%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM710^1 : 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 : n022.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 09:24:24 AM UTC 2026
% Result : Theorem 1.61s 1.44s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 68 unt; 0 typ; 3 def)
% Number of atoms : 474 ( 204 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1016 ( 27 ~; 52 |; 0 &; 845 @)
% ( 3 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-2 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 196 ( 99 ^; 97 !; 0 ?; 196 :)
% 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,
ts: 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_10,type,
pl: nat > nat > nat ).
thf(func_def_20,type,
sK1: set > nat ).
thf(func_def_21,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f458,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f177,f367,f402,f456]) ).
thf(f456,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f455]) ).
thf(f455,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f449]) ).
thf(f449,plain,
( ( ( ts @ x @ y )
!= ( ts @ x @ y ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f26,f436]) ).
thf(f436,plain,
( ! [X0: nat] :
( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ! [X0: nat] :
( ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) )
| ( $false = $true ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f83,f171]) ).
thf(f171,plain,
( ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f170]) ).
thf(f170,definition,
( spl0_2
<=> ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f83,plain,
! [X0: nat] :
( ( $false
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X0: nat] :
( ( $false
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ( $true
= ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: nat] :
( $true
= ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
=> ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: nat] :
( ( ^ [Y0: nat > $o] :
( ( esti @ X0 @ ( setof @ Y0 ) )
=> ( Y0 @ X0 ) )
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) )
= $true ),
inference(heuristic_instantiation,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: nat] :
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,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/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',estie) ).
thf(f26,plain,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
( ( ts @ x @ y )
!= ( ts @ y @ x ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ( ts @ x @ y )
= ( ts @ y @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz29) ).
thf(f402,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f401]) ).
thf(f401,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f400]) ).
thf(f400,plain,
( ( $false = $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f399]) ).
thf(f399,plain,
( ( $false
= ( x = x ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f398,f36]) ).
thf(f36,plain,
! [X1: nat] :
( ( ts @ n_1 @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: nat] :
( ( ( ts @ n_1 @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ts @ n_1 @ Y0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ts @ n_1 @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ts @ n_1 @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat] :
( ( ts @ n_1 @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: nat] :
( ( ts @ n_1 @ X2 )
= X2 ),
file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28c) ).
thf(f398,plain,
( ( ( x
= ( ts @ n_1 @ x ) )
= $false )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f382,f44]) ).
thf(f44,plain,
! [X1: nat] :
( ( ts @ X1 @ n_1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: nat] :
( $true
= ( ( ts @ X1 @ n_1 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( ts @ Y0 @ n_1 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ts @ Y0 @ n_1 )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ts @ Y0 @ n_1 )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat] :
( ( ts @ X0 @ n_1 )
= X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat] :
( ( ts @ X2 @ n_1 )
= X2 ),
file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28a) ).
thf(f382,plain,
( ( ( ( ts @ x @ n_1 )
= ( ts @ n_1 @ x ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f381]) ).
thf(f381,plain,
( ( ( ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) )
@ n_1 )
= $false )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f377]) ).
thf(f377,plain,
( ( ( ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) )
@ n_1 )
= $false )
| ( $false = $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f175,f53]) ).
thf(f53,plain,
! [X2: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X2 ) )
= $true )
| ( $false
= ( X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: nat > $o,X1: nat] :
( ( ( X2 @ X1 )
=> ( esti @ X1 @ ( setof @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( Y0 @ X1 )
=> ( esti @ X1 @ ( setof @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: nat] :
( ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( Y0 @ X1 )
=> ( esti @ X1 @ ( setof @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) )
@ X1 ) ),
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)],[f14]) ).
thf(f14,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( Y1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,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.E0Kb8TYXyL/DTF2THF_1265.p',estii) ).
thf(f175,plain,
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f173]) ).
thf(f173,definition,
( spl0_3
<=> ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f367,plain,
spl0_1,
inference(avatar_split_clause,[status(thm)],[f364,f166]) ).
thf(f166,definition,
( spl0_1
<=> ( ( ts
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x )
= ( ts @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f364,plain,
( ( ts
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x )
= ( ts @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f362,f73]) ).
thf(f73,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ ( suc @ X2 ) )
= ( pl @ ( ts @ X1 @ X2 ) @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( ts @ X1 @ ( suc @ X2 ) )
= ( pl @ ( ts @ X1 @ X2 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ts @ X1 @ ( suc @ Y0 ) )
= ( pl @ ( ts @ X1 @ Y0 ) @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ts @ X1 @ ( suc @ Y0 ) )
= ( pl @ ( ts @ X1 @ Y0 ) @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ts @ Y0 @ ( suc @ Y1 ) )
= ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ts @ Y0 @ ( suc @ Y1 ) )
= ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ts @ Y0 @ ( suc @ Y1 ) )
= ( pl @ ( ts @ Y0 @ Y1 ) @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( ts @ X1 @ ( suc @ X0 ) )
= ( pl @ ( ts @ X1 @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: nat,X2: nat] :
( ( pl @ ( ts @ X2 @ X3 ) @ X2 )
= ( ts @ X2 @ ( suc @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28f) ).
thf(f362,plain,
( ( ts
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x )
= ( pl
@ ( ts @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x ) ),
inference(superposition,[status(thm)],[f41,f180]) ).
thf(f180,plain,
( ( ts @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= ( ts
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
@ x ) ),
inference(equality_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( $true
= ( ( ts @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= ( ts
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
@ x ) ) ),
inference(subsumption_resolution,[status(thm)],[f178,f44]) ).
thf(f178,plain,
( ( x
!= ( ts @ x @ n_1 ) )
| ( $true
= ( ( ts @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= ( ts
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
@ x ) ) ) ),
inference(forward_demodulation,[status(thm)],[f159,f36]) ).
thf(f159,plain,
( ( ( ts @ x @ n_1 )
!= ( ts @ n_1 @ x ) )
| ( $true
= ( ( ts @ x
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= ( ts
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
@ x ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( ts @ x @ n_1 )
!= ( ts @ n_1 @ x ) )
| ( ( ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $false = $true )
| ( ( ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) )
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
= $true )
| ( ( ts @ x @ n_1 )
!= ( ts @ n_1 @ x ) ) ),
inference(superposition,[status(thm)],[f55,f121]) ).
thf(f121,plain,
! [X0: nat > $o] :
( ( $false
= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( $true
= ( X0 @ ( sK1 @ ( setof @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: nat > $o] :
( ( $false = $true )
| ( $false
= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( $true
= ( X0 @ ( sK1 @ ( setof @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f68,f86]) ).
thf(f86,plain,
! [X2: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X2 ) )
= $false )
| ( $true
= ( X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ( esti @ X1 @ ( setof @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f75]) ).
thf(f68,plain,
! [X0: set] :
( ( $true
= ( esti @ ( sK1 @ X0 ) @ X0 ) )
| ( $false
= ( esti @ n_1 @ X0 ) ) ),
inference(condensation,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( $true
= ( esti @ ( sK1 @ X1 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,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)],[f64]) ).
thf(f64,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
= $false )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,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)],[f61]) ).
thf(f61,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)],[f60]) ).
thf(f60,plain,
! [X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( $true
= ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: set] :
( $true
= ( ( esti @ n_1 @ X1 )
=> ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,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)],[f30]) ).
thf(f30,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)],[f12]) ).
thf(f12,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)],[f11]) ).
thf(f11,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.E0Kb8TYXyL/DTF2THF_1265.p',ax5) ).
thf(f55,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ( ( ts @ x @ X0 )
!= ( ts @ X0 @ x ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: nat] :
( ( $false
= ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) ) )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: nat] :
( $true
= ( ( ( ts @ x @ X0 )
= ( ts @ X0 @ x ) )
=> ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: nat] :
( ( ^ [Y0: nat > $o] :
( ( Y0 @ X0 )
=> ( esti @ X0 @ ( setof @ Y0 ) ) )
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) )
= $true ),
inference(heuristic_instantiation,[status(thm)],[f46]) ).
thf(f41,plain,
! [X2: nat,X1: nat] :
( ( ts @ ( suc @ X1 ) @ X2 )
= ( pl @ ( ts @ X1 @ X2 ) @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: nat,X1: nat] :
( $true
= ( ( pl @ ( ts @ X1 @ X2 ) @ X2 )
= ( ts @ ( suc @ X1 ) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( pl @ ( ts @ X1 @ Y0 ) @ Y0 )
= ( ts @ ( suc @ X1 ) @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ ( ts @ X1 @ Y0 ) @ Y0 )
= ( ts @ ( suc @ X1 ) @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y1 )
= ( ts @ ( suc @ Y0 ) @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y1 )
= ( ts @ ( suc @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( pl @ ( ts @ Y0 @ Y1 ) @ Y1 )
= ( ts @ ( suc @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( pl @ ( ts @ X1 @ X0 ) @ X0 )
= ( ts @ ( suc @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X3: nat,X2: nat] :
( ( ts @ ( suc @ X2 ) @ X3 )
= ( pl @ ( ts @ X2 @ X3 ) @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28d) ).
thf(f177,plain,
( ~ spl0_1
| spl0_3
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f160,f170,f173,f166]) ).
thf(f160,plain,
! [X0: nat] :
( ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
= $false )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ( ( ts
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x )
!= ( ts @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
| ( ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) )
= $false )
| ( $false = $true )
| ( ( ts
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) )
@ x )
!= ( ts @ x
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( ts @ x @ Y0 )
= ( ts @ Y0 @ x ) ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f66,f55]) ).
thf(f66,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)],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM710^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:11:51 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 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 : NUM710^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Number Theory
% 0.20/0.46 % Problem : Landau theorem 29
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : ts x y = ts y x
% 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 : satz29 [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 : 44 ( 0 ~; 0 |; 0 &; 39 @)
% 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 : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 9 ( 8 usr; 3 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(ts,type,
% 0.20/0.46 ts: 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(satz28a,axiom,
% 0.20/0.46 ! [Xx: nat] :
% 0.20/0.46 ( ( ts @ Xx @ n_1 )
% 0.20/0.46 = Xx ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz28c,axiom,
% 0.20/0.46 ! [Xx: nat] :
% 0.20/0.46 ( ( ts @ n_1 @ Xx )
% 0.20/0.46 = Xx ) ).
% 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(satz28f,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] :
% 0.20/0.46 ( ( pl @ ( ts @ Xx @ Xy ) @ Xx )
% 0.20/0.46 = ( ts @ Xx @ ( suc @ Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz28d,axiom,
% 0.20/0.46 ! [Xx: nat,Xy: nat] :
% 0.20/0.46 ( ( ts @ ( suc @ Xx ) @ Xy )
% 0.20/0.46 = ( pl @ ( ts @ Xx @ Xy ) @ Xy ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(satz29,conjecture,
% 0.20/0.46 ( ( ts @ x @ y )
% 0.20/0.46 = ( ts @ y @ x ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 11:11:52 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2DTF1265.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(nat_type,type,
% 1.50/1.26 nat: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(x,type,
% 1.50/1.26 x: nat ).
% 1.50/1.26
% 1.50/1.26 thf(y,type,
% 1.50/1.26 y: nat ).
% 1.50/1.26
% 1.50/1.26 thf(ts,type,
% 1.50/1.26 ts: nat > nat > nat ).
% 1.50/1.26
% 1.50/1.26 thf(set_type,type,
% 1.50/1.26 set: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(esti,type,
% 1.50/1.26 esti: nat > set > $o ).
% 1.50/1.26
% 1.50/1.26 thf(setof,type,
% 1.50/1.26 setof: ( nat > $o ) > set ).
% 1.50/1.26
% 1.50/1.26 thf(estie,axiom,
% 1.50/1.26 ! [Xp: nat > $o,Xs: nat] :
% 1.50/1.26 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.50/1.26 => ( Xp @ Xs ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(n_1,type,
% 1.50/1.26 n_1: nat ).
% 1.50/1.26
% 1.50/1.26 thf(suc,type,
% 1.50/1.26 suc: nat > nat ).
% 1.50/1.26
% 1.50/1.26 thf(ax5,axiom,
% 1.50/1.26 ! [Xs: set] :
% 1.50/1.26 ( ( esti @ n_1 @ Xs )
% 1.50/1.26 => ( ! [Xx: nat] :
% 1.50/1.26 ( ( esti @ Xx @ Xs )
% 1.50/1.26 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.50/1.26 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(estii,axiom,
% 1.50/1.26 ! [Xp: nat > $o,Xs: nat] :
% 1.50/1.26 ( ( Xp @ Xs )
% 1.50/1.26 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(satz28a,axiom,
% 1.50/1.26 ! [Xx: nat] :
% 1.50/1.26 ( ( ts @ Xx @ n_1 )
% 1.50/1.26 = Xx ) ).
% 1.50/1.26
% 1.50/1.26 thf(satz28c,axiom,
% 1.50/1.26 ! [Xx: nat] :
% 1.50/1.26 ( ( ts @ n_1 @ Xx )
% 1.50/1.26 = Xx ) ).
% 1.50/1.26
% 1.50/1.26 thf(pl,type,
% 1.50/1.26 pl: nat > nat > nat ).
% 1.50/1.26
% 1.50/1.26 thf(satz28f,axiom,
% 1.50/1.26 ! [Xx: nat,Xy: nat] :
% 1.50/1.26 ( ( pl @ ( ts @ Xx @ Xy ) @ Xx )
% 1.50/1.26 = ( ts @ Xx @ ( suc @ Xy ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(satz28d,axiom,
% 1.50/1.26 ! [Xx: nat,Xy: nat] :
% 1.50/1.26 ( ( ts @ ( suc @ Xx ) @ Xy )
% 1.50/1.26 = ( pl @ ( ts @ Xx @ Xy ) @ Xy ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(satz29,conjecture,
% 1.50/1.26 ( ( ts @ x @ y )
% 1.50/1.26 = ( ts @ y @ x ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.28 % (1371)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/183Mi)
% 1.50/1.28 % (1374)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/2Mi)
% 1.50/1.28 % (1373)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_1265 for (2999ds/27Mi)
% 1.50/1.28 % (1374)Instruction limit reached!
% 1.50/1.28 % (1374)------------------------------
% 1.50/1.28 % (1374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (1374)Termination reason: Unknown
% 1.50/1.28 % (1374)Termination phase: Preprocessing 3
% 1.50/1.28
% 1.50/1.28 % (1374)Memory used [KB]: 895
% 1.50/1.28 % (1374)Time elapsed: 0.002 s
% 1.50/1.28 % (1374)Instructions burned: 2 (million)
% 1.50/1.28 % (1374)------------------------------
% 1.50/1.28 % (1374)------------------------------
% 1.50/1.28 % (1372)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_1265 for (2999ds/4Mi)
% 1.50/1.28 % (1375)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_1265 for (2999ds/2Mi)
% 1.50/1.28 % (1376)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_1265 for (2999ds/275Mi)
% 1.50/1.28 % (1377)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/18Mi)
% 1.50/1.28 % (1375)Instruction limit reached!
% 1.50/1.28 % (1375)------------------------------
% 1.50/1.28 % (1375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (1375)Termination reason: Unknown
% 1.50/1.28 % (1375)Termination phase: Property scanning
% 1.50/1.28
% 1.50/1.28 % (1375)Memory used [KB]: 1023
% 1.50/1.28 % (1375)Time elapsed: 0.003 s
% 1.50/1.28 % (1375)Instructions burned: 2 (million)
% 1.50/1.28 % (1375)------------------------------
% 1.50/1.28 % (1375)------------------------------
% 1.50/1.29 % (1376)Refutation not found, incomplete strategy
% 1.50/1.29 % (1376)------------------------------
% 1.50/1.29 % (1376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (1376)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (1376)Memory used [KB]: 5373
% 1.50/1.29 % (1376)Time elapsed: 0.003 s
% 1.50/1.29 % (1376)Instructions burned: 2 (million)
% 1.50/1.29 % (1376)------------------------------
% 1.50/1.29 % (1376)------------------------------
% 1.50/1.29 % (1382)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/3Mi)
% 1.50/1.29 % (1372)Instruction limit reached!
% 1.50/1.29 % (1372)------------------------------
% 1.50/1.29 % (1372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (1372)Termination reason: Unknown
% 1.50/1.29 % (1372)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (1372)Memory used [KB]: 5500
% 1.50/1.29 % (1372)Time elapsed: 0.005 s
% 1.50/1.29 % (1372)Instructions burned: 4 (million)
% 1.50/1.29 % (1372)------------------------------
% 1.50/1.29 % (1372)------------------------------
% 1.50/1.29 % (1373)Instruction limit reached!
% 1.50/1.29 % (1373)------------------------------
% 1.50/1.29 % (1373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (1373)Termination reason: Unknown
% 1.50/1.29 % (1373)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (1373)Memory used [KB]: 5628
% 1.50/1.29 % (1373)Time elapsed: 0.011 s
% 1.50/1.29 % (1373)Instructions burned: 28 (million)
% 1.50/1.29 % (1373)------------------------------
% 1.50/1.29 % (1373)------------------------------
% 1.50/1.29 % (1382)Instruction limit reached!
% 1.50/1.29 % (1382)------------------------------
% 1.50/1.29 % (1382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (1382)Termination reason: Unknown
% 1.50/1.29 % (1382)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (1382)Memory used [KB]: 5500
% 1.50/1.29 % (1382)Time elapsed: 0.002 s
% 1.50/1.29 % (1382)Instructions burned: 3 (million)
% 1.50/1.29 % (1382)------------------------------
% 1.50/1.29 % (1382)------------------------------
% 1.50/1.30 % (1377)Instruction limit reached!
% 1.50/1.30 % (1377)------------------------------
% 1.50/1.30 % (1377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (1377)Termination reason: Unknown
% 1.50/1.30 % (1377)Termination phase: Saturation
% 1.50/1.30
% 1.50/1.30 % (1377)Memory used [KB]: 5628
% 1.50/1.30 % (1377)Time elapsed: 0.014 s
% 1.50/1.30 % (1377)Instructions burned: 18 (million)
% 1.50/1.30 % (1377)------------------------------
% 1.50/1.30 % (1377)------------------------------
% 1.50/1.30 % (1387)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/7Mi)
% 1.61/1.30 % (1386)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_1265 for (2999ds/1041Mi)
% 1.61/1.30 % (1387)Instruction limit reached!
% 1.61/1.30 % (1387)------------------------------
% 1.61/1.30 % (1387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (1387)Termination reason: Unknown
% 1.61/1.30 % (1387)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (1387)Memory used [KB]: 1023
% 1.61/1.30 % (1387)Time elapsed: 0.004 s
% 1.61/1.30 % (1387)Instructions burned: 9 (million)
% 1.61/1.30 % (1387)------------------------------
% 1.61/1.30 % (1387)------------------------------
% 1.61/1.30 % (1383)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_1265 for (2999ds/37Mi)
% 1.61/1.30 % (1385)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_1265 for (2999ds/3Mi)
% 1.61/1.31 % (1385)Instruction limit reached!
% 1.61/1.31 % (1385)------------------------------
% 1.61/1.31 % (1385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (1385)Termination reason: Unknown
% 1.61/1.31 % (1385)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (1385)Memory used [KB]: 5500
% 1.61/1.31 % (1385)Time elapsed: 0.004 s
% 1.61/1.31 % (1385)Instructions burned: 3 (million)
% 1.61/1.31 % (1385)------------------------------
% 1.61/1.31 % (1385)------------------------------
% 1.61/1.31 % (1389)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_1265 for (2999ds/3Mi)
% 1.61/1.31 % (1389)Instruction limit reached!
% 1.61/1.31 % (1389)------------------------------
% 1.61/1.31 % (1389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (1389)Termination reason: Unknown
% 1.61/1.31 % (1389)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (1389)Memory used [KB]: 5500
% 1.61/1.31 % (1389)Time elapsed: 0.002 s
% 1.61/1.31 % (1389)Instructions burned: 3 (million)
% 1.61/1.31 % (1389)------------------------------
% 1.61/1.31 % (1389)------------------------------
% 1.61/1.31 % (1388)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/16Mi)
% 1.61/1.32 % (1384)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_1265 for (2999ds/15Mi)
% 1.61/1.32 % (1390)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_1265 for (2999ds/3Mi)
% 1.61/1.32 % (1384)Refutation not found, incomplete strategy
% 1.61/1.32 % (1384)------------------------------
% 1.61/1.32 % (1384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (1384)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.32
% 1.61/1.32
% 1.61/1.32 % (1384)Memory used [KB]: 5500
% 1.61/1.32 % (1384)Time elapsed: 0.005 s
% 1.61/1.32 % (1384)Instructions burned: 3 (million)
% 1.61/1.32 % (1384)------------------------------
% 1.61/1.32 % (1384)------------------------------
% 1.61/1.32 % (1391)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/7Mi)
% 1.61/1.32 % (1390)Instruction limit reached!
% 1.61/1.32 % (1390)------------------------------
% 1.61/1.32 % (1390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (1390)Termination reason: Unknown
% 1.61/1.32 % (1390)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (1390)Memory used [KB]: 1023
% 1.61/1.32 % (1390)Time elapsed: 0.003 s
% 1.61/1.32 % (1390)Instructions burned: 4 (million)
% 1.61/1.32 % (1390)------------------------------
% 1.61/1.32 % (1390)------------------------------
% 1.61/1.32 % (1391)Refutation not found, incomplete strategy
% 1.61/1.32 % (1391)------------------------------
% 1.61/1.32 % (1391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (1391)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.32
% 1.61/1.32
% 1.61/1.32 % (1391)Memory used [KB]: 5500
% 1.61/1.32 % (1391)Time elapsed: 0.003 s
% 1.61/1.32 % (1391)Instructions burned: 5 (million)
% 1.61/1.32 % (1391)------------------------------
% 1.61/1.32 % (1391)------------------------------
% 1.61/1.32 % (1383)Instruction limit reached!
% 1.61/1.32 % (1383)------------------------------
% 1.61/1.32 % (1383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (1383)Termination reason: Unknown
% 1.61/1.32 % (1383)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (1383)Memory used [KB]: 5884
% 1.61/1.32 % (1383)Time elapsed: 0.024 s
% 1.61/1.32 % (1383)Instructions burned: 37 (million)
% 1.61/1.32 % (1383)------------------------------
% 1.61/1.32 % (1383)------------------------------
% 1.61/1.32 % (1388)Instruction limit reached!
% 1.61/1.32 % (1388)------------------------------
% 1.61/1.32 % (1388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (1388)Termination reason: Unknown
% 1.61/1.32 % (1388)Termination phase: Saturation
% 1.61/1.32
% 1.61/1.32 % (1388)Memory used [KB]: 5628
% 1.61/1.32 % (1388)Time elapsed: 0.013 s
% 1.61/1.32 % (1388)Instructions burned: 16 (million)
% 1.61/1.32 % (1388)------------------------------
% 1.61/1.32 % (1388)------------------------------
% 1.61/1.33 % (1392)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/3Mi)
% 1.61/1.33 % (1371)Instruction limit reached!
% 1.61/1.33 % (1371)------------------------------
% 1.61/1.33 % (1371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (1371)Termination reason: Unknown
% 1.61/1.33 % (1371)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (1371)Memory used [KB]: 6652
% 1.61/1.33 % (1371)Time elapsed: 0.056 s
% 1.61/1.33 % (1371)Instructions burned: 185 (million)
% 1.61/1.33 % (1371)------------------------------
% 1.61/1.33 % (1371)------------------------------
% 1.61/1.33 % (1394)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/18Mi)
% 1.61/1.33 % (1392)Instruction limit reached!
% 1.61/1.33 % (1392)------------------------------
% 1.61/1.33 % (1392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.33 % (1392)Termination reason: Unknown
% 1.61/1.33 % (1392)Termination phase: Saturation
% 1.61/1.33
% 1.61/1.33 % (1392)Memory used [KB]: 5500
% 1.61/1.33 % (1392)Time elapsed: 0.003 s
% 1.61/1.33 % (1392)Instructions burned: 4 (million)
% 1.61/1.33 % (1392)------------------------------
% 1.61/1.33 % (1392)------------------------------
% 1.61/1.34 % (1394)Instruction limit reached!
% 1.61/1.34 % (1394)------------------------------
% 1.61/1.34 % (1394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (1394)Termination reason: Unknown
% 1.61/1.34 % (1394)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (1394)Memory used [KB]: 5500
% 1.61/1.34 % (1394)Time elapsed: 0.007 s
% 1.61/1.34 % (1394)Instructions burned: 19 (million)
% 1.61/1.34 % (1394)------------------------------
% 1.61/1.34 % (1394)------------------------------
% 1.61/1.34 % (1393)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/4Mi)
% 1.61/1.34 % (1397)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_1265 for (2999ds/902Mi)
% 1.61/1.34 % (1393)Instruction limit reached!
% 1.61/1.34 % (1393)------------------------------
% 1.61/1.34 % (1393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (1393)Termination reason: Unknown
% 1.61/1.34 % (1393)Termination phase: Saturation
% 1.61/1.34
% 1.61/1.34 % (1393)Memory used [KB]: 5500
% 1.61/1.34 % (1393)Time elapsed: 0.005 s
% 1.61/1.34 % (1393)Instructions burned: 4 (million)
% 1.61/1.34 % (1393)------------------------------
% 1.61/1.34 % (1393)------------------------------
% 1.61/1.34 % (1398)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_1265 for (2999ds/21Mi)
% 1.61/1.34 % (1397)Refutation not found, incomplete strategy
% 1.61/1.34 % (1397)------------------------------
% 1.61/1.34 % (1397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.34 % (1397)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.34
% 1.61/1.34
% 1.61/1.34 % (1397)Memory used [KB]: 5500
% 1.61/1.34 % (1397)Time elapsed: 0.001 s
% 1.61/1.34 % (1397)Instructions burned: 1 (million)
% 1.61/1.34 % (1397)------------------------------
% 1.61/1.34 % (1397)------------------------------
% 1.61/1.34 % (1395)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/710Mi)
% 1.61/1.34 % (1396)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/6Mi)
% 1.61/1.35 % (1399)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/5Mi)
% 1.61/1.35 % (1396)Instruction limit reached!
% 1.61/1.35 % (1396)------------------------------
% 1.61/1.35 % (1396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (1396)Termination reason: Unknown
% 1.61/1.35 % (1396)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (1396)Memory used [KB]: 5500
% 1.61/1.35 % (1396)Time elapsed: 0.006 s
% 1.61/1.35 % (1396)Instructions burned: 6 (million)
% 1.61/1.35 % (1396)------------------------------
% 1.61/1.35 % (1396)------------------------------
% 1.61/1.35 % (1399)Instruction limit reached!
% 1.61/1.35 % (1399)------------------------------
% 1.61/1.35 % (1399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (1399)Termination reason: Unknown
% 1.61/1.35 % (1399)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (1399)Memory used [KB]: 5500
% 1.61/1.35 % (1399)Time elapsed: 0.003 s
% 1.61/1.35 % (1399)Instructions burned: 6 (million)
% 1.61/1.35 % (1399)------------------------------
% 1.61/1.35 % (1399)------------------------------
% 1.61/1.35 % (1398)Instruction limit reached!
% 1.61/1.35 % (1398)------------------------------
% 1.61/1.35 % (1398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.35 % (1398)Termination reason: Unknown
% 1.61/1.35 % (1398)Termination phase: Saturation
% 1.61/1.35
% 1.61/1.35 % (1398)Memory used [KB]: 5628
% 1.61/1.35 % (1398)Time elapsed: 0.010 s
% 1.61/1.35 % (1398)Instructions burned: 23 (million)
% 1.61/1.35 % (1398)------------------------------
% 1.61/1.35 % (1398)------------------------------
% 1.61/1.35 % (1401)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/377Mi)
% 1.61/1.36 % (1403)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_1265 for (2999ds/19Mi)
% 1.61/1.36 % (1400)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_1265 for (2999ds/6Mi)
% 1.61/1.36 % (1403)Refutation not found, incomplete strategy
% 1.61/1.36 % (1403)------------------------------
% 1.61/1.36 % (1403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (1403)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.36
% 1.61/1.36
% 1.61/1.36 % (1403)Memory used [KB]: 5500
% 1.61/1.36 % (1403)Time elapsed: 0.001 s
% 1.61/1.36 % (1403)Instructions burned: 1 (million)
% 1.61/1.36 % (1403)------------------------------
% 1.61/1.36 % (1403)------------------------------
% 1.61/1.36 % (1404)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/879Mi)
% 1.61/1.36 % (1400)Refutation not found, incomplete strategy
% 1.61/1.36 % (1400)------------------------------
% 1.61/1.36 % (1400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.36 % (1400)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.36
% 1.61/1.36
% 1.61/1.36 % (1400)Memory used [KB]: 5500
% 1.61/1.36 % (1400)Time elapsed: 0.003 s
% 1.61/1.36 % (1400)Instructions burned: 2 (million)
% 1.61/1.36 % (1400)------------------------------
% 1.61/1.36 % (1400)------------------------------
% 1.61/1.36 % (1402)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_1265 for (2999ds/779Mi)
% 1.61/1.37 % (1405)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/17Mi)
% 1.61/1.37 % (1405)Instruction limit reached!
% 1.61/1.37 % (1405)------------------------------
% 1.61/1.37 % (1405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.37 % (1405)Termination reason: Unknown
% 1.61/1.37 % (1405)Termination phase: Saturation
% 1.61/1.37
% 1.61/1.37 % (1405)Memory used [KB]: 5500
% 1.61/1.37 % (1405)Time elapsed: 0.007 s
% 1.61/1.37 % (1405)Instructions burned: 19 (million)
% 1.61/1.37 % (1405)------------------------------
% 1.61/1.37 % (1405)------------------------------
% 1.61/1.38 % (1406)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/3Mi)
% 1.61/1.38 % (1406)Instruction limit reached!
% 1.61/1.38 % (1406)------------------------------
% 1.61/1.38 % (1406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.38 % (1406)Termination reason: Unknown
% 1.61/1.38 % (1406)Termination phase: Saturation
% 1.61/1.38
% 1.61/1.38 % (1406)Memory used [KB]: 1023
% 1.61/1.38 % (1406)Time elapsed: 0.004 s
% 1.61/1.38 % (1406)Instructions burned: 4 (million)
% 1.61/1.38 % (1406)------------------------------
% 1.61/1.38 % (1406)------------------------------
% 1.61/1.38 % (1409)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/30Mi)
% 1.61/1.39 % (1409)Instruction limit reached!
% 1.61/1.39 % (1409)------------------------------
% 1.61/1.39 % (1409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.39 % (1409)Termination reason: Unknown
% 1.61/1.39 % (1409)Termination phase: Saturation
% 1.61/1.39
% 1.61/1.39 % (1409)Memory used [KB]: 5628
% 1.61/1.39 % (1409)Time elapsed: 0.011 s
% 1.61/1.39 % (1409)Instructions burned: 30 (million)
% 1.61/1.39 % (1409)------------------------------
% 1.61/1.39 % (1409)------------------------------
% 1.61/1.40 % (1412)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1265 for (2999ds/127Mi)
% 1.61/1.40 % (1419)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1265 for (2998ds/100Mi)
% 1.61/1.43 % (1419)First to succeed.
% 1.61/1.44 % (1419)Refutation found. Thanks to Tanya!
% 1.61/1.44 % SZS status Theorem for DTF2THF_1265
% 1.61/1.44 % SZS output start Proof for DTF2THF_1265
% 1.61/1.44 thf(type_def_5, type, nat: $tType).
% 1.61/1.44 thf(type_def_7, type, set: $tType).
% 1.61/1.44 thf(func_def_0, type, nat: $tType).
% 1.61/1.44 thf(func_def_1, type, x: nat).
% 1.61/1.44 thf(func_def_2, type, y: nat).
% 1.61/1.44 thf(func_def_3, type, ts: nat > nat > nat).
% 1.61/1.44 thf(func_def_4, type, set: $tType).
% 1.61/1.44 thf(func_def_5, type, esti: nat > set > $o).
% 1.61/1.44 thf(func_def_6, type, setof: (nat > $o) > set).
% 1.61/1.44 thf(func_def_8, type, n_1: nat).
% 1.61/1.44 thf(func_def_9, type, suc: nat > nat).
% 1.61/1.44 thf(func_def_10, type, pl: nat > nat > nat).
% 1.61/1.44 thf(func_def_20, type, sK1: set > nat).
% 1.61/1.44 thf(func_def_21, type, ph2: !>[X0: $tType]:(X0)).
% 1.61/1.44 thf(f458,plain,(
% 1.61/1.44 $false),
% 1.61/1.44 inference(avatar_sat_refutation,[status(thm)],[f177,f367,f402,f456])).
% 1.61/1.44 thf(f456,plain,(
% 1.61/1.44 ~spl0_2),
% 1.61/1.44 inference(avatar_contradiction_clause,[status(thm)],[f455])).
% 1.61/1.44 thf(f455,plain,(
% 1.61/1.44 $false | ~spl0_2),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f449])).
% 1.61/1.44 thf(f449,plain,(
% 1.61/1.44 ((ts @ x @ y) != (ts @ x @ y)) | ~spl0_2),
% 1.61/1.44 inference(superposition,[status(thm)],[f26,f436])).
% 1.61/1.44 thf(f436,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (((ts @ x @ X0) = (ts @ X0 @ x))) ) | ~spl0_2),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.61/1.44 thf(f422,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (((ts @ x @ X0) = (ts @ X0 @ x)) | ($false = $true)) ) | ~spl0_2),
% 1.61/1.44 inference(superposition,[status(thm)],[f83,f171])).
% 1.61/1.44 thf(f171,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))) ) | ~spl0_2),
% 1.61/1.44 inference(avatar_component_clause,[status(thm)],[f170])).
% 1.61/1.44 thf(f170,definition,(
% 1.61/1.44 spl0_2 <=> ! [X0 : nat] : ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))),
% 1.61/1.44 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.61/1.44 thf(f83,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($false = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) | ((ts @ x @ X0) = (ts @ X0 @ x))) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f82])).
% 1.61/1.44 thf(f82,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($false = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) | ($true = ((ts @ x @ X0) = (ts @ X0 @ x)))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.61/1.44 thf(f81,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($true = ((esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) => ((ts @ x @ X0) = (ts @ X0 @ x))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.61/1.44 thf(f76,plain,(
% 1.61/1.44 ( ! [X0 : nat] : ((((^[Y0 : nat > $o]: ((esti @ X0 @ (setof @ Y0)) => (Y0 @ X0))) @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))) = $true)) )),
% 1.61/1.44 inference(heuristic_instantiation,[status(thm)],[f75])).
% 1.61/1.44 thf(f75,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1)))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f74])).
% 1.61/1.44 thf(f74,plain,(
% 1.61/1.44 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0))))) @ X1) = $true)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f33])).
% 1.61/1.44 thf(f33,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))))),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f18])).
% 1.61/1.44 thf(f18,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))))),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f17])).
% 1.61/1.44 thf(f17,plain,(
% 1.61/1.44 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.61/1.44 inference(rectify,[status(thm)],[f1])).
% 1.61/1.44 thf(f1,axiom,(
% 1.61/1.44 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',estie)).
% 1.61/1.44 thf(f26,plain,(
% 1.61/1.44 ((ts @ x @ y) != (ts @ y @ x))),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f25])).
% 1.61/1.44 thf(f25,plain,(
% 1.61/1.44 ((ts @ x @ y) != (ts @ y @ x))),
% 1.61/1.44 inference(flattening,[status(thm)],[f9])).
% 1.61/1.44 thf(f9,negated_conjecture,(
% 1.61/1.44 ~((ts @ x @ y) = (ts @ y @ x))),
% 1.61/1.44 inference(negated_conjecture,[status(cth)],[f8])).
% 1.61/1.44 thf(f8,conjecture,(
% 1.61/1.44 ((ts @ x @ y) = (ts @ y @ x))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz29)).
% 1.61/1.44 thf(f402,plain,(
% 1.61/1.44 ~spl0_3),
% 1.61/1.44 inference(avatar_contradiction_clause,[status(thm)],[f401])).
% 1.61/1.44 thf(f401,plain,(
% 1.61/1.44 $false | ~spl0_3),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f400])).
% 1.61/1.44 thf(f400,plain,(
% 1.61/1.44 ($false = $true) | ~spl0_3),
% 1.61/1.44 inference(boolean_simplification,[status(thm)],[f399])).
% 1.61/1.44 thf(f399,plain,(
% 1.61/1.44 ($false = (x = x)) | ~spl0_3),
% 1.61/1.44 inference(forward_demodulation,[status(thm)],[f398,f36])).
% 1.61/1.44 thf(f36,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (((ts @ n_1 @ X1) = X1)) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.61/1.44 thf(f35,plain,(
% 1.61/1.44 ( ! [X1 : nat] : ((((ts @ n_1 @ X1) = X1) = $true)) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.61/1.44 thf(f34,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((ts @ n_1 @ Y0) = Y0)) @ X1))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f28])).
% 1.61/1.44 thf(f28,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: ((ts @ n_1 @ Y0) = Y0))))),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.44 thf(f20,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: ((ts @ n_1 @ Y0) = Y0))))),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f19])).
% 1.61/1.44 thf(f19,plain,(
% 1.61/1.44 ! [X0 : nat] : ((ts @ n_1 @ X0) = X0)),
% 1.61/1.44 inference(rectify,[status(thm)],[f5])).
% 1.61/1.44 thf(f5,axiom,(
% 1.61/1.44 ! [X2 : nat] : ((ts @ n_1 @ X2) = X2)),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28c)).
% 1.61/1.44 thf(f398,plain,(
% 1.61/1.44 ((x = (ts @ n_1 @ x)) = $false) | ~spl0_3),
% 1.61/1.44 inference(forward_demodulation,[status(thm)],[f382,f44])).
% 1.61/1.44 thf(f44,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (((ts @ X1 @ n_1) = X1)) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f43])).
% 1.61/1.44 thf(f43,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = ((ts @ X1 @ n_1) = X1))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.61/1.44 thf(f42,plain,(
% 1.61/1.44 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((ts @ Y0 @ n_1) = Y0)) @ X1) = $true)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f27])).
% 1.61/1.44 thf(f27,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: ((ts @ Y0 @ n_1) = Y0))))),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f22])).
% 1.61/1.44 thf(f22,plain,(
% 1.61/1.44 ($true = (!! @ nat @ (^[Y0 : nat]: ((ts @ Y0 @ n_1) = Y0))))),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f21])).
% 1.61/1.44 thf(f21,plain,(
% 1.61/1.44 ! [X0 : nat] : ((ts @ X0 @ n_1) = X0)),
% 1.61/1.44 inference(rectify,[status(thm)],[f4])).
% 1.61/1.44 thf(f4,axiom,(
% 1.61/1.44 ! [X2 : nat] : ((ts @ X2 @ n_1) = X2)),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28a)).
% 1.61/1.44 thf(f382,plain,(
% 1.61/1.44 (((ts @ x @ n_1) = (ts @ n_1 @ x)) = $false) | ~spl0_3),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f381])).
% 1.61/1.44 thf(f381,plain,(
% 1.61/1.44 (((^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))) @ n_1) = $false) | ~spl0_3),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f377])).
% 1.61/1.44 thf(f377,plain,(
% 1.61/1.44 (((^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))) @ n_1) = $false) | ($false = $true) | ~spl0_3),
% 1.61/1.44 inference(superposition,[status(thm)],[f175,f53])).
% 1.61/1.44 thf(f53,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : (((esti @ X1 @ (setof @ X2)) = $true) | ($false = (X2 @ X1))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.61/1.44 thf(f52,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : ((((X2 @ X1) => (esti @ X1 @ (setof @ X2))) = $true)) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.61/1.44 thf(f49,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat > $o]: ((Y0 @ X1) => (esti @ X1 @ (setof @ Y0)))) @ X2))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f46])).
% 1.61/1.44 thf(f46,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (((!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((Y0 @ X1) => (esti @ X1 @ (setof @ Y0))))) = $true)) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.61/1.44 thf(f45,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1)))))) @ X1))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f31])).
% 1.61/1.44 thf(f31,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))) = $true)),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.44 thf(f14,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((Y1 @ Y0) => (esti @ Y0 @ (setof @ Y1))))))) = $true)),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f13])).
% 1.61/1.44 thf(f13,plain,(
% 1.61/1.44 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.61/1.44 inference(rectify,[status(thm)],[f3])).
% 1.61/1.44 thf(f3,axiom,(
% 1.61/1.44 ! [X0 : nat > $o,X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',estii)).
% 1.61/1.44 thf(f175,plain,(
% 1.61/1.44 ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) = $false) | ~spl0_3),
% 1.61/1.44 inference(avatar_component_clause,[status(thm)],[f173])).
% 1.61/1.44 thf(f173,definition,(
% 1.61/1.44 spl0_3 <=> ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) = $false)),
% 1.61/1.44 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.61/1.44 thf(f367,plain,(
% 1.61/1.44 spl0_1),
% 1.61/1.44 inference(avatar_split_clause,[status(thm)],[f364,f166])).
% 1.61/1.44 thf(f166,definition,(
% 1.61/1.44 spl0_1 <=> ((ts @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x) = (ts @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))))),
% 1.61/1.44 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.61/1.44 thf(f364,plain,(
% 1.61/1.44 ((ts @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x) = (ts @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))))),
% 1.61/1.44 inference(forward_demodulation,[status(thm)],[f362,f73])).
% 1.61/1.44 thf(f73,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (((ts @ X1 @ (suc @ X2)) = (pl @ (ts @ X1 @ X2) @ X1))) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f72])).
% 1.61/1.44 thf(f72,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (($true = ((ts @ X1 @ (suc @ X2)) = (pl @ (ts @ X1 @ X2) @ X1)))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.61/1.44 thf(f71,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ts @ X1 @ (suc @ Y0)) = (pl @ (ts @ X1 @ Y0) @ X1))) @ X2))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f70])).
% 1.61/1.44 thf(f70,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ts @ X1 @ (suc @ Y0)) = (pl @ (ts @ X1 @ Y0) @ X1)))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.61/1.44 thf(f69,plain,(
% 1.61/1.44 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ts @ Y0 @ (suc @ Y1)) = (pl @ (ts @ Y0 @ Y1) @ Y0))))) @ X1) = $true)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f32])).
% 1.61/1.44 thf(f32,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ts @ Y0 @ (suc @ Y1)) = (pl @ (ts @ Y0 @ Y1) @ Y0)))))) = $true)),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f16])).
% 1.61/1.44 thf(f16,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ts @ Y0 @ (suc @ Y1)) = (pl @ (ts @ Y0 @ Y1) @ Y0)))))) = $true)),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f15])).
% 1.61/1.44 thf(f15,plain,(
% 1.61/1.44 ! [X0 : nat,X1 : nat] : ((ts @ X1 @ (suc @ X0)) = (pl @ (ts @ X1 @ X0) @ X1))),
% 1.61/1.44 inference(rectify,[status(thm)],[f6])).
% 1.61/1.44 thf(f6,axiom,(
% 1.61/1.44 ! [X3 : nat,X2 : nat] : ((pl @ (ts @ X2 @ X3) @ X2) = (ts @ X2 @ (suc @ X3)))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28f)).
% 1.61/1.44 thf(f362,plain,(
% 1.61/1.44 ((ts @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x) = (pl @ (ts @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x))),
% 1.61/1.44 inference(superposition,[status(thm)],[f41,f180])).
% 1.61/1.44 thf(f180,plain,(
% 1.61/1.44 ((ts @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = (ts @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) @ x))),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f179])).
% 1.61/1.44 thf(f179,plain,(
% 1.61/1.44 ($true = ((ts @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = (ts @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) @ x)))),
% 1.61/1.44 inference(subsumption_resolution,[status(thm)],[f178,f44])).
% 1.61/1.44 thf(f178,plain,(
% 1.61/1.44 (x != (ts @ x @ n_1)) | ($true = ((ts @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = (ts @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) @ x)))),
% 1.61/1.44 inference(forward_demodulation,[status(thm)],[f159,f36])).
% 1.61/1.44 thf(f159,plain,(
% 1.61/1.44 ((ts @ x @ n_1) != (ts @ n_1 @ x)) | ($true = ((ts @ x @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = (ts @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) @ x)))),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f158])).
% 1.61/1.44 thf(f158,plain,(
% 1.61/1.44 ((ts @ x @ n_1) != (ts @ n_1 @ x)) | (((^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))) @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = $true)),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.61/1.44 thf(f150,plain,(
% 1.61/1.44 ($false = $true) | (((^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))) @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) = $true) | ((ts @ x @ n_1) != (ts @ n_1 @ x))),
% 1.61/1.44 inference(superposition,[status(thm)],[f55,f121])).
% 1.61/1.44 thf(f121,plain,(
% 1.61/1.44 ( ! [X0 : nat > $o] : (($false = (esti @ n_1 @ (setof @ X0))) | ($true = (X0 @ (sK1 @ (setof @ X0))))) )),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.61/1.44 thf(f118,plain,(
% 1.61/1.44 ( ! [X0 : nat > $o] : (($false = $true) | ($false = (esti @ n_1 @ (setof @ X0))) | ($true = (X0 @ (sK1 @ (setof @ X0))))) )),
% 1.61/1.44 inference(superposition,[status(thm)],[f68,f86])).
% 1.61/1.44 thf(f86,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : (((esti @ X1 @ (setof @ X2)) = $false) | ($true = (X2 @ X1))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.61/1.44 thf(f79,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((esti @ X1 @ (setof @ X2)) => (X2 @ X1)))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.61/1.44 thf(f78,plain,(
% 1.61/1.44 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1))) @ X2))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f75])).
% 1.61/1.44 thf(f68,plain,(
% 1.61/1.44 ( ! [X0 : set] : (($true = (esti @ (sK1 @ X0) @ X0)) | ($false = (esti @ n_1 @ X0))) )),
% 1.61/1.44 inference(condensation,[status(thm)],[f67])).
% 1.61/1.44 thf(f67,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false) | ($true = (esti @ (sK1 @ X1) @ X1))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.61/1.44 thf(f65,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (((esti @ n_1 @ X1) = $false) | ($false = ((esti @ (sK1 @ X1) @ X1) => (esti @ (suc @ (sK1 @ X1)) @ X1))) | ((esti @ X2 @ X1) = $true)) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.61/1.44 thf(f64,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false) | ($false = ((^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))) @ (sK1 @ X1)))) )),
% 1.61/1.44 inference(sigma_clausification,[status(thm)],[f63])).
% 1.61/1.44 thf(f63,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false) | ((esti @ n_1 @ X1) = $false)) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.61/1.44 thf(f62,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (($true = ((^[Y0 : nat]: (esti @ Y0 @ X1)) @ X2)) | ((esti @ n_1 @ X1) = $false) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f61])).
% 1.61/1.44 thf(f61,plain,(
% 1.61/1.44 ( ! [X1 : set] : (($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) | ((esti @ n_1 @ X1) = $false) | ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) = $false)) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.61/1.44 thf(f60,plain,(
% 1.61/1.44 ( ! [X1 : set] : (((esti @ n_1 @ X1) = $false) | ($true = ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.61/1.44 thf(f59,plain,(
% 1.61/1.44 ( ! [X1 : set] : (($true = ((esti @ n_1 @ X1) => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.61/1.44 thf(f58,plain,(
% 1.61/1.44 ( ! [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) = $true)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f30])).
% 1.61/1.44 thf(f30,plain,(
% 1.61/1.44 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f12])).
% 1.61/1.44 thf(f12,plain,(
% 1.61/1.44 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f11])).
% 1.61/1.44 thf(f11,plain,(
% 1.61/1.44 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.61/1.44 inference(rectify,[status(thm)],[f2])).
% 1.61/1.44 thf(f2,axiom,(
% 1.61/1.44 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',ax5)).
% 1.61/1.44 thf(f55,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) | ((ts @ x @ X0) != (ts @ X0 @ x))) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.61/1.44 thf(f54,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($false = ((ts @ x @ X0) = (ts @ X0 @ x))) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.61/1.44 thf(f51,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($true = (((ts @ x @ X0) = (ts @ X0 @ x)) => (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.61/1.44 thf(f47,plain,(
% 1.61/1.44 ( ! [X0 : nat] : ((((^[Y0 : nat > $o]: ((Y0 @ X0) => (esti @ X0 @ (setof @ Y0)))) @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))) = $true)) )),
% 1.61/1.44 inference(heuristic_instantiation,[status(thm)],[f46])).
% 1.61/1.44 thf(f41,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (((ts @ (suc @ X1) @ X2) = (pl @ (ts @ X1 @ X2) @ X2))) )),
% 1.61/1.44 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.61/1.44 thf(f40,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (($true = ((pl @ (ts @ X1 @ X2) @ X2) = (ts @ (suc @ X1) @ X2)))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.61/1.44 thf(f39,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((pl @ (ts @ X1 @ Y0) @ Y0) = (ts @ (suc @ X1) @ Y0))) @ X2))) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f38])).
% 1.61/1.44 thf(f38,plain,(
% 1.61/1.44 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((pl @ (ts @ X1 @ Y0) @ Y0) = (ts @ (suc @ X1) @ Y0)))))) )),
% 1.61/1.44 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.61/1.44 thf(f37,plain,(
% 1.61/1.44 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y1) = (ts @ (suc @ Y0) @ Y1))))) @ X1) = $true)) )),
% 1.61/1.44 inference(pi_clausification,[status(thm)],[f29])).
% 1.61/1.44 thf(f29,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y1) = (ts @ (suc @ Y0) @ Y1)))))) = $true)),
% 1.61/1.44 inference(cnf_transformation,[status(thm)],[f24])).
% 1.61/1.44 thf(f24,plain,(
% 1.61/1.44 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((pl @ (ts @ Y0 @ Y1) @ Y1) = (ts @ (suc @ Y0) @ Y1)))))) = $true)),
% 1.61/1.44 inference(fool_elimination,[status(thm)],[f23])).
% 1.61/1.44 thf(f23,plain,(
% 1.61/1.44 ! [X0 : nat,X1 : nat] : ((pl @ (ts @ X1 @ X0) @ X0) = (ts @ (suc @ X1) @ X0))),
% 1.61/1.44 inference(rectify,[status(thm)],[f7])).
% 1.61/1.44 thf(f7,axiom,(
% 1.61/1.44 ! [X3 : nat,X2 : nat] : ((ts @ (suc @ X2) @ X3) = (pl @ (ts @ X2 @ X3) @ X3))),
% 1.61/1.44 file('/export/starexec/sandbox2/tmp/tmp.E0Kb8TYXyL/DTF2THF_1265.p',satz28d)).
% 1.61/1.44 thf(f177,plain,(
% 1.61/1.44 ~spl0_1 | spl0_3 | spl0_2),
% 1.61/1.44 inference(avatar_split_clause,[status(thm)],[f160,f170,f173,f166])).
% 1.61/1.44 thf(f160,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) = $false) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) | ((ts @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x) != (ts @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))))) )),
% 1.61/1.44 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.61/1.44 thf(f152,plain,(
% 1.61/1.44 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) | ((esti @ n_1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))) = $false) | ($false = $true) | ((ts @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x)))))) @ x) != (ts @ x @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: ((ts @ x @ Y0) = (ts @ Y0 @ x))))))))) )),
% 1.61/1.44 inference(superposition,[status(thm)],[f66,f55])).
% 1.61/1.44 thf(f66,plain,(
% 1.61/1.44 ( ! [X2 : nat,X1 : set] : (((esti @ (suc @ (sK1 @ X1)) @ X1) = $false) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.61/1.44 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.61/1.44 % SZS output end Proof for DTF2THF_1265
% 1.61/1.44 % (1419)------------------------------
% 1.61/1.44 % (1419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.44 % (1419)Termination reason: Refutation
% 1.61/1.44
% 1.61/1.44 % (1419)Memory used [KB]: 5884
% 1.61/1.44 % (1419)Time elapsed: 0.033 s
% 1.61/1.44 % (1419)Instructions burned: 97 (million)
% 1.61/1.44 % (1419)------------------------------
% 1.61/1.44 % (1419)------------------------------
% 1.61/1.44 % (1365)Success in time 0.155 s
%------------------------------------------------------------------------------