.66/1.35 % (9017)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/2Mi)
% 1.66/1.35 % (9020)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/18Mi)
% 1.66/1.35 % (9018)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_8829 for (2999ds/2Mi)
% 1.66/1.35 % (9017)Instruction limit reached!
% 1.66/1.35 % (9017)------------------------------
% 1.66/1.35 % (9017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (9017)Termination reason: Unknown
% 1.66/1.35 % (9017)Termination phase: Preprocessing 3
% 1.66/1.35
% 1.66/1.35 % (9017)Memory used [KB]: 895
% 1.66/1.35 % (9017)Time elapsed: 0.003 s
% 1.66/1.35 % (9017)Instructions burned: 2 (million)
% 1.66/1.35 % (9017)------------------------------
% 1.66/1.35 % (9017)------------------------------
% 1.66/1.35 % (9018)Instruction limit reached!
% 1.66/1.35 % (9018)------------------------------
% 1.66/1.35 % (9018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (9018)Termination reason: Unknown
% 1.66/1.35 % (9018)Termination phase: shuffling
% 1.66/1.35
% 1.66/1.35 % (9018)Memory used [KB]: 895
% 1.66/1.35 % (9018)Time elapsed: 0.003 s
% 1.66/1.35 % (9018)Instructions burned: 2 (million)
% 1.66/1.35 % (9018)------------------------------
% 1.66/1.35 % (9018)------------------------------
% 1.66/1.35 % (9025)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/3Mi)
% 1.66/1.35 % (9025)Instruction limit reached!
% 1.66/1.35 % (9025)------------------------------
% 1.66/1.35 % (9025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (9025)Termination reason: Unknown
% 1.66/1.35 % (9025)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (9025)Memory used [KB]: 5500
% 1.66/1.35 % (9025)Time elapsed: 0.002 s
% 1.66/1.35 % (9025)Instructions burned: 3 (million)
% 1.66/1.35 % (9025)------------------------------
% 1.66/1.35 % (9025)------------------------------
% 1.66/1.35 % (9026)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_8829 for (2999ds/37Mi)
% 1.66/1.36 % (9020)Instruction limit reached!
% 1.66/1.36 % (9020)------------------------------
% 1.66/1.36 % (9020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (9020)Termination reason: Unknown
% 1.66/1.36 % (9020)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (9020)Memory used [KB]: 5628
% 1.66/1.36 % (9020)Time elapsed: 0.014 s
% 1.66/1.36 % (9020)Instructions burned: 19 (million)
% 1.66/1.36 % (9020)------------------------------
% 1.66/1.36 % (9020)------------------------------
% 1.66/1.36 % (9028)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_8829 for (2999ds/15Mi)
% 1.66/1.36 % (9028)Refutation not found, incomplete strategy
% 1.66/1.36 % (9028)------------------------------
% 1.66/1.36 % (9028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (9028)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.36
% 1.66/1.36
% 1.66/1.36 % (9028)Memory used [KB]: 5500
% 1.66/1.36 % (9028)Time elapsed: 0.002 s
% 1.66/1.36 % (9028)Instructions burned: 2 (million)
% 1.66/1.36 % (9028)------------------------------
% 1.66/1.36 % (9028)------------------------------
% 1.66/1.36 % (9033)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/7Mi)
% 1.66/1.36 % (9026)Instruction limit reached!
% 1.66/1.36 % (9026)------------------------------
% 1.66/1.36 % (9026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (9026)Termination reason: Unknown
% 1.66/1.36 % (9026)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (9026)Memory used [KB]: 5884
% 1.66/1.36 % (9026)Time elapsed: 0.014 s
% 1.66/1.36 % (9026)Instructions burned: 37 (million)
% 1.66/1.36 % (9026)------------------------------
% 1.66/1.36 % (9026)------------------------------
% 1.66/1.36 % (9030)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_8829 for (2999ds/3Mi)
% 1.66/1.36 % (9031)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_8829 for (2999ds/1041Mi)
% 1.66/1.37 % (9030)Instruction limit reached!
% 1.66/1.37 % (9030)------------------------------
% 1.66/1.37 % (9030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (9030)Termination reason: Unknown
% 1.66/1.37 % (9030)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (9030)Memory used [KB]: 5500
% 1.66/1.37 % (9030)Time elapsed: 0.004 s
% 1.66/1.37 % (9030)Instructions burned: 3 (million)
% 1.66/1.37 % (9030)------------------------------
% 1.66/1.37 % (9030)------------------------------
% 1.66/1.37 % (9033)Instruction limit reached!
% 1.66/1.37 % (9033)------------------------------
% 1.66/1.37 % (9033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (9033)Termination reason: Unknown
% 1.66/1.37 % (9033)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (9033)Memory used [KB]: 1023
% 1.66/1.37 % (9033)Time elapsed: 0.007 s
% 1.66/1.37 % (9033)Instructions burned: 7 (million)
% 1.66/1.37 % (9033)------------------------------
% 1.66/1.37 % (9033)------------------------------
% 1.66/1.37 % (9039)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_8829 for (2999ds/3Mi)
% 1.66/1.37 % (9039)Instruction limit reached!
% 1.66/1.37 % (9039)------------------------------
% 1.66/1.37 % (9039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (9039)Termination reason: Unknown
% 1.66/1.37 % (9039)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (9039)Memory used [KB]: 5500
% 1.66/1.37 % (9039)Time elapsed: 0.003 s
% 1.66/1.37 % (9039)Instructions burned: 3 (million)
% 1.66/1.37 % (9039)------------------------------
% 1.66/1.37 % (9039)------------------------------
% 1.66/1.37 % (9041)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_8829 for (2999ds/3Mi)
% 1.66/1.37 % (9041)Instruction limit reached!
% 1.66/1.37 % (9041)------------------------------
% 1.66/1.37 % (9041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (9041)Termination reason: Unknown
% 1.66/1.37 % (9041)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (9041)Memory used [KB]: 1023
% 1.66/1.37 % (9041)Time elapsed: 0.003 s
% 1.66/1.37 % (9041)Instructions burned: 4 (million)
% 1.66/1.37 % (9041)------------------------------
% 1.66/1.37 % (9041)------------------------------
% 1.66/1.38 % (9037)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/16Mi)
% 1.66/1.38 % (9048)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/4Mi)
% 1.66/1.38 % (9044)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/7Mi)
% 1.66/1.38 % (9048)Instruction limit reached!
% 1.66/1.38 % (9048)------------------------------
% 1.66/1.38 % (9048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (9048)Termination reason: Unknown
% 1.66/1.38 % (9048)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (9048)Memory used [KB]: 5500
% 1.66/1.38 % (9048)Time elapsed: 0.004 s
% 1.66/1.38 % (9048)Instructions burned: 6 (million)
% 1.66/1.38 % (9048)------------------------------
% 1.66/1.38 % (9048)------------------------------
% 1.66/1.38 % (9044)Refutation not found, incomplete strategy
% 1.66/1.38 % (9044)------------------------------
% 1.66/1.38 % (9044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (9044)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (9044)Memory used [KB]: 5500
% 1.66/1.38 % (9044)Time elapsed: 0.003 s
% 1.66/1.38 % (9044)Instructions burned: 4 (million)
% 1.66/1.38 % (9044)------------------------------
% 1.66/1.38 % (9044)------------------------------
% 1.66/1.38 % (9045)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/3Mi)
% 1.66/1.38 % (9049)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/18Mi)
% 1.66/1.39 % (9045)Instruction limit reached!
% 1.66/1.39 % (9045)------------------------------
% 1.66/1.39 % (9045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (9045)Termination reason: Unknown
% 1.66/1.39 % (9045)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (9045)Memory used [KB]: 5500
% 1.66/1.39 % (9045)Time elapsed: 0.003 s
% 1.66/1.39 % (9045)Instructions burned: 4 (million)
% 1.66/1.39 % (9045)------------------------------
% 1.66/1.39 % (9045)------------------------------
% 1.66/1.39 % (9037)Instruction limit reached!
% 1.66/1.39 % (9037)------------------------------
% 1.66/1.39 % (9037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (9037)Termination reason: Unknown
% 1.66/1.39 % (9037)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (9037)Memory used [KB]: 5628
% 1.66/1.39 % (9037)Time elapsed: 0.013 s
% 1.66/1.39 % (9037)Instructions burned: 16 (million)
% 1.66/1.39 % (9037)------------------------------
% 1.66/1.39 % (9037)------------------------------
% 1.66/1.39 % (9049)Refutation not found, incomplete strategy
% 1.66/1.39 % (9049)------------------------------
% 1.66/1.39 % (9049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (9049)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.39
% 1.66/1.39
% 1.66/1.39 % (9049)Memory used [KB]: 5500
% 1.66/1.39 % (9049)Time elapsed: 0.004 s
% 1.66/1.39 % (9049)Instructions burned: 6 (million)
% 1.66/1.39 % (9049)------------------------------
% 1.66/1.39 % (9049)------------------------------
% 1.66/1.39 % (9055)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/710Mi)
% 1.66/1.39 % (9056)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/6Mi)
% 1.70/1.40 % (9056)Instruction limit reached!
% 1.70/1.40 % (9056)------------------------------
% 1.70/1.40 % (9056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (9056)Termination reason: Unknown
% 1.70/1.40 % (9056)Termination phase: Saturation
% 1.70/1.40
% 1.70/1.40 % (9056)Memory used [KB]: 5500
% 1.70/1.40 % (9056)Time elapsed: 0.004 s
% 1.70/1.40 % (9056)Instructions burned: 6 (million)
% 1.70/1.40 % (9056)------------------------------
% 1.70/1.40 % (9056)------------------------------
% 1.70/1.40 % (9059)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/5Mi)
% 1.70/1.40 % (9057)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/902Mi)
% 1.70/1.40 % (9057)Refutation not found, incomplete strategy
% 1.70/1.40 % (9057)------------------------------
% 1.70/1.40 % (9057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (9057)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.40
% 1.70/1.40
% 1.70/1.40 % (9057)Memory used [KB]: 5500
% 1.70/1.40 % (9057)Time elapsed: 0.002 s
% 1.70/1.40 % (9057)Instructions burned: 2 (million)
% 1.70/1.40 % (9057)------------------------------
% 1.70/1.40 % (9057)------------------------------
% 1.70/1.40 % (9059)Instruction limit reached!
% 1.70/1.40 % (9059)------------------------------
% 1.70/1.40 % (9059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (9059)Termination reason: Unknown
% 1.70/1.40 % (9059)Termination phase: Saturation
% 1.70/1.40
% 1.70/1.40 % (9059)Memory used [KB]: 5500
% 1.70/1.40 % (9059)Time elapsed: 0.004 s
% 1.70/1.40 % (9059)Instructions burned: 6 (million)
% 1.70/1.40 % (9059)------------------------------
% 1.70/1.40 % (9059)------------------------------
% 1.70/1.40 % (9058)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_8829 for (2999ds/21Mi)
% 1.70/1.41 % (9062)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/6Mi)
% 1.70/1.41 % (9062)Refutation not found, incomplete strategy
% 1.70/1.41 % (9062)------------------------------
% 1.70/1.41 % (9062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.41 % (9062)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.41
% 1.70/1.41
% 1.70/1.41 % (9062)Memory used [KB]: 5500
% 1.70/1.41 % (9062)Time elapsed: 0.003 s
% 1.70/1.41 % (9062)Instructions burned: 4 (million)
% 1.70/1.41 % (9062)------------------------------
% 1.70/1.41 % (9062)------------------------------
% 1.70/1.41 % (9065)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/377Mi)
% 1.70/1.41 % (9066)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/779Mi)
% 1.70/1.42 % (9058)Instruction limit reached!
% 1.70/1.42 % (9058)------------------------------
% 1.70/1.42 % (9058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (9058)Termination reason: Unknown
% 1.70/1.42 % (9058)Termination phase: Saturation
% 1.70/1.42
% 1.70/1.42 % (9058)Memory used [KB]: 5628
% 1.70/1.42 % (9058)Time elapsed: 0.016 s
% 1.70/1.42 % (9058)Instructions burned: 22 (million)
% 1.70/1.42 % (9058)------------------------------
% 1.70/1.42 % (9058)------------------------------
% 1.70/1.42 % (9072)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/19Mi)
% 1.70/1.42 % (9072)Refutation not found, incomplete strategy
% 1.70/1.42 % (9072)------------------------------
% 1.70/1.42 % (9072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.42 % (9072)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.42
% 1.70/1.42
% 1.70/1.42 % (9072)Memory used [KB]: 5500
% 1.70/1.42 % (9072)Time elapsed: 0.003 s
% 1.70/1.42 % (9072)Instructions burned: 4 (million)
% 1.70/1.42 % (9072)------------------------------
% 1.70/1.42 % (9072)------------------------------
% 1.70/1.43 % (9014)Instruction limit reached!
% 1.70/1.43 % (9014)------------------------------
% 1.70/1.43 % (9014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.43 % (9014)Termination reason: Unknown
% 1.70/1.43 % (9014)Termination phase: Saturation
% 1.70/1.43
% 1.70/1.43 % (9014)Memory used [KB]: 6524
% 1.70/1.43 % (9014)Time elapsed: 0.082 s
% 1.70/1.43 % (9014)Instructions burned: 183 (million)
% 1.70/1.43 % (9014)------------------------------
% 1.70/1.43 % (9014)------------------------------
% 1.70/1.43 % (9074)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/17Mi)
% 1.70/1.43 % (9073)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/879Mi)
% 1.70/1.44 % (9080)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/3Mi)
% 1.70/1.44 % (9074)Instruction limit reached!
% 1.70/1.44 % (9074)------------------------------
% 1.70/1.44 % (9074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (9074)Termination reason: Unknown
% 1.70/1.44 % (9074)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (9074)Memory used [KB]: 5628
% 1.70/1.44 % (9074)Time elapsed: 0.008 s
% 1.70/1.44 % (9074)Instructions burned: 18 (million)
% 1.70/1.44 % (9074)------------------------------
% 1.70/1.44 % (9074)------------------------------
% 1.70/1.44 % (9080)Instruction limit reached!
% 1.70/1.44 % (9080)------------------------------
% 1.70/1.44 % (9080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (9080)Termination reason: Unknown
% 1.70/1.44 % (9080)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (9080)Memory used [KB]: 1023
% 1.70/1.44 % (9080)Time elapsed: 0.003 s
% 1.70/1.44 % (9080)Instructions burned: 4 (million)
% 1.70/1.44 % (9080)------------------------------
% 1.70/1.44 % (9080)------------------------------
% 1.70/1.45 % (9089)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/127Mi)
% 1.70/1.45 % (9073)Refutation not found, incomplete strategy
% 1.70/1.45 % (9073)------------------------------
% 1.70/1.45 % (9073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.45 % (9073)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.45
% 1.70/1.45
% 1.70/1.45 % (9073)Memory used [KB]: 5628
% 1.70/1.45 % (9073)Time elapsed: 0.018 s
% 1.70/1.45 % (9073)Instructions burned: 39 (million)
% 1.70/1.45 % (9073)------------------------------
% 1.70/1.45 % (9073)------------------------------
% 1.70/1.45 % (9088)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8829 for (2999ds/30Mi)
% 1.70/1.46 % (9031)Refutation not found, incomplete strategy
% 1.70/1.46 % (9031)------------------------------
% 1.70/1.46 % (9031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.46 % (9031)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.46
% 1.70/1.46
% 1.70/1.46 % (9031)Memory used [KB]: 5884
% 1.70/1.46 % (9031)Time elapsed: 0.094 s
% 1.70/1.46 % (9031)Instructions burned: 224 (million)
% 1.70/1.46 % (9031)------------------------------
% 1.70/1.46 % (9031)------------------------------
% 1.70/1.46 % (9098)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8829 for (2998ds/100Mi)
% 1.70/1.47 % (9099)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_8829 for (2998ds/3Mi)
% 1.70/1.47 % (9099)Instruction limit reached!
% 1.70/1.47 % (9099)------------------------------
% 1.70/1.47 % (9099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (9099)Termination reason: Unknown
% 1.70/1.47 % (9099)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (9099)Memory used [KB]: 5500
% 1.70/1.47 % (9099)Time elapsed: 0.002 s
% 1.70/1.47 % (9099)Instructions burned: 3 (million)
% 1.70/1.47 % (9099)------------------------------
% 1.70/1.47 % (9099)------------------------------
% 1.70/1.47 % (9088)Instruction limit reached!
% 1.70/1.47 % (9088)------------------------------
% 1.70/1.47 % (9088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.47 % (9088)Termination reason: Unknown
% 1.70/1.47 % (9088)Termination phase: Saturation
% 1.70/1.47
% 1.70/1.47 % (9088)Memory used [KB]: 5628
% 1.70/1.47 % (9088)Time elapsed: 0.043 s
% 1.70/1.47 % (9088)Instructions burned: 31 (million)
% 1.70/1.47 % (9088)------------------------------
% 1.70/1.47 % (9088)------------------------------
% 1.70/1.48 % (9103)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_8829 for (2998ds/20Mi)
% 1.70/1.48 % (9103)Refutation not found, incomplete strategy
% 1.70/1.48 % (9103)------------------------------
% 1.70/1.48 % (9103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.48 % (9103)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.48
% 1.70/1.48
% 1.70/1.48 % (9103)Memory used [KB]: 5500
% 1.70/1.48 % (9103)Time elapsed: 0.002 s
% 1.70/1.48 % (9103)Instructions burned: 3 (million)
% 1.70/1.48 % (9103)------------------------------
% 1.70/1.48 % (9103)------------------------------
% 1.70/1.49 % (9115)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_8829 for (2998ds/107Mi)
% 1.70/1.49 % (9115)Refutation not found, incomplete strategy
% 1.70/1.49 % (9115)------------------------------
% 1.70/1.49 % (9115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (9115)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.49
% 1.70/1.49
% 1.70/1.49 % (9115)Memory used [KB]: 5500
% 1.70/1.49 % (9115)Time elapsed: 0.002 s
% 1.70/1.49 % (9115)Instructions burned: 3 (million)
% 1.70/1.49 % (9115)------------------------------
% 1.70/1.49 % (9115)------------------------------
% 1.70/1.49 % (9098)First to succeed.
% 1.70/1.49 % (9089)Instruction limit reached!
% 1.70/1.49 % (9089)------------------------------
% 1.70/1.49 % (9089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (9089)Termination reason: Unknown
% 1.70/1.49 % (9089)Termination phase: Saturation
% 1.70/1.49
% 1.70/1.49 % (9089)Memory used [KB]: 6012
% 1.70/1.49 % (9089)Time elapsed: 0.067 s
% 1.70/1.49 % (9089)Instructions burned: 128 (million)
% 1.70/1.49 % (9089)------------------------------
% 1.70/1.49 % (9089)------------------------------
% 1.70/1.49 % (9111)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_8829 for (2998ds/86Mi)
% 1.70/1.49 % (9098)Refutation found. Thanks to Tanya!
% 1.70/1.49 % SZS status Theorem for DTF2THF_8829
% 1.70/1.49 % SZS output start Proof for DTF2THF_8829
% 1.70/1.49 thf(type_def_5, type, nat: $tType).
% 1.70/1.49 thf(type_def_7, type, set: $tType).
% 1.70/1.49 thf(func_def_0, type, nat: $tType).
% 1.70/1.49 thf(func_def_1, type, x: nat).
% 1.70/1.49 thf(func_def_2, type, y: nat).
% 1.70/1.49 thf(func_def_3, type, z: nat).
% 1.70/1.49 thf(func_def_4, type, pl: nat > nat > nat).
% 1.70/1.49 thf(func_def_5, type, set: $tType).
% 1.70/1.49 thf(func_def_6, type, esti: nat > set > $o).
% 1.70/1.49 thf(func_def_7, type, setof: (nat > $o) > set).
% 1.70/1.49 thf(func_def_9, type, n_1: nat).
% 1.70/1.49 thf(func_def_10, type, suc: nat > nat).
% 1.70/1.49 thf(func_def_20, type, sK1: set > nat).
% 1.70/1.49 thf(func_def_21, type, ph2: !>[X0: $tType]:(X0)).
% 1.70/1.49 thf(f473,plain,(
% 1.70/1.49 $false),
% 1.70/1.49 inference(avatar_sat_refutation,[status(thm)],[f354,f367,f373,f403,f466])).
% 1.70/1.49 thf(f466,plain,(
% 1.70/1.49 ~spl0_16),
% 1.70/1.49 inference(avatar_contradiction_clause,[status(thm)],[f465])).
% 1.70/1.49 thf(f465,plain,(
% 1.70/1.49 $false | ~spl0_16),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f462])).
% 1.70/1.49 thf(f462,plain,(
% 1.70/1.49 ((pl @ x @ (pl @ y @ z)) != (pl @ x @ (pl @ y @ z))) | ~spl0_16),
% 1.70/1.49 inference(superposition,[status(thm)],[f28,f446])).
% 1.70/1.49 thf(f446,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (((pl @ x @ (pl @ y @ X0)) = (pl @ (pl @ x @ y) @ X0))) ) | ~spl0_16),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f441])).
% 1.70/1.49 thf(f441,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = ((pl @ (pl @ x @ y) @ X0) = (pl @ x @ (pl @ y @ X0))))) ) | ~spl0_16),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f440])).
% 1.70/1.49 thf(f440,plain,(
% 1.70/1.49 ( ! [X0 : nat] : ((((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ X0) = $true)) ) | ~spl0_16),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f427])).
% 1.70/1.49 thf(f427,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = $false) | (((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ X0) = $true)) ) | ~spl0_16),
% 1.70/1.49 inference(superposition,[status(thm)],[f61,f350])).
% 1.70/1.49 thf(f350,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) ) | ~spl0_16),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f349])).
% 1.70/1.49 thf(f349,definition,(
% 1.70/1.49 spl0_16 <=> ! [X0 : nat] : ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.70/1.49 thf(f61,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat > $o] : (($false = (esti @ X2 @ (setof @ X1))) | ((X1 @ X2) = $true)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.70/1.49 thf(f60,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((esti @ X2 @ (setof @ X1)) => (X1 @ X2)))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.70/1.49 thf(f59,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat > $o] : ((((^[Y0 : nat]: ((esti @ Y0 @ (setof @ X1)) => (X1 @ Y0))) @ X2) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f43])).
% 1.70/1.49 thf(f43,plain,(
% 1.70/1.49 ( ! [X1 : nat > $o] : (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ (setof @ X1)) => (X1 @ Y0)))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.70/1.49 thf(f41,plain,(
% 1.70/1.49 ( ! [X1 : nat > $o] : ((((^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1))))) @ X1) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f26])).
% 1.70/1.49 thf(f26,plain,(
% 1.70/1.49 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1)))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f20])).
% 1.70/1.49 thf(f20,plain,(
% 1.70/1.49 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1)))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f19])).
% 1.70/1.49 thf(f19,plain,(
% 1.70/1.49 ! [X0 : nat,X1 : nat > $o] : ((esti @ X0 @ (setof @ X1)) => (X1 @ X0))),
% 1.70/1.49 inference(rectify,[status(thm)],[f1])).
% 1.70/1.49 thf(f1,axiom,(
% 1.70/1.49 ! [X1 : nat,X0 : nat > $o] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',estie)).
% 1.70/1.49 thf(f28,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ z) != (pl @ x @ (pl @ y @ z)))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f25])).
% 1.70/1.49 thf(f25,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ z) != (pl @ x @ (pl @ y @ z)))),
% 1.70/1.49 inference(flattening,[status(thm)],[f9])).
% 1.70/1.49 thf(f9,negated_conjecture,(
% 1.70/1.49 ~((pl @ (pl @ x @ y) @ z) = (pl @ x @ (pl @ y @ z)))),
% 1.70/1.49 inference(negated_conjecture,[status(cth)],[f8])).
% 1.70/1.49 thf(f8,conjecture,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ z) = (pl @ x @ (pl @ y @ z)))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz5)).
% 1.70/1.49 thf(f403,plain,(
% 1.70/1.49 ~spl0_10),
% 1.70/1.49 inference(avatar_contradiction_clause,[status(thm)],[f402])).
% 1.70/1.49 thf(f402,plain,(
% 1.70/1.49 $false | ~spl0_10),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f401])).
% 1.70/1.49 thf(f401,plain,(
% 1.70/1.49 ($true = $false) | ~spl0_10),
% 1.70/1.49 inference(boolean_simplification,[status(thm)],[f400])).
% 1.70/1.49 thf(f400,plain,(
% 1.70/1.49 (((suc @ (pl @ x @ y)) = (suc @ (pl @ x @ y))) = $false) | ~spl0_10),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f399,f70])).
% 1.70/1.49 thf(f70,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat] : (((suc @ (pl @ X2 @ X1)) = (pl @ X2 @ (suc @ X1)))) )),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f69])).
% 1.70/1.49 thf(f69,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat] : ((((suc @ (pl @ X2 @ X1)) = (pl @ X2 @ (suc @ X1))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.70/1.49 thf(f68,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((suc @ (pl @ Y0 @ X1)) = (pl @ Y0 @ (suc @ X1)))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f67])).
% 1.70/1.49 thf(f67,plain,(
% 1.70/1.49 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((suc @ (pl @ Y0 @ X1)) = (pl @ Y0 @ (suc @ X1))))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.70/1.49 thf(f66,plain,(
% 1.70/1.49 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ Y1 @ (suc @ Y0)))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f30])).
% 1.70/1.49 thf(f30,plain,(
% 1.70/1.49 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ Y1 @ (suc @ Y0))))))) = $true)),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f14])).
% 1.70/1.49 thf(f14,plain,(
% 1.70/1.49 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ Y1 @ (suc @ Y0))))))) = $true)),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f13])).
% 1.70/1.49 thf(f13,plain,(
% 1.70/1.49 ! [X0 : nat,X1 : nat] : ((suc @ (pl @ X0 @ X1)) = (pl @ X0 @ (suc @ X1)))),
% 1.70/1.49 inference(rectify,[status(thm)],[f5])).
% 1.70/1.49 thf(f5,axiom,(
% 1.70/1.49 ! [X2 : nat,X3 : nat] : ((suc @ (pl @ X2 @ X3)) = (pl @ X2 @ (suc @ X3)))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz4f)).
% 1.70/1.49 thf(f399,plain,(
% 1.70/1.49 (((suc @ (pl @ x @ y)) = (pl @ x @ (suc @ y))) = $false) | ~spl0_10),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f398,f36])).
% 1.70/1.49 thf(f36,plain,(
% 1.70/1.49 ( ! [X1 : nat] : (((suc @ X1) = (pl @ X1 @ n_1))) )),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.70/1.49 thf(f35,plain,(
% 1.70/1.49 ( ! [X1 : nat] : (($true = ((pl @ X1 @ n_1) = (suc @ X1)))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.70/1.49 thf(f34,plain,(
% 1.70/1.49 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((pl @ Y0 @ n_1) = (suc @ Y0))) @ X1) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f27])).
% 1.70/1.49 thf(f27,plain,(
% 1.70/1.49 ($true = (!! @ nat @ (^[Y0 : nat]: ((pl @ Y0 @ n_1) = (suc @ Y0)))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f16])).
% 1.70/1.49 thf(f16,plain,(
% 1.70/1.49 ($true = (!! @ nat @ (^[Y0 : nat]: ((pl @ Y0 @ n_1) = (suc @ Y0)))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f15])).
% 1.70/1.49 thf(f15,plain,(
% 1.70/1.49 ! [X0 : nat] : ((pl @ X0 @ n_1) = (suc @ X0))),
% 1.70/1.49 inference(rectify,[status(thm)],[f6])).
% 1.70/1.49 thf(f6,axiom,(
% 1.70/1.49 ! [X2 : nat] : ((suc @ X2) = (pl @ X2 @ n_1))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',satz4a)).
% 1.70/1.49 thf(f398,plain,(
% 1.70/1.49 (((suc @ (pl @ x @ y)) = (pl @ x @ (pl @ y @ n_1))) = $false) | ~spl0_10),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f379,f36])).
% 1.70/1.49 thf(f379,plain,(
% 1.70/1.49 ($false = ((pl @ (pl @ x @ y) @ n_1) = (pl @ x @ (pl @ y @ n_1)))) | ~spl0_10),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f378])).
% 1.70/1.49 thf(f378,plain,(
% 1.70/1.49 (((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ n_1) = $false) | ~spl0_10),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.70/1.49 thf(f376,plain,(
% 1.70/1.49 (((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ n_1) = $false) | ($true = $false) | ~spl0_10),
% 1.70/1.49 inference(superposition,[status(thm)],[f94,f263])).
% 1.70/1.49 thf(f263,plain,(
% 1.70/1.49 ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false) | ~spl0_10),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f261])).
% 1.70/1.49 thf(f261,definition,(
% 1.70/1.49 spl0_10 <=> ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false)),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.70/1.49 thf(f94,plain,(
% 1.70/1.49 ( ! [X2 : nat > $o,X1 : nat] : (($true = (esti @ X1 @ (setof @ X2))) | ((X2 @ X1) = $false)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.70/1.49 thf(f93,plain,(
% 1.70/1.49 ( ! [X2 : nat > $o,X1 : nat] : ((((X2 @ X1) => (esti @ X1 @ (setof @ X2))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.70/1.49 thf(f88,plain,(
% 1.70/1.49 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat > $o]: ((Y0 @ X1) => (esti @ X1 @ (setof @ Y0)))) @ X2))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f83])).
% 1.70/1.49 thf(f83,plain,(
% 1.70/1.49 ( ! [X1 : nat] : (((!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((Y0 @ X1) => (esti @ X1 @ (setof @ Y0))))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.70/1.49 thf(f82,plain,(
% 1.70/1.49 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1)))))) @ X1) = $true)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f31])).
% 1.70/1.49 thf(f31,plain,(
% 1.70/1.49 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))) = $true)),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f22])).
% 1.70/1.49 thf(f22,plain,(
% 1.70/1.49 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))) = $true)),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f21])).
% 1.70/1.49 thf(f21,plain,(
% 1.70/1.49 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.70/1.49 inference(rectify,[status(thm)],[f3])).
% 1.70/1.49 thf(f3,axiom,(
% 1.70/1.49 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',estii)).
% 1.70/1.49 thf(f373,plain,(
% 1.70/1.49 spl0_9),
% 1.70/1.49 inference(avatar_split_clause,[status(thm)],[f372,f257])).
% 1.70/1.49 thf(f257,definition,(
% 1.70/1.49 spl0_9 <=> ((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.70/1.49 thf(f372,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f361])).
% 1.70/1.49 thf(f361,plain,(
% 1.70/1.49 (((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) = $true)),
% 1.70/1.49 inference(subsumption_resolution,[status(thm)],[f360,f36])).
% 1.70/1.49 thf(f360,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ n_1) != (suc @ (pl @ x @ y))) | (((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) = $true)),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f359,f70])).
% 1.70/1.49 thf(f359,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ n_1) != (pl @ x @ (suc @ y))) | (((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) = $true)),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f332,f36])).
% 1.70/1.49 thf(f332,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ n_1) != (pl @ x @ (pl @ y @ n_1))) | (((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) = $true)),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f331])).
% 1.70/1.49 thf(f331,plain,(
% 1.70/1.49 ($true = ((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) | ((pl @ (pl @ x @ y) @ n_1) != (pl @ x @ (pl @ y @ n_1)))),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f326])).
% 1.70/1.49 thf(f326,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ n_1) != (pl @ x @ (pl @ y @ n_1))) | ($true = $false) | ($true = ((^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))),
% 1.70/1.49 inference(superposition,[status(thm)],[f98,f121])).
% 1.70/1.49 thf(f121,plain,(
% 1.70/1.49 ( ! [X0 : nat > $o] : (($false = (esti @ n_1 @ (setof @ X0))) | ($true = (X0 @ (sK1 @ (setof @ X0))))) )),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.70/1.49 thf(f119,plain,(
% 1.70/1.49 ( ! [X0 : nat > $o] : (($true = (X0 @ (sK1 @ (setof @ X0)))) | ($false = (esti @ n_1 @ (setof @ X0))) | ($true = $false)) )),
% 1.70/1.49 inference(superposition,[status(thm)],[f61,f81])).
% 1.70/1.49 thf(f81,plain,(
% 1.70/1.49 ( ! [X0 : set] : (($true = (esti @ (sK1 @ X0) @ X0)) | ((esti @ n_1 @ X0) = $false)) )),
% 1.70/1.49 inference(condensation,[status(thm)],[f80])).
% 1.70/1.49 thf(f80,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (((esti @ (sK1 @ X1) @ X1) = $true) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.70/1.49 thf(f78,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false) | (((esti @ (sK1 @ X1) @ X1) => (esti @ (suc @ (sK1 @ X1)) @ X1)) = $false)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f77])).
% 1.70/1.49 thf(f77,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false) | (((^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))) @ (sK1 @ X1)) = $false)) )),
% 1.70/1.49 inference(sigma_clausification,[status(thm)],[f76])).
% 1.70/1.49 thf(f76,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (((esti @ n_1 @ X1) = $false) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false) | ((esti @ X2 @ X1) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.70/1.49 thf(f75,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (($true = ((^[Y0 : nat]: (esti @ Y0 @ X1)) @ X2)) | ((esti @ n_1 @ X1) = $false) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false)) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f74])).
% 1.70/1.49 thf(f74,plain,(
% 1.70/1.49 ( ! [X1 : set] : (((!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))) = $true) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false) | ((esti @ n_1 @ X1) = $false)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.70/1.49 thf(f73,plain,(
% 1.70/1.49 ( ! [X1 : set] : (((esti @ n_1 @ X1) = $false) | (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) = $true)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.70/1.49 thf(f72,plain,(
% 1.70/1.49 ( ! [X1 : set] : ((((esti @ n_1 @ X1) => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))))) = $true)) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.70/1.49 thf(f71,plain,(
% 1.70/1.49 ( ! [X1 : set] : (($true = ((^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0)))))) @ X1))) )),
% 1.70/1.49 inference(pi_clausification,[status(thm)],[f32])).
% 1.70/1.49 thf(f32,plain,(
% 1.70/1.49 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.70/1.49 inference(cnf_transformation,[status(thm)],[f18])).
% 1.70/1.49 thf(f18,plain,(
% 1.70/1.49 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.70/1.49 inference(fool_elimination,[status(thm)],[f17])).
% 1.70/1.49 thf(f17,plain,(
% 1.70/1.49 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.70/1.49 inference(rectify,[status(thm)],[f2])).
% 1.70/1.49 thf(f2,axiom,(
% 1.70/1.49 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.70/1.49 file('/export/starexec/sandbox2/tmp/tmp.OAnZzavSMB/DTF2THF_8829.p',ax5)).
% 1.70/1.49 thf(f98,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) | ((pl @ x @ (pl @ y @ X0)) != (pl @ (pl @ x @ y) @ X0))) )),
% 1.70/1.49 inference(equality_proxy_clausification,[status(thm)],[f97])).
% 1.70/1.49 thf(f97,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) | (((pl @ (pl @ x @ y) @ X0) = (pl @ x @ (pl @ y @ X0))) = $false)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.70/1.49 thf(f91,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = (((pl @ (pl @ x @ y) @ X0) = (pl @ x @ (pl @ y @ X0))) => (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) )),
% 1.70/1.49 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.70/1.49 thf(f86,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = ((^[Y0 : nat > $o]: ((Y0 @ X0) => (esti @ X0 @ (setof @ Y0)))) @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) )),
% 1.70/1.49 inference(heuristic_instantiation,[status(thm)],[f83])).
% 1.70/1.49 thf(f367,plain,(
% 1.70/1.49 ~spl0_9 | spl0_15),
% 1.70/1.49 inference(avatar_contradiction_clause,[status(thm)],[f366])).
% 1.70/1.49 thf(f366,plain,(
% 1.70/1.49 $false | (~spl0_9 | spl0_15)),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f365])).
% 1.70/1.49 thf(f365,plain,(
% 1.70/1.49 ((suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) != (suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | (~spl0_9 | spl0_15)),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f364,f259])).
% 1.70/1.49 thf(f259,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) = (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) | ~spl0_9),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f257])).
% 1.70/1.49 thf(f364,plain,(
% 1.70/1.49 ((suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) != (suc @ (pl @ (pl @ x @ y) @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))) | spl0_15),
% 1.70/1.49 inference(superposition,[status(thm)],[f347,f70])).
% 1.70/1.49 thf(f347,plain,(
% 1.70/1.49 ((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) != (suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | spl0_15),
% 1.70/1.49 inference(avatar_component_clause,[status(thm)],[f345])).
% 1.70/1.49 thf(f345,definition,(
% 1.70/1.49 spl0_15 <=> ((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) = (suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))))))),
% 1.70/1.49 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.70/1.49 thf(f354,plain,(
% 1.70/1.49 spl0_10 | ~spl0_15 | spl0_16),
% 1.70/1.49 inference(avatar_split_clause,[status(thm)],[f353,f349,f345,f261])).
% 1.70/1.49 thf(f353,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) | ((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) != (suc @ (pl @ x @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false)) )),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f352,f70])).
% 1.70/1.49 thf(f352,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) != (pl @ x @ (suc @ (pl @ y @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false)) )),
% 1.70/1.49 inference(forward_demodulation,[status(thm)],[f337,f70])).
% 1.70/1.49 thf(f337,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) != (pl @ x @ (pl @ y @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) )),
% 1.70/1.49 inference(trivial_inequality_removal,[status(thm)],[f330])).
% 1.70/1.49 thf(f330,plain,(
% 1.70/1.49 ( ! [X0 : nat] : (((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))) = $false) | ((pl @ (pl @ x @ y) @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))) != (pl @ x @ (pl @ y @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0)))))))))) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ (pl @ x @ y) @ Y0) = (pl @ x @ (pl @ y @ Y0))))))) | ($true = $false)) )),
% 1.70/1.49 inference(superposition,[status(thm)],[f79,f98])).
% 1.70/1.49 thf(f79,plain,(
% 1.70/1.49 ( ! [X2 : nat,X1 : set] : (((esti @ (suc @ (sK1 @ X1)) @ X1) = $false) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.70/1.49 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.70/1.49 % SZS output end Proof for DTF2THF_8829
% 1.70/1.49 % (9098)------------------------------
% 1.70/1.49 % (9098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.49 % (9098)Termination reason: Refutation
% 1.70/1.49
% 1.70/1.49 % (9098)Memory used [KB]: 5756
% 1.70/1.49 % (9098)Time elapsed: 0.033 s
% 1.70/1.49 % (9098)Instructions burned: 84 (million)
% 1.70/1.49 % (9098)------------------------------
% 1.70/1.49 % (9098)------------------------------
% 1.70/1.49 % (9011)Success in time 0.169 s
%------------------------------------------------------------------------------