%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM644^1 : 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 : n006.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 1.62s 1.51s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 61 unt; 0 typ; 3 def)
% Number of atoms : 457 ( 192 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 996 ( 30 ~; 54 |; 0 &; 822 @)
% ( 3 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 9 con; 0-2 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 194 ( 100 ^; 94 !; 0 ?; 194 :)
% 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,
pl: nat > nat > nat ).
thf(func_def_4,type,
set: $tType ).
thf(func_def_5,type,
esti: nat > set > $o ).
thf(func_def_6,type,
setof: ( nat > $o ) > set ).
thf(func_def_8,type,
n_1: nat ).
thf(func_def_9,type,
suc: nat > nat ).
thf(func_def_19,type,
sK1: set > nat ).
thf(func_def_20,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f311,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f158,f228,f259,f310]) ).
thf(f310,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f309]) ).
thf(f309,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f306]) ).
thf(f306,plain,
( ( ( pl @ x @ y )
!= ( pl @ x @ y ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f31,f300]) ).
thf(f300,plain,
( ! [X0: nat] :
( ( pl @ X0 @ x )
= ( pl @ x @ X0 ) )
| ~ spl0_7 ),
inference(equality_proxy_clausification,[status(thm)],[f295]) ).
thf(f295,plain,
( ! [X0: nat] :
( ( ( pl @ x @ X0 )
= ( pl @ X0 @ x ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f294]) ).
thf(f294,plain,
( ! [X0: nat] :
( ( ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) )
@ X0 )
= $true )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f281]) ).
thf(f281,plain,
( ! [X0: nat] :
( ( ( ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) )
@ X0 )
= $true )
| ( $false = $true ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f56,f218]) ).
thf(f218,plain,
( ! [X0: nat] :
( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f217]) ).
thf(f217,definition,
( spl0_7
<=> ! [X0: nat] :
( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f56,plain,
! [X2: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X2 ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X2 ) )
=> ( X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: nat] :
( ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: nat > $o,X1: nat] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: nat > $o,X1: nat] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',estie) ).
thf(f31,plain,
( ( pl @ x @ y )
!= ( pl @ y @ x ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( pl @ x @ y )
!= ( pl @ y @ x ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
( ( pl @ x @ y )
!= ( pl @ y @ x ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ( pl @ x @ y )
= ( pl @ y @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz6) ).
thf(f259,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f258]) ).
thf(f258,plain,
( $false
| ~ spl0_4 ),
inference(subsumption_resolution,[status(thm)],[f257,f47]) ).
thf(f47,plain,
! [X1: nat] :
( ( pl @ X1 @ n_1 )
= ( suc @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: nat] :
( ( ( suc @ X1 )
= ( pl @ X1 @ n_1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( suc @ Y0 )
= ( pl @ Y0 @ n_1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= ( pl @ Y0 @ n_1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ Y0 )
= ( pl @ Y0 @ n_1 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat] :
( ( suc @ X0 )
= ( pl @ X0 @ n_1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ X2 @ n_1 ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4a) ).
thf(f257,plain,
( ( ( pl @ x @ n_1 )
!= ( suc @ x ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f238,f81]) ).
thf(f81,plain,
! [X1: nat] :
( ( pl @ n_1 @ X1 )
= ( suc @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: nat] :
( ( ( pl @ n_1 @ X1 )
= ( suc @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ n_1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4c) ).
thf(f238,plain,
( ( ( pl @ x @ n_1 )
!= ( pl @ n_1 @ x ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f237]) ).
thf(f237,plain,
( ( ( pl @ x @ n_1 )
!= ( pl @ n_1 @ x ) )
| ( $false = $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f73,f155]) ).
thf(f155,plain,
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f153]) ).
thf(f153,definition,
( spl0_4
<=> ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f73,plain,
! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ( ( pl @ X0 @ x )
!= ( pl @ x @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: nat] :
( ( $false
= ( ( pl @ x @ X0 )
= ( pl @ X0 @ x ) ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: nat] :
( $true
= ( ( ( pl @ x @ X0 )
= ( pl @ X0 @ x ) )
=> ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: nat] :
( ( ^ [Y0: nat > $o] :
( ( Y0 @ X0 )
=> ( esti @ X0 @ ( setof @ Y0 ) ) )
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) )
= $true ),
inference(heuristic_instantiation,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: nat] :
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( Y0 @ X1 )
=> ( esti @ X1 @ ( setof @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,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/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',estii) ).
thf(f228,plain,
( spl0_7
| spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f227,f149,f153,f217]) ).
thf(f149,definition,
( spl0_3
<=> ( ( pl @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
@ x ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f227,plain,
( ! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false ) )
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f226,f78]) ).
thf(f78,plain,
! [X2: nat,X1: nat] :
( ( suc @ ( pl @ X1 @ X2 ) )
= ( pl @ X1 @ ( suc @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( pl @ X1 @ ( suc @ X2 ) )
= ( suc @ ( pl @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( pl @ X1 @ ( suc @ Y0 ) )
= ( suc @ ( pl @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ X1 @ ( suc @ Y0 ) )
= ( suc @ ( pl @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ Y0 @ ( suc @ Y1 ) )
= ( suc @ ( pl @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ Y0 @ ( suc @ Y1 ) )
= ( suc @ ( pl @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ Y0 @ ( suc @ Y1 ) )
= ( suc @ ( pl @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( pl @ X1 @ ( suc @ X0 ) )
= ( suc @ ( pl @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: nat,X2: nat] :
( ( suc @ ( pl @ X2 @ X3 ) )
= ( pl @ X2 @ ( suc @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4f) ).
thf(f226,plain,
( ! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false )
| ( ( pl @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) )
!= ( suc
@ ( pl @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f225,f151]) ).
thf(f151,plain,
( ( ( pl @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
@ x ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f149]) ).
thf(f225,plain,
! [X0: nat] :
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false )
| ( ( pl @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) )
!= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
@ x ) ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f207,f86]) ).
thf(f86,plain,
! [X2: nat,X1: nat] :
( ( pl @ ( suc @ X2 ) @ X1 )
= ( suc @ ( pl @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: nat,X1: nat] :
( ( ( suc @ ( pl @ X2 @ X1 ) )
= ( pl @ ( suc @ X2 ) @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( suc @ ( pl @ Y0 @ X1 ) )
= ( pl @ ( suc @ Y0 ) @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ ( pl @ Y0 @ X1 ) )
= ( pl @ ( suc @ Y0 ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ ( suc @ Y1 ) @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ ( suc @ Y1 ) @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y1 @ Y0 ) )
= ( pl @ ( suc @ Y1 ) @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( suc @ ( pl @ X0 @ X1 ) )
= ( pl @ ( suc @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X2: nat,X3: nat] :
( ( suc @ ( pl @ X2 @ X3 ) )
= ( pl @ ( suc @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4d) ).
thf(f207,plain,
! [X0: nat] :
( ( ( pl @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) )
!= ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
@ x ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f201]) ).
thf(f201,plain,
! [X0: nat] :
( ( ( pl @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) ) )
!= ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
@ x ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $true )
| ( $false = $true )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f42,f73]) ).
thf(f42,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)],[f41]) ).
thf(f41,plain,
! [X2: nat,X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( $false
= ( ( esti @ ( sK1 @ X1 ) @ X1 )
=> ( esti @ ( suc @ ( sK1 @ X1 ) ) @ X1 ) ) )
| ( ( esti @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: nat,X1: set] :
( ( ( ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: nat,X1: set] :
( ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( esti @ X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: nat,X1: set] :
( ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false )
| ( $true
= ( ^ [Y0: nat] : ( esti @ Y0 @ X1 )
@ X2 ) )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: set] :
( ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,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)],[f35]) ).
thf(f35,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)],[f34]) ).
thf(f34,plain,
! [X1: set] :
( ( ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ set
@ ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ set
@ ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) ) )
= $true ),
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/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',ax5) ).
thf(f158,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f144,f149,f153]) ).
thf(f144,plain,
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false )
| ( ( pl @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
@ x ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $false = $true )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
= $false )
| ( ( pl @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
@ x ) ) ),
inference(superposition,[status(thm)],[f60,f44]) ).
thf(f44,plain,
! [X0: set] :
( ( $true
= ( esti @ ( sK1 @ X0 ) @ X0 ) )
| ( $false
= ( esti @ n_1 @ X0 ) ) ),
inference(condensation,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: nat,X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( ( esti @ ( sK1 @ X1 ) @ X1 )
= $true )
| ( ( esti @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f60,plain,
! [X0: nat] :
( ( $false
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
| ( ( pl @ X0 @ x )
= ( pl @ x @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: nat] :
( ( $false
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) ) )
| ( ( ( pl @ x @ X0 )
= ( pl @ X0 @ x ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) ) )
=> ( ( pl @ x @ X0 )
= ( pl @ X0 @ x ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: nat] :
( ( ^ [Y0: nat > $o] :
( ( esti @ X0 @ ( setof @ Y0 ) )
=> ( Y0 @ X0 ) )
@ ^ [Y0: nat] :
( ( pl @ x @ Y0 )
= ( pl @ Y0 @ x ) ) )
= $true ),
inference(heuristic_instantiation,[status(thm)],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM644^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n006.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 11:08:45 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : NUM644^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.39 % Domain : Number Theory
% 0.17/0.39 % Problem : Landau theorem 6
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English : pl x y = pl y x
% 0.17/0.39
% 0.17/0.39 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.17/0.39 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.17/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : satz6 [Lan30]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % : Without extensionality : Theorem
% 0.17/0.39 % 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
% 0.17/0.39 % Syntax : Number of formulae : 17 ( 7 unt; 9 typ; 0 def)
% 0.17/0.39 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 4 ( 1 avg)
% 0.17/0.39 % Number of connectives : 44 ( 0 ~; 0 |; 0 &; 39 @)
% 0.17/0.39 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 9 ( 4 avg)
% 0.17/0.39 % Number of types : 3 ( 2 usr)
% 0.17/0.39 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments :
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(nat_type,type,
% 0.17/0.39 nat: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(x,type,
% 0.17/0.39 x: nat ).
% 0.17/0.39
% 0.17/0.39 thf(y,type,
% 0.17/0.39 y: nat ).
% 0.17/0.39
% 0.17/0.39 thf(pl,type,
% 0.17/0.39 pl: nat > nat > nat ).
% 0.17/0.39
% 0.17/0.39 thf(set_type,type,
% 0.17/0.39 set: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(esti,type,
% 0.17/0.39 esti: nat > set > $o ).
% 0.17/0.39
% 0.17/0.39 thf(setof,type,
% 0.17/0.39 setof: ( nat > $o ) > set ).
% 0.17/0.39
% 0.17/0.39 thf(estie,axiom,
% 0.17/0.39 ! [Xp: nat > $o,Xs: nat] :
% 0.17/0.39 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.17/0.39 => ( Xp @ Xs ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(n_1,type,
% 0.17/0.39 n_1: nat ).
% 0.17/0.39
% 0.17/0.39 thf(suc,type,
% 0.17/0.39 suc: nat > nat ).
% 0.17/0.39
% 0.17/0.39 thf(ax5,axiom,
% 0.17/0.39 ! [Xs: set] :
% 0.17/0.39 ( ( esti @ n_1 @ Xs )
% 0.17/0.39 => ( ! [Xx: nat] :
% 0.17/0.39 ( ( esti @ Xx @ Xs )
% 0.17/0.39 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.17/0.39 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(estii,axiom,
% 0.17/0.39 ! [Xp: nat > $o,Xs: nat] :
% 0.17/0.39 ( ( Xp @ Xs )
% 0.17/0.39 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(satz4a,axiom,
% 0.17/0.39 ! [Xx: nat] :
% 0.17/0.39 ( ( pl @ Xx @ n_1 )
% 0.17/0.39 = ( suc @ Xx ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(satz4c,axiom,
% 0.17/0.39 ! [Xx: nat] :
% 0.17/0.39 ( ( pl @ n_1 @ Xx )
% 0.17/0.39 = ( suc @ Xx ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(satz4f,axiom,
% 0.17/0.39 ! [Xx: nat,Xy: nat] :
% 0.17/0.39 ( ( suc @ ( pl @ Xx @ Xy ) )
% 0.17/0.39 = ( pl @ Xx @ ( suc @ Xy ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(satz4d,axiom,
% 0.17/0.39 ! [Xx: nat,Xy: nat] :
% 0.17/0.39 ( ( pl @ ( suc @ Xx ) @ Xy )
% 0.17/0.39 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(satz6,conjecture,
% 0.17/0.39 ( ( pl @ x @ y )
% 0.17/0.39 = ( pl @ y @ x ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.60/1.31 ---- Embedded in THF ---
% 1.60/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.31 %%% Generated on Tue Feb 24 11:08:46 EST 2026
% 1.60/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.31 %%% Logic specification used:
% 1.60/1.31 %%% thf(spec, logic, $$dhol).
% 1.60/1.31
% 1.60/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2DTF22208.p
% See solution above
% 1.60/1.31 ------------------------
% 1.60/1.32 ---- Cleaned THF ---
% 1.60/1.32 thf(nat_type,type,
% 1.60/1.32 nat: $tType ).
% 1.60/1.32
% 1.60/1.32 thf(x,type,
% 1.60/1.32 x: nat ).
% 1.60/1.32
% 1.60/1.32 thf(y,type,
% 1.60/1.32 y: nat ).
% 1.60/1.32
% 1.60/1.32 thf(pl,type,
% 1.60/1.32 pl: nat > nat > nat ).
% 1.60/1.32
% 1.60/1.32 thf(set_type,type,
% 1.60/1.32 set: $tType ).
% 1.60/1.32
% 1.60/1.32 thf(esti,type,
% 1.60/1.32 esti: nat > set > $o ).
% 1.60/1.32
% 1.60/1.32 thf(setof,type,
% 1.60/1.32 setof: ( nat > $o ) > set ).
% 1.60/1.32
% 1.60/1.32 thf(estie,axiom,
% 1.60/1.32 ! [Xp: nat > $o,Xs: nat] :
% 1.60/1.32 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.60/1.32 => ( Xp @ Xs ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(n_1,type,
% 1.60/1.32 n_1: nat ).
% 1.60/1.32
% 1.60/1.32 thf(suc,type,
% 1.60/1.32 suc: nat > nat ).
% 1.60/1.32
% 1.60/1.32 thf(ax5,axiom,
% 1.60/1.32 ! [Xs: set] :
% 1.60/1.32 ( ( esti @ n_1 @ Xs )
% 1.60/1.32 => ( ! [Xx: nat] :
% 1.60/1.32 ( ( esti @ Xx @ Xs )
% 1.60/1.32 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.60/1.32 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(estii,axiom,
% 1.60/1.32 ! [Xp: nat > $o,Xs: nat] :
% 1.60/1.32 ( ( Xp @ Xs )
% 1.60/1.32 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(satz4a,axiom,
% 1.60/1.32 ! [Xx: nat] :
% 1.60/1.32 ( ( pl @ Xx @ n_1 )
% 1.60/1.32 = ( suc @ Xx ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(satz4c,axiom,
% 1.60/1.32 ! [Xx: nat] :
% 1.60/1.32 ( ( pl @ n_1 @ Xx )
% 1.60/1.32 = ( suc @ Xx ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(satz4f,axiom,
% 1.60/1.32 ! [Xx: nat,Xy: nat] :
% 1.60/1.32 ( ( suc @ ( pl @ Xx @ Xy ) )
% 1.60/1.32 = ( pl @ Xx @ ( suc @ Xy ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(satz4d,axiom,
% 1.60/1.32 ! [Xx: nat,Xy: nat] :
% 1.60/1.32 ( ( pl @ ( suc @ Xx ) @ Xy )
% 1.60/1.32 = ( suc @ ( pl @ Xx @ Xy ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(satz6,conjecture,
% 1.60/1.32 ( ( pl @ x @ y )
% 1.60/1.32 = ( pl @ y @ x ) ) ).
% 1.60/1.32 ------------------------
% 1.60/1.34 % (22310)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_22208 for (2999ds/275Mi)
% 1.60/1.34 % (22305)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/183Mi)
% 1.60/1.34 % (22307)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_22208 for (2999ds/27Mi)
% 1.60/1.34 % (22308)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/2Mi)
% 1.60/1.34 % (22306)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_22208 for (2999ds/4Mi)
% 1.60/1.34 % (22311)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/18Mi)
% 1.60/1.34 % (22309)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_22208 for (2999ds/2Mi)
% 1.60/1.34 % (22308)Instruction limit reached!
% 1.60/1.34 % (22308)------------------------------
% 1.60/1.34 % (22308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22308)Termination reason: Unknown
% 1.60/1.34 % (22308)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (22309)Instruction limit reached!
% 1.60/1.34 % (22309)------------------------------
% 1.60/1.34 % (22309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22309)Termination reason: Unknown
% 1.60/1.34 % (22309)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (22309)Memory used [KB]: 1023
% 1.60/1.34 % (22309)Time elapsed: 0.003 s
% 1.60/1.34 % (22309)Instructions burned: 3 (million)
% 1.60/1.34 % (22309)------------------------------
% 1.60/1.34 % (22309)------------------------------
% 1.60/1.34 % (22308)Memory used [KB]: 5500
% 1.60/1.34 % (22308)Time elapsed: 0.003 s
% 1.60/1.34 % (22308)Instructions burned: 2 (million)
% 1.60/1.34 % (22308)------------------------------
% 1.60/1.34 % (22308)------------------------------
% 1.60/1.34 % (22310)Refutation not found, incomplete strategy
% 1.60/1.34 % (22310)------------------------------
% 1.60/1.34 % (22310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22310)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.34
% 1.60/1.34
% 1.60/1.34 % (22310)Memory used [KB]: 5500
% 1.60/1.34 % (22310)Time elapsed: 0.003 s
% 1.60/1.34 % (22310)Instructions burned: 2 (million)
% 1.60/1.34 % (22310)------------------------------
% 1.60/1.34 % (22310)------------------------------
% 1.60/1.34 % (22306)Instruction limit reached!
% 1.60/1.34 % (22306)------------------------------
% 1.60/1.34 % (22306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22306)Termination reason: Unknown
% 1.60/1.34 % (22306)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (22306)Memory used [KB]: 5500
% 1.60/1.34 % (22306)Time elapsed: 0.004 s
% 1.60/1.34 % (22306)Instructions burned: 4 (million)
% 1.60/1.34 % (22306)------------------------------
% 1.60/1.34 % (22306)------------------------------
% 1.60/1.34 % (22307)Refutation not found, incomplete strategy
% 1.60/1.34 % (22307)------------------------------
% 1.60/1.34 % (22307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22307)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.34
% 1.60/1.34
% 1.60/1.34 % (22307)Memory used [KB]: 5500
% 1.60/1.34 % (22307)Time elapsed: 0.005 s
% 1.60/1.34 % (22307)Instructions burned: 5 (million)
% 1.60/1.34 % (22307)------------------------------
% 1.60/1.34 % (22307)------------------------------
% 1.60/1.35 % (22311)Instruction limit reached!
% 1.60/1.35 % (22311)------------------------------
% 1.60/1.35 % (22311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (22311)Termination reason: Unknown
% 1.60/1.35 % (22311)Termination phase: Saturation
% 1.60/1.35
% 1.60/1.35 % (22311)Memory used [KB]: 5628
% 1.60/1.35 % (22311)Time elapsed: 0.012 s
% 1.60/1.35 % (22311)Instructions burned: 19 (million)
% 1.60/1.35 % (22311)------------------------------
% 1.60/1.35 % (22311)------------------------------
% 1.60/1.36 % (22312)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/3Mi)
% 1.60/1.36 % (22313)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_22208 for (2999ds/37Mi)
% 1.60/1.36 % (22314)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_22208 for (2999ds/15Mi)
% 1.60/1.36 % (22315)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_22208 for (2999ds/3Mi)
% 1.60/1.36 % (22312)Instruction limit reached!
% 1.60/1.36 % (22312)------------------------------
% 1.60/1.36 % (22312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (22312)Termination reason: Unknown
% 1.60/1.36 % (22312)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (22312)Memory used [KB]: 5500
% 1.60/1.36 % (22312)Time elapsed: 0.003 s
% 1.60/1.36 % (22312)Instructions burned: 3 (million)
% 1.60/1.36 % (22312)------------------------------
% 1.60/1.36 % (22312)------------------------------
% 1.60/1.36 % (22314)Refutation not found, incomplete strategy
% 1.60/1.36 % (22314)------------------------------
% 1.60/1.36 % (22314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (22314)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.36
% 1.60/1.36
% 1.60/1.36 % (22314)Memory used [KB]: 5500
% 1.60/1.36 % (22314)Time elapsed: 0.003 s
% 1.60/1.36 % (22314)Instructions burned: 3 (million)
% 1.60/1.36 % (22314)------------------------------
% 1.60/1.36 % (22314)------------------------------
% 1.60/1.36 % (22315)Instruction limit reached!
% 1.60/1.36 % (22315)------------------------------
% 1.60/1.36 % (22315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.36 % (22315)Termination reason: Unknown
% 1.60/1.36 % (22315)Termination phase: Saturation
% 1.60/1.36
% 1.60/1.36 % (22315)Memory used [KB]: 5500
% 1.60/1.36 % (22315)Time elapsed: 0.003 s
% 1.60/1.36 % (22315)Instructions burned: 3 (million)
% 1.60/1.36 % (22315)------------------------------
% 1.60/1.36 % (22315)------------------------------
% 1.60/1.36 % (22316)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_22208 for (2999ds/1041Mi)
% 1.60/1.37 % (22317)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/7Mi)
% 1.60/1.37 % (22317)Instruction limit reached!
% 1.60/1.37 % (22317)------------------------------
% 1.60/1.37 % (22317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.37 % (22317)Termination reason: Unknown
% 1.60/1.37 % (22317)Termination phase: Saturation
% 1.60/1.37
% 1.60/1.37 % (22317)Memory used [KB]: 1023
% 1.60/1.37 % (22317)Time elapsed: 0.006 s
% 1.60/1.37 % (22317)Instructions burned: 7 (million)
% 1.60/1.37 % (22317)------------------------------
% 1.60/1.37 % (22317)------------------------------
% 1.60/1.38 % (22318)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/16Mi)
% 1.60/1.38 % (22319)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_22208 for (2999ds/3Mi)
% 1.60/1.38 % (22320)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_22208 for (2999ds/3Mi)
% 1.60/1.38 % (22313)Instruction limit reached!
% 1.60/1.38 % (22313)------------------------------
% 1.60/1.38 % (22313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (22313)Termination reason: Unknown
% 1.60/1.38 % (22313)Termination phase: Saturation
% 1.60/1.38
% 1.60/1.38 % (22313)Memory used [KB]: 5884
% 1.60/1.38 % (22313)Time elapsed: 0.020 s
% 1.60/1.38 % (22313)Instructions burned: 37 (million)
% 1.60/1.38 % (22313)------------------------------
% 1.60/1.38 % (22313)------------------------------
% 1.60/1.38 % (22319)Instruction limit reached!
% 1.60/1.38 % (22319)------------------------------
% 1.60/1.38 % (22319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (22319)Termination reason: Unknown
% 1.60/1.38 % (22319)Termination phase: Saturation
% 1.60/1.38
% 1.60/1.38 % (22319)Memory used [KB]: 5500
% 1.60/1.38 % (22319)Time elapsed: 0.003 s
% 1.60/1.38 % (22319)Instructions burned: 3 (million)
% 1.60/1.38 % (22319)------------------------------
% 1.60/1.38 % (22319)------------------------------
% 1.60/1.38 % (22320)Instruction limit reached!
% 1.60/1.38 % (22320)------------------------------
% 1.60/1.38 % (22320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (22320)Termination reason: Unknown
% 1.60/1.38 % (22320)Termination phase: Saturation
% 1.60/1.38
% 1.60/1.38 % (22320)Memory used [KB]: 1023
% 1.60/1.38 % (22320)Time elapsed: 0.003 s
% 1.60/1.38 % (22320)Instructions burned: 4 (million)
% 1.60/1.38 % (22320)------------------------------
% 1.60/1.38 % (22320)------------------------------
% 1.60/1.38 % (22318)Instruction limit reached!
% 1.60/1.38 % (22318)------------------------------
% 1.60/1.38 % (22318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.38 % (22318)Termination reason: Unknown
% 1.60/1.38 % (22318)Termination phase: Saturation
% 1.60/1.38
% 1.60/1.38 % (22318)Memory used [KB]: 5628
% 1.60/1.38 % (22318)Time elapsed: 0.011 s
% 1.60/1.38 % (22318)Instructions burned: 16 (million)
% 1.60/1.38 % (22318)------------------------------
% 1.60/1.38 % (22318)------------------------------
% 1.60/1.39 % (22321)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/7Mi)
% 1.60/1.39 % (22321)Refutation not found, incomplete strategy
% 1.60/1.39 % (22321)------------------------------
% 1.60/1.39 % (22321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.39 % (22321)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.39
% 1.60/1.39
% 1.60/1.39 % (22321)Memory used [KB]: 5500
% 1.60/1.39 % (22321)Time elapsed: 0.004 s
% 1.60/1.39 % (22321)Instructions burned: 4 (million)
% 1.60/1.39 % (22321)------------------------------
% 1.60/1.39 % (22321)------------------------------
% 1.60/1.39 % (22322)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/3Mi)
% 1.60/1.39 % (22323)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/4Mi)
% 1.60/1.39 % (22324)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/18Mi)
% 1.60/1.39 % (22322)Instruction limit reached!
% 1.60/1.39 % (22322)------------------------------
% 1.60/1.39 % (22322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.39 % (22322)Termination reason: Unknown
% 1.60/1.39 % (22322)Termination phase: Saturation
% 1.60/1.39
% 1.60/1.39 % (22322)Memory used [KB]: 1023
% 1.60/1.39 % (22322)Time elapsed: 0.003 s
% 1.60/1.39 % (22322)Instructions burned: 3 (million)
% 1.60/1.39 % (22322)------------------------------
% 1.60/1.39 % (22322)------------------------------
% 1.60/1.40 % (22323)Instruction limit reached!
% 1.60/1.40 % (22323)------------------------------
% 1.60/1.40 % (22323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.40 % (22323)Termination reason: Unknown
% 1.60/1.40 % (22323)Termination phase: Saturation
% 1.60/1.40
% 1.62/1.40 % (22323)Memory used [KB]: 5500
% 1.62/1.40 % (22323)Time elapsed: 0.004 s
% 1.62/1.40 % (22323)Instructions burned: 5 (million)
% 1.62/1.40 % (22323)------------------------------
% 1.62/1.40 % (22323)------------------------------
% 1.62/1.40 % (22324)Refutation not found, incomplete strategy
% 1.62/1.40 % (22324)------------------------------
% 1.62/1.40 % (22324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (22324)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.40
% 1.62/1.40
% 1.62/1.40 % (22324)Memory used [KB]: 5500
% 1.62/1.40 % (22324)Time elapsed: 0.007 s
% 1.62/1.40 % (22324)Instructions burned: 10 (million)
% 1.62/1.40 % (22324)------------------------------
% 1.62/1.40 % (22324)------------------------------
% 1.62/1.40 % (22325)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/710Mi)
% 1.62/1.41 % (22326)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/6Mi)
% 1.62/1.41 % (22327)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_22208 for (2999ds/902Mi)
% 1.62/1.41 % (22326)Instruction limit reached!
% 1.62/1.41 % (22326)------------------------------
% 1.62/1.41 % (22326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (22326)Termination reason: Unknown
% 1.62/1.41 % (22326)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (22326)Memory used [KB]: 5500
% 1.62/1.41 % (22326)Time elapsed: 0.005 s
% 1.62/1.41 % (22326)Instructions burned: 7 (million)
% 1.62/1.41 % (22326)------------------------------
% 1.62/1.41 % (22326)------------------------------
% 1.62/1.41 % (22327)Refutation not found, incomplete strategy
% 1.62/1.41 % (22327)------------------------------
% 1.62/1.41 % (22327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (22327)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.41
% 1.62/1.41
% 1.62/1.41 % (22327)Memory used [KB]: 5500
% 1.62/1.41 % (22327)Time elapsed: 0.002 s
% 1.62/1.41 % (22327)Instructions burned: 2 (million)
% 1.62/1.41 % (22327)------------------------------
% 1.62/1.41 % (22327)------------------------------
% 1.62/1.41 % (22328)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_22208 for (2999ds/21Mi)
% 1.62/1.42 % (22329)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/5Mi)
% 1.62/1.42 % (22329)Instruction limit reached!
% 1.62/1.42 % (22329)------------------------------
% 1.62/1.42 % (22329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.42 % (22329)Termination reason: Unknown
% 1.62/1.42 % (22329)Termination phase: Saturation
% 1.62/1.42
% 1.62/1.42 % (22329)Memory used [KB]: 5500
% 1.62/1.42 % (22329)Time elapsed: 0.004 s
% 1.62/1.42 % (22329)Instructions burned: 5 (million)
% 1.62/1.42 % (22329)------------------------------
% 1.62/1.42 % (22329)------------------------------
% 1.62/1.42 % (22328)Instruction limit reached!
% 1.62/1.42 % (22328)------------------------------
% 1.62/1.42 % (22328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.42 % (22328)Termination reason: Unknown
% 1.62/1.42 % (22328)Termination phase: Saturation
% 1.62/1.42
% 1.62/1.42 % (22328)Memory used [KB]: 5628
% 1.62/1.42 % (22328)Time elapsed: 0.013 s
% 1.62/1.42 % (22328)Instructions burned: 22 (million)
% 1.62/1.42 % (22328)------------------------------
% 1.62/1.42 % (22328)------------------------------
% 1.62/1.43 % (22305)Instruction limit reached!
% 1.62/1.43 % (22305)------------------------------
% 1.62/1.43 % (22305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (22305)Termination reason: Unknown
% 1.62/1.43 % (22305)Termination phase: Saturation
% 1.62/1.43
% 1.62/1.43 % (22305)Memory used [KB]: 6524
% 1.62/1.43 % (22305)Time elapsed: 0.087 s
% 1.62/1.43 % (22305)Instructions burned: 183 (million)
% 1.62/1.43 % (22305)------------------------------
% 1.62/1.43 % (22305)------------------------------
% 1.62/1.43 % (22330)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_22208 for (2999ds/6Mi)
% 1.62/1.43 % (22331)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/377Mi)
% 1.62/1.43 % (22330)Refutation not found, incomplete strategy
% 1.62/1.43 % (22330)------------------------------
% 1.62/1.43 % (22330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (22330)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.43
% 1.62/1.43
% 1.62/1.43 % (22330)Memory used [KB]: 5500
% 1.62/1.43 % (22330)Time elapsed: 0.004 s
% 1.62/1.43 % (22330)Instructions burned: 5 (million)
% 1.62/1.43 % (22330)------------------------------
% 1.62/1.43 % (22330)------------------------------
% 1.62/1.44 % (22332)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_22208 for (2999ds/779Mi)
% 1.62/1.44 % (22333)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_22208 for (2999ds/19Mi)
% 1.62/1.44 % (22334)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/879Mi)
% 1.62/1.44 % (22333)Refutation not found, incomplete strategy
% 1.62/1.44 % (22333)------------------------------
% 1.62/1.44 % (22333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (22333)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.44
% 1.62/1.44
% 1.62/1.44 % (22333)Memory used [KB]: 5500
% 1.62/1.44 % (22333)Time elapsed: 0.003 s
% 1.62/1.44 % (22333)Instructions burned: 3 (million)
% 1.62/1.44 % (22333)------------------------------
% 1.62/1.44 % (22333)------------------------------
% 1.62/1.45 % (22335)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22208 for (2999ds/17Mi)
% 1.62/1.46 % (22335)Instruction limit reached!
% 1.62/1.46 % (22335)------------------------------
% 1.62/1.46 % (22335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (22335)Termination reason: Unknown
% 1.62/1.46 % (22335)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (22335)Memory used [KB]: 5628
% 1.62/1.46 % (22335)Time elapsed: 0.011 s
% 1.62/1.46 % (22335)Instructions burned: 19 (million)
% 1.62/1.46 % (22335)------------------------------
% 1.62/1.46 % (22335)------------------------------
% 1.62/1.46 % (22336)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22208 for (2998ds/3Mi)
% 1.62/1.46 % (22336)Instruction limit reached!
% 1.62/1.46 % (22336)------------------------------
% 1.62/1.46 % (22336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (22336)Termination reason: Unknown
% 1.62/1.46 % (22336)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (22336)Memory used [KB]: 1023
% 1.62/1.46 % (22336)Time elapsed: 0.003 s
% 1.62/1.46 % (22336)Instructions burned: 3 (million)
% 1.62/1.46 % (22336)------------------------------
% 1.62/1.46 % (22336)------------------------------
% 1.62/1.46 % (22334)Refutation not found, incomplete strategy
% 1.62/1.46 % (22334)------------------------------
% 1.62/1.46 % (22334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (22334)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.46
% 1.62/1.46
% 1.62/1.46 % (22334)Memory used [KB]: 5628
% 1.62/1.46 % (22334)Time elapsed: 0.023 s
% 1.62/1.46 % (22334)Instructions burned: 41 (million)
% 1.62/1.46 % (22334)------------------------------
% 1.62/1.46 % (22334)------------------------------
% 1.62/1.47 % (22337)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22208 for (2998ds/30Mi)
% 1.62/1.48 % (22338)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22208 for (2998ds/127Mi)
% 1.62/1.48 % (22339)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22208 for (2998ds/100Mi)
% 1.62/1.49 % (22337)Instruction limit reached!
% 1.62/1.49 % (22337)------------------------------
% 1.62/1.49 % (22337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.49 % (22337)Termination reason: Unknown
% 1.62/1.49 % (22337)Termination phase: Saturation
% 1.62/1.49
% 1.62/1.49 % (22337)Memory used [KB]: 5628
% 1.62/1.49 % (22337)Time elapsed: 0.018 s
% 1.62/1.49 % (22337)Instructions burned: 31 (million)
% 1.62/1.49 % (22337)------------------------------
% 1.62/1.49 % (22337)------------------------------
% 1.62/1.49 % (22316)Refutation not found, incomplete strategy
% 1.62/1.49 % (22316)------------------------------
% 1.62/1.49 % (22316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.49 % (22316)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.49
% 1.62/1.49
% 1.62/1.49 % (22316)Memory used [KB]: 6012
% 1.62/1.49 % (22316)Time elapsed: 0.130 s
% 1.62/1.49 % (22316)Instructions burned: 262 (million)
% 1.62/1.49 % (22316)------------------------------
% 1.62/1.49 % (22316)------------------------------
% 1.62/1.50 % (22339)First to succeed.
% 1.62/1.51 % (22340)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_22208 for (2998ds/3Mi)
% 1.62/1.51 % (22341)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_22208 for (2998ds/20Mi)
% 1.62/1.51 % (22339)Refutation found. Thanks to Tanya!
% 1.62/1.51 % SZS status Theorem for DTF2THF_22208
% 1.62/1.51 % SZS output start Proof for DTF2THF_22208
% 1.62/1.51 thf(type_def_5, type, nat: $tType).
% 1.62/1.51 thf(type_def_7, type, set: $tType).
% 1.62/1.51 thf(func_def_0, type, nat: $tType).
% 1.62/1.51 thf(func_def_1, type, x: nat).
% 1.62/1.51 thf(func_def_2, type, y: nat).
% 1.62/1.51 thf(func_def_3, type, pl: nat > nat > nat).
% 1.62/1.51 thf(func_def_4, type, set: $tType).
% 1.62/1.51 thf(func_def_5, type, esti: nat > set > $o).
% 1.62/1.51 thf(func_def_6, type, setof: (nat > $o) > set).
% 1.62/1.51 thf(func_def_8, type, n_1: nat).
% 1.62/1.51 thf(func_def_9, type, suc: nat > nat).
% 1.62/1.51 thf(func_def_19, type, sK1: set > nat).
% 1.62/1.51 thf(func_def_20, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.51 thf(f311,plain,(
% 1.62/1.51 $false),
% 1.62/1.51 inference(avatar_sat_refutation,[status(thm)],[f158,f228,f259,f310])).
% 1.62/1.51 thf(f310,plain,(
% 1.62/1.51 ~spl0_7),
% 1.62/1.51 inference(avatar_contradiction_clause,[status(thm)],[f309])).
% 1.62/1.51 thf(f309,plain,(
% 1.62/1.51 $false | ~spl0_7),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.62/1.51 thf(f306,plain,(
% 1.62/1.51 ((pl @ x @ y) != (pl @ x @ y)) | ~spl0_7),
% 1.62/1.51 inference(superposition,[status(thm)],[f31,f300])).
% 1.62/1.51 thf(f300,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((pl @ X0 @ x) = (pl @ x @ X0))) ) | ~spl0_7),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f295])).
% 1.62/1.51 thf(f295,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((pl @ x @ X0) = (pl @ X0 @ x)) = $true)) ) | ~spl0_7),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f294])).
% 1.62/1.51 thf(f294,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))) @ X0) = $true)) ) | ~spl0_7),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f281])).
% 1.62/1.51 thf(f281,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))) @ X0) = $true) | ($false = $true)) ) | ~spl0_7),
% 1.62/1.51 inference(superposition,[status(thm)],[f56,f218])).
% 1.62/1.51 thf(f218,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true)) ) | ~spl0_7),
% 1.62/1.51 inference(avatar_component_clause,[status(thm)],[f217])).
% 1.62/1.51 thf(f217,definition,(
% 1.62/1.51 spl0_7 <=> ! [X0 : nat] : ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true)),
% 1.62/1.51 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.62/1.51 thf(f56,plain,(
% 1.62/1.51 ( ! [X2 : nat > $o,X1 : nat] : (((esti @ X1 @ (setof @ X2)) = $false) | ((X2 @ X1) = $true)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.62/1.51 thf(f55,plain,(
% 1.62/1.51 ( ! [X2 : nat > $o,X1 : nat] : ((((esti @ X1 @ (setof @ X2)) => (X2 @ X1)) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.62/1.51 thf(f52,plain,(
% 1.62/1.51 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1))) @ X2))) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f49])).
% 1.62/1.51 thf(f49,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (((!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1)))) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.62/1.51 thf(f48,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0))))) @ X1))) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f30])).
% 1.62/1.51 thf(f30,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.51 thf(f12,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.51 thf(f11,plain,(
% 1.62/1.51 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.62/1.51 inference(rectify,[status(thm)],[f1])).
% 1.62/1.51 thf(f1,axiom,(
% 1.62/1.51 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',estie)).
% 1.62/1.51 thf(f31,plain,(
% 1.62/1.51 ((pl @ x @ y) != (pl @ y @ x))),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f25])).
% 1.62/1.51 thf(f25,plain,(
% 1.62/1.51 ((pl @ x @ y) != (pl @ y @ x))),
% 1.62/1.51 inference(flattening,[status(thm)],[f9])).
% 1.62/1.51 thf(f9,negated_conjecture,(
% 1.62/1.51 ~((pl @ x @ y) = (pl @ y @ x))),
% 1.62/1.51 inference(negated_conjecture,[status(cth)],[f8])).
% 1.62/1.51 thf(f8,conjecture,(
% 1.62/1.51 ((pl @ x @ y) = (pl @ y @ x))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz6)).
% 1.62/1.51 thf(f259,plain,(
% 1.62/1.51 ~spl0_4),
% 1.62/1.51 inference(avatar_contradiction_clause,[status(thm)],[f258])).
% 1.62/1.51 thf(f258,plain,(
% 1.62/1.51 $false | ~spl0_4),
% 1.62/1.51 inference(subsumption_resolution,[status(thm)],[f257,f47])).
% 1.62/1.51 thf(f47,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (((pl @ X1 @ n_1) = (suc @ X1))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.62/1.51 thf(f46,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((suc @ X1) = (pl @ X1 @ n_1)) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.62/1.51 thf(f45,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((suc @ Y0) = (pl @ Y0 @ n_1))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f29])).
% 1.62/1.51 thf(f29,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: ((suc @ Y0) = (pl @ Y0 @ n_1)))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.51 thf(f14,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: ((suc @ Y0) = (pl @ Y0 @ n_1)))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f13])).
% 1.62/1.51 thf(f13,plain,(
% 1.62/1.51 ! [X0 : nat] : ((suc @ X0) = (pl @ X0 @ n_1))),
% 1.62/1.51 inference(rectify,[status(thm)],[f4])).
% 1.62/1.51 thf(f4,axiom,(
% 1.62/1.51 ! [X2 : nat] : ((suc @ X2) = (pl @ X2 @ n_1))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4a)).
% 1.62/1.51 thf(f257,plain,(
% 1.62/1.51 ((pl @ x @ n_1) != (suc @ x)) | ~spl0_4),
% 1.62/1.51 inference(forward_demodulation,[status(thm)],[f238,f81])).
% 1.62/1.51 thf(f81,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (((pl @ n_1 @ X1) = (suc @ X1))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f80])).
% 1.62/1.51 thf(f80,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((pl @ n_1 @ X1) = (suc @ X1)) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.62/1.51 thf(f79,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f27])).
% 1.62/1.51 thf(f27,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0)))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f16])).
% 1.62/1.51 thf(f16,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0)))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f15])).
% 1.62/1.51 thf(f15,plain,(
% 1.62/1.51 ! [X0 : nat] : ((pl @ n_1 @ X0) = (suc @ X0))),
% 1.62/1.51 inference(rectify,[status(thm)],[f5])).
% 1.62/1.51 thf(f5,axiom,(
% 1.62/1.51 ! [X2 : nat] : ((suc @ X2) = (pl @ n_1 @ X2))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4c)).
% 1.62/1.51 thf(f238,plain,(
% 1.62/1.51 ((pl @ x @ n_1) != (pl @ n_1 @ x)) | ~spl0_4),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f237])).
% 1.62/1.51 thf(f237,plain,(
% 1.62/1.51 ((pl @ x @ n_1) != (pl @ n_1 @ x)) | ($false = $true) | ~spl0_4),
% 1.62/1.51 inference(superposition,[status(thm)],[f73,f155])).
% 1.62/1.51 thf(f155,plain,(
% 1.62/1.51 ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false) | ~spl0_4),
% 1.62/1.51 inference(avatar_component_clause,[status(thm)],[f153])).
% 1.62/1.51 thf(f153,definition,(
% 1.62/1.51 spl0_4 <=> ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false)),
% 1.62/1.51 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.62/1.51 thf(f73,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true) | ((pl @ X0 @ x) != (pl @ x @ X0))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f72])).
% 1.62/1.51 thf(f72,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (($false = ((pl @ x @ X0) = (pl @ X0 @ x))) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.62/1.51 thf(f66,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (($true = (((pl @ x @ X0) = (pl @ X0 @ x)) => (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.62/1.51 thf(f63,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((^[Y0 : nat > $o]: ((Y0 @ X0) => (esti @ X0 @ (setof @ Y0)))) @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))) = $true)) )),
% 1.62/1.51 inference(heuristic_instantiation,[status(thm)],[f62])).
% 1.62/1.51 thf(f62,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((Y0 @ X1) => (esti @ X1 @ (setof @ Y0))))))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.62/1.51 thf(f61,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1)))))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f32])).
% 1.62/1.51 thf(f32,plain,(
% 1.62/1.51 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))))),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f24])).
% 1.62/1.51 thf(f24,plain,(
% 1.62/1.51 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))))),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f23])).
% 1.62/1.51 thf(f23,plain,(
% 1.62/1.51 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f3])).
% 1.62/1.51 thf(f3,axiom,(
% 1.62/1.51 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',estii)).
% 1.62/1.51 thf(f228,plain,(
% 1.62/1.51 spl0_7 | spl0_4 | ~spl0_3),
% 1.62/1.51 inference(avatar_split_clause,[status(thm)],[f227,f149,f153,f217])).
% 1.62/1.51 thf(f149,definition,(
% 1.62/1.51 spl0_3 <=> ((pl @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) @ x))),
% 1.62/1.51 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.62/1.51 thf(f227,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false)) ) | ~spl0_3),
% 1.62/1.51 inference(subsumption_resolution,[status(thm)],[f226,f78])).
% 1.62/1.51 thf(f78,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : (((suc @ (pl @ X1 @ X2)) = (pl @ X1 @ (suc @ X2)))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f77])).
% 1.62/1.51 thf(f77,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : (($true = ((pl @ X1 @ (suc @ X2)) = (suc @ (pl @ X1 @ X2))))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.62/1.51 thf(f76,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((pl @ X1 @ (suc @ Y0)) = (suc @ (pl @ X1 @ Y0)))) @ X2) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f75])).
% 1.62/1.51 thf(f75,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((pl @ X1 @ (suc @ Y0)) = (suc @ (pl @ X1 @ Y0))))) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.62/1.51 thf(f74,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ Y0 @ (suc @ Y1)) = (suc @ (pl @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f28])).
% 1.62/1.51 thf(f28,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ Y0 @ (suc @ Y1)) = (suc @ (pl @ Y0 @ Y1))))))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f20])).
% 1.62/1.51 thf(f20,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ Y0 @ (suc @ Y1)) = (suc @ (pl @ Y0 @ Y1))))))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f19])).
% 1.62/1.51 thf(f19,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat] : ((pl @ X1 @ (suc @ X0)) = (suc @ (pl @ X1 @ X0)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f6])).
% 1.62/1.51 thf(f6,axiom,(
% 1.62/1.51 ! [X3 : nat,X2 : nat] : ((suc @ (pl @ X2 @ X3)) = (pl @ X2 @ (suc @ X3)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4f)).
% 1.62/1.51 thf(f226,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false) | ((pl @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))))) != (suc @ (pl @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))))))) ) | ~spl0_3),
% 1.62/1.51 inference(forward_demodulation,[status(thm)],[f225,f151])).
% 1.62/1.51 thf(f151,plain,(
% 1.62/1.51 ((pl @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) @ x)) | ~spl0_3),
% 1.62/1.51 inference(avatar_component_clause,[status(thm)],[f149])).
% 1.62/1.51 thf(f225,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false) | ((pl @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))))) != (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) @ x))) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true)) )),
% 1.62/1.51 inference(forward_demodulation,[status(thm)],[f207,f86])).
% 1.62/1.51 thf(f86,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : (((pl @ (suc @ X2) @ X1) = (suc @ (pl @ X2 @ X1)))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f85])).
% 1.62/1.51 thf(f85,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : ((((suc @ (pl @ X2 @ X1)) = (pl @ (suc @ X2) @ X1)) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.62/1.51 thf(f84,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((suc @ (pl @ Y0 @ X1)) = (pl @ (suc @ Y0) @ X1))) @ X2) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f83])).
% 1.62/1.51 thf(f83,plain,(
% 1.62/1.51 ( ! [X1 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((suc @ (pl @ Y0 @ X1)) = (pl @ (suc @ Y0) @ X1)))) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f82])).
% 1.62/1.51 thf(f82,plain,(
% 1.62/1.51 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ (suc @ Y1) @ Y0))))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f33])).
% 1.62/1.51 thf(f33,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ (suc @ Y1) @ Y0)))))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f22])).
% 1.62/1.51 thf(f22,plain,(
% 1.62/1.51 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y1 @ Y0)) = (pl @ (suc @ Y1) @ Y0)))))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f21])).
% 1.62/1.51 thf(f21,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat] : ((suc @ (pl @ X0 @ X1)) = (pl @ (suc @ X0) @ X1))),
% 1.62/1.51 inference(rectify,[status(thm)],[f7])).
% 1.62/1.51 thf(f7,axiom,(
% 1.62/1.51 ! [X2 : nat,X3 : nat] : ((suc @ (pl @ X2 @ X3)) = (pl @ (suc @ X2) @ X3))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',satz4d)).
% 1.62/1.51 thf(f207,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((pl @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))))) != (pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) @ x)) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false)) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.62/1.51 thf(f201,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((pl @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))))) != (pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) @ x)) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $true) | ($false = $true) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f42,f73])).
% 1.62/1.51 thf(f42,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : (((esti @ (suc @ (sK1 @ X1)) @ X1) = $false) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.62/1.51 thf(f41,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : (((esti @ n_1 @ X1) = $false) | ($false = ((esti @ (sK1 @ X1) @ X1) => (esti @ (suc @ (sK1 @ X1)) @ X1))) | ((esti @ X2 @ X1) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.62/1.51 thf(f40,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : ((((^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))) @ (sK1 @ X1)) = $false) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.62/1.51 inference(sigma_clausification,[status(thm)],[f39])).
% 1.62/1.51 thf(f39,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false) | ((esti @ n_1 @ X1) = $false) | ((esti @ X2 @ X1) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.62/1.51 thf(f38,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false) | ($true = ((^[Y0 : nat]: (esti @ Y0 @ X1)) @ X2)) | ((esti @ n_1 @ X1) = $false)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f37])).
% 1.62/1.51 thf(f37,plain,(
% 1.62/1.51 ( ! [X1 : set] : (($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) | ((esti @ n_1 @ X1) = $false) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.62/1.51 thf(f36,plain,(
% 1.62/1.51 ( ! [X1 : set] : (((esti @ n_1 @ X1) = $false) | (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) = $true)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.51 thf(f35,plain,(
% 1.62/1.51 ( ! [X1 : set] : ((((esti @ n_1 @ X1) => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))))) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.62/1.51 thf(f34,plain,(
% 1.62/1.51 ( ! [X1 : set] : ((((^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0)))))) @ X1) = $true)) )),
% 1.62/1.51 inference(pi_clausification,[status(thm)],[f26])).
% 1.62/1.51 thf(f26,plain,(
% 1.62/1.51 ((!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))) = $true)),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.62/1.51 thf(f18,plain,(
% 1.62/1.51 ((!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))) = $true)),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f17])).
% 1.62/1.51 thf(f17,plain,(
% 1.62/1.51 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f2])).
% 1.62/1.51 thf(f2,axiom,(
% 1.62/1.51 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.dIwPUI3HUy/DTF2THF_22208.p',ax5)).
% 1.62/1.51 thf(f158,plain,(
% 1.62/1.51 spl0_4 | spl0_3),
% 1.62/1.51 inference(avatar_split_clause,[status(thm)],[f144,f149,f153])).
% 1.62/1.51 thf(f144,plain,(
% 1.62/1.51 ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false) | ((pl @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) @ x))),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.62/1.51 thf(f139,plain,(
% 1.62/1.51 ($false = $true) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) = $false) | ((pl @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) @ x))),
% 1.62/1.51 inference(superposition,[status(thm)],[f60,f44])).
% 1.62/1.51 thf(f44,plain,(
% 1.62/1.51 ( ! [X0 : set] : (($true = (esti @ (sK1 @ X0) @ X0)) | ($false = (esti @ n_1 @ X0))) )),
% 1.62/1.51 inference(condensation,[status(thm)],[f43])).
% 1.62/1.51 thf(f43,plain,(
% 1.62/1.51 ( ! [X2 : nat,X1 : set] : (((esti @ n_1 @ X1) = $false) | ((esti @ (sK1 @ X1) @ X1) = $true) | ((esti @ X2 @ X1) = $true)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.62/1.51 thf(f60,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (($false = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) | ((pl @ X0 @ x) = (pl @ x @ X0))) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f59])).
% 1.62/1.51 thf(f59,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (($false = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))))) | (((pl @ x @ X0) = (pl @ X0 @ x)) = $true)) )),
% 1.62/1.51 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.62/1.51 thf(f53,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((esti @ X0 @ (setof @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x))))) => ((pl @ x @ X0) = (pl @ X0 @ x))) = $true)) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.62/1.51 thf(f50,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((((^[Y0 : nat > $o]: ((esti @ X0 @ (setof @ Y0)) => (Y0 @ X0))) @ (^[Y0 : nat]: ((pl @ x @ Y0) = (pl @ Y0 @ x)))) = $true)) )),
% 1.62/1.51 inference(heuristic_instantiation,[status(thm)],[f49])).
% 1.62/1.51 % SZS output end Proof for DTF2THF_22208
% 1.62/1.51 % (22339)------------------------------
% 1.62/1.51 % (22339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (22339)Termination reason: Refutation
% 1.62/1.51
% 1.62/1.51 % (22339)Memory used [KB]: 5756
% 1.62/1.51 % (22339)Time elapsed: 0.027 s
% 1.62/1.51 % (22339)Instructions burned: 45 (million)
% 1.62/1.51 % (22339)------------------------------
% 1.62/1.51 % (22339)------------------------------
% 1.62/1.51 % (22304)Success in time 0.166 s
%------------------------------------------------------------------------------