%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM646^1 : 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 : n004.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 09:24:04 AM UTC 2026
% Result : Theorem 1.69s 1.48s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 121 ( 58 unt; 0 typ; 4 def)
% Number of atoms : 545 ( 246 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1191 ( 125 ~; 73 |; 0 &; 890 @)
% ( 4 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 11 con; 0-2 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 217 ( 111 ^; 106 !; 0 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
set: $tType ).
thf(func_def_0,type,
nat: $tType ).
thf(func_def_1,type,
x: nat ).
thf(func_def_2,type,
y: nat ).
thf(func_def_3,type,
z: nat ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_5,type,
set: $tType ).
thf(func_def_6,type,
esti: nat > set > $o ).
thf(func_def_7,type,
setof: ( nat > $o ) > set ).
thf(func_def_9,type,
n_1: nat ).
thf(func_def_10,type,
suc: nat > nat ).
thf(func_def_21,type,
sK1: set > nat ).
thf(func_def_22,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f442,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f302,f345,f376,f429,f441]) ).
thf(f441,plain,
( spl0_12
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f440]) ).
thf(f440,plain,
( $false
| spl0_12
| ~ spl0_15 ),
inference(subsumption_resolution,[status(thm)],[f439,f294]) ).
thf(f294,plain,
( ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y )
!= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) )
| spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f292]) ).
thf(f292,definition,
( spl0_12
<=> ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f439,plain,
( ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y )
= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) )
| ~ spl0_15 ),
inference(equality_resolution,[status(thm)],[f435]) ).
thf(f435,plain,
( ! [X0: nat] :
( ( ( suc @ X0 )
!= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y ) ) )
| ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z )
= X0 ) )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f108,f433]) ).
thf(f433,plain,
( ( ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y ) )
= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) ) )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f72,f336]) ).
thf(f336,plain,
( ( ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ z )
= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f334]) ).
thf(f334,definition,
( spl0_15
<=> ( ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ z )
= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f72,plain,
! [X2: nat,X1: nat] :
( ( pl @ ( suc @ X1 ) @ X2 )
= ( suc @ ( pl @ X1 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: nat,X1: nat] :
( ( ( suc @ ( pl @ X1 @ X2 ) )
= ( pl @ ( suc @ X1 ) @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: nat,X1: nat] :
( ( ^ [Y0: nat] :
( ( suc @ ( pl @ X1 @ Y0 ) )
= ( pl @ ( suc @ X1 ) @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( suc @ ( pl @ X1 @ Y0 ) )
= ( pl @ ( suc @ X1 ) @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( suc @ ( pl @ Y0 @ Y1 ) )
= ( pl @ ( suc @ Y0 ) @ Y1 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( suc @ ( pl @ X1 @ X0 ) )
= ( pl @ ( suc @ X1 ) @ X0 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X3: nat,X2: nat] :
( ( suc @ ( pl @ X2 @ X3 ) )
= ( pl @ ( suc @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz4h) ).
thf(f108,plain,
! [X2: nat,X1: nat] :
( ( ( suc @ X2 )
!= ( suc @ X1 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: nat,X1: nat] :
( ( $true
= ( X2 = X1 ) )
| ( ( suc @ X2 )
!= ( suc @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X2: nat,X1: nat] :
( ( $false
= ( ( suc @ X2 )
= ( suc @ X1 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X2: nat,X1: nat] :
( ( $true
= ( ( suc @ X2 )
!= ( suc @ X1 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: nat,X1: nat] :
( ( ( X2 != X1 )
= $false )
| ( $true
= ( ( suc @ X2 )
!= ( suc @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: nat,X1: nat] :
( ( ( X2 != X1 )
=> ( ( suc @ X2 )
!= ( suc @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: nat,X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( Y0 != X1 )
=> ( ( suc @ Y0 )
!= ( suc @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( Y0 != X1 )
=> ( ( suc @ Y0 )
!= ( suc @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y1 != Y0 )
=> ( ( suc @ Y1 )
!= ( suc @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y1 != Y0 )
=> ( ( suc @ Y1 )
!= ( suc @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y1 != Y0 )
=> ( ( suc @ Y1 )
!= ( suc @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( suc @ X0 )
!= ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X3: nat,X2: nat] :
( ( X2 != X3 )
=> ( ( suc @ X2 )
!= ( suc @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz1) ).
thf(f429,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[status(thm)],[f428]) ).
thf(f428,plain,
( $false
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f426]) ).
thf(f426,plain,
( ( ( pl @ x @ y )
!= ( pl @ x @ y ) )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f418,f30]) ).
thf(f30,plain,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( ( ( pl @ x @ y )
!= ( pl @ x @ z ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( ( pl @ x @ y )
!= ( pl @ x @ z ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz8) ).
thf(f418,plain,
( ! [X0: nat] :
( ( pl @ X0 @ y )
!= ( pl @ X0 @ z ) )
| ~ spl0_14 ),
inference(equality_proxy_clausification,[status(thm)],[f417]) ).
thf(f417,plain,
( ! [X0: nat] :
( $false
= ( ( pl @ X0 @ y )
= ( pl @ X0 @ z ) ) )
| ~ spl0_14 ),
inference(not_proxy_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
( ! [X0: nat] :
( ( ( pl @ X0 @ y )
!= ( pl @ X0 @ z ) )
= $true )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f414]) ).
thf(f414,plain,
( ! [X0: nat] :
( $true
= ( ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
@ X0 ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f396]) ).
thf(f396,plain,
( ! [X0: nat] :
( ( $true
= ( ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
@ X0 ) )
| ( $false = $true ) )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f332,f49]) ).
thf(f49,plain,
! [X2: nat > $o,X1: nat] :
( ( $false
= ( esti @ X1 @ ( setof @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X2 ) )
=> ( X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: nat > $o,X1: nat] :
( ( ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: nat] :
( ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( esti @ X1 @ ( setof @ Y0 ) )
=> ( Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( esti @ Y0 @ ( setof @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat > $o,X1: nat] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat > $o,X1: nat] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',estie) ).
thf(f332,plain,
( ! [X0: nat] :
( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f331]) ).
thf(f331,definition,
( spl0_14
<=> ! [X0: nat] :
( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f376,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[status(thm)],[f375]) ).
thf(f375,plain,
( $false
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f374,f25]) ).
thf(f25,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
y != z,
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
y != z,
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',n) ).
thf(f374,plain,
( ( y = z )
| ~ spl0_13 ),
inference(equality_resolution,[status(thm)],[f371]) ).
thf(f371,plain,
( ! [X0: nat] :
( ( ( suc @ X0 )
!= ( suc @ y ) )
| ( z = X0 ) )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f108,f359]) ).
thf(f359,plain,
( ( ( suc @ y )
= ( suc @ z ) )
| ~ spl0_13 ),
inference(equality_proxy_clausification,[status(thm)],[f358]) ).
thf(f358,plain,
( ( $true
= ( ( suc @ y )
= ( suc @ z ) ) )
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f357]) ).
thf(f357,plain,
( ( $false
= ( ( suc @ y )
!= ( suc @ z ) ) )
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f356,f35]) ).
thf(f35,plain,
! [X1: nat] :
( ( suc @ X1 )
= ( pl @ n_1 @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: nat] :
( ( ( pl @ n_1 @ X1 )
= ( suc @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( pl @ n_1 @ Y0 )
= ( suc @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: nat] :
( ( pl @ n_1 @ X0 )
= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X2: nat] :
( ( suc @ X2 )
= ( pl @ n_1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz4g) ).
thf(f356,plain,
( ( $false
= ( ( suc @ y )
!= ( pl @ n_1 @ z ) ) )
| ~ spl0_13 ),
inference(forward_demodulation,[status(thm)],[f355,f35]) ).
thf(f355,plain,
( ( $false
= ( ( pl @ n_1 @ y )
!= ( pl @ n_1 @ z ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f354]) ).
thf(f354,plain,
( ( ( ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
@ n_1 )
= $false )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ( $false = $true )
| ( ( ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
@ n_1 )
= $false )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f298,f88]) ).
thf(f88,plain,
! [X2: nat,X1: nat > $o] :
( ( $true
= ( esti @ X2 @ ( setof @ X1 ) ) )
| ( $false
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: nat,X1: nat > $o] :
( ( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ^ [Y0: nat] :
( ( X1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: nat > $o] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( X1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: nat > $o] :
( $true
= ( ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: nat > $o] :
( ( X1 @ X0 )
=> ( esti @ X0 @ ( setof @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: nat,X0: nat > $o] :
( ( X0 @ X1 )
=> ( esti @ X1 @ ( setof @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',estii) ).
thf(f298,plain,
( ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f296]) ).
thf(f296,definition,
( spl0_13
<=> ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f345,plain,
( spl0_14
| spl0_13
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f344,f334,f296,f331]) ).
thf(f344,plain,
! [X0: nat] :
( ( ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ z )
= ( suc
@ ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y ) ) )
| ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f313,f72]) ).
thf(f313,plain,
! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true )
| ( ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ z )
= ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ y ) )
| ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f312]) ).
thf(f312,plain,
! [X0: nat] :
( ( ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ z )
= ( pl
@ ( suc
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
@ y ) )
| ( $false = $true )
| ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f64,f99]) ).
thf(f99,plain,
! [X1: nat] :
( ( ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true )
| ( ( pl @ X1 @ z )
= ( pl @ X1 @ y ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: nat] :
( ( $true
= ( ( pl @ X1 @ y )
= ( pl @ X1 @ z ) ) )
| ( ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: nat] :
( ( $false
= ( ( pl @ X1 @ y )
!= ( pl @ X1 @ z ) ) )
| ( ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: nat] :
( ( ( ( pl @ X1 @ y )
!= ( pl @ X1 @ z ) )
=> ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
=> ( esti @ Y0
@ ( setof
@ ^ [Y1: nat] :
( ( pl @ Y1 @ y )
!= ( pl @ Y1 @ z ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) )
=> ( esti @ Y0
@ ( setof
@ ^ [Y1: nat] :
( ( pl @ Y1 @ y )
!= ( pl @ Y1 @ z ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) )
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ),
inference(heuristic_instantiation,[status(thm)],[f27]) ).
thf(f64,plain,
! [X2: nat,X1: set] :
( ( $false
= ( esti @ ( suc @ ( sK1 @ X1 ) ) @ X1 ) )
| ( ( esti @ X2 @ X1 )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( $false
= ( ( esti @ ( sK1 @ X1 ) @ X1 )
=> ( esti @ ( suc @ ( sK1 @ X1 ) ) @ X1 ) ) )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: nat,X1: set] :
( ( $false
= ( ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) )
@ ( sK1 @ X1 ) ) )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( ( esti @ X2 @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: nat,X1: set] :
( ( ( esti @ X2 @ X1 )
= $true )
| ( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) ) )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: nat,X1: set] :
( ( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) ) )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: nat] : ( esti @ Y0 @ X1 )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: set] :
( ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) )
| ( ( esti @ n_1 @ X1 )
= $false )
| ( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: set] :
( ( ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) )
= $true )
| ( ( esti @ n_1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,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)],[f56]) ).
thf(f56,plain,
! [X1: set] :
( $true
= ( ^ [Y0: set] :
( ( esti @ n_1 @ Y0 )
=> ( ( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ Y0 )
=> ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
=> ( !! @ nat
@ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,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)],[f19]) ).
thf(f19,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)],[f18]) ).
thf(f18,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)],[f3]) ).
thf(f3,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.iEVdslmYxZ/DTF2THF_22332.p',ax5) ).
thf(f302,plain,
( ~ spl0_12
| spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f287,f296,f292]) ).
thf(f287,plain,
( ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y )
!= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) )
| ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f284]) ).
thf(f284,plain,
( ( ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ y )
!= ( pl
@ ( sK1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
@ z ) )
| ( $false
= ( esti @ n_1
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f66,f48]) ).
thf(f48,plain,
! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $false )
| ( ( pl @ X0 @ y )
!= ( pl @ X0 @ z ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: nat] :
( ( $false
= ( ( pl @ X0 @ y )
= ( pl @ X0 @ z ) ) )
| ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: nat] :
( ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
= $false )
| ( ( ( pl @ X0 @ y )
!= ( pl @ X0 @ z ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: nat] :
( $true
= ( ( esti @ X0
@ ( setof
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) )
=> ( ( pl @ X0 @ y )
!= ( pl @ X0 @ z ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( esti @ X0 @ ( setof @ Y0 ) )
=> ( Y0 @ X0 ) )
@ ^ [Y0: nat] :
( ( pl @ Y0 @ y )
!= ( pl @ Y0 @ z ) ) ) ),
inference(heuristic_instantiation,[status(thm)],[f37]) ).
thf(f66,plain,
! [X0: set] :
( ( $true
= ( esti @ ( sK1 @ X0 ) @ X0 ) )
| ( ( esti @ n_1 @ X0 )
= $false ) ),
inference(condensation,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: nat,X1: set] :
( ( ( esti @ n_1 @ X1 )
= $false )
| ( ( esti @ X2 @ X1 )
= $true )
| ( $true
= ( esti @ ( sK1 @ X1 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM646^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 11:08:56 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : NUM646^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.45 % Domain : Number Theory
% 0.30/0.45 % Problem : Landau theorem 8
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : ~(pl x y = pl x z)
% 0.30/0.45
% 0.30/0.45 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.45 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : satz8 [Lan30]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % : Without extensionality : Theorem
% 0.30/0.45 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.80 v8.2.0, 1.00 v8.1.0, 0.91 v7.5.0, 1.00 v3.7.0
% 0.30/0.45 % Syntax : Number of formulae : 18 ( 6 unt; 10 typ; 0 def)
% 0.30/0.45 % Number of atoms : 12 ( 6 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 4 ( 1 avg)
% 0.30/0.45 % Number of connectives : 42 ( 4 ~; 0 |; 0 &; 32 @)
% 0.30/0.45 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 4 avg)
% 0.30/0.45 % Number of types : 3 ( 2 usr)
% 0.30/0.45 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(nat_type,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(x,type,
% 0.30/0.45 x: nat ).
% 0.30/0.45
% 0.30/0.45 thf(y,type,
% 0.30/0.45 y: nat ).
% 0.30/0.45
% 0.30/0.45 thf(z,type,
% 0.30/0.45 z: nat ).
% 0.30/0.45
% 0.30/0.45 thf(n,axiom,
% 0.30/0.45 y != z ).
% 0.30/0.45
% 0.30/0.45 thf(pl,type,
% 0.30/0.45 pl: nat > nat > nat ).
% 0.30/0.45
% 0.30/0.45 thf(set_type,type,
% 0.30/0.45 set: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(esti,type,
% 0.30/0.45 esti: nat > set > $o ).
% 0.30/0.45
% 0.30/0.45 thf(setof,type,
% 0.30/0.45 setof: ( nat > $o ) > set ).
% 0.30/0.45
% 0.30/0.45 thf(estie,axiom,
% 0.30/0.45 ! [Xp: nat > $o,Xs: nat] :
% 0.30/0.45 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.30/0.45 => ( Xp @ Xs ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(n_1,type,
% 0.30/0.45 n_1: nat ).
% 0.30/0.45
% 0.30/0.45 thf(suc,type,
% 0.30/0.45 suc: nat > nat ).
% 0.30/0.45
% 0.30/0.45 thf(ax5,axiom,
% 0.30/0.45 ! [Xs: set] :
% 0.30/0.45 ( ( esti @ n_1 @ Xs )
% 0.30/0.45 => ( ! [Xx: nat] :
% 0.30/0.45 ( ( esti @ Xx @ Xs )
% 0.30/0.45 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.30/0.45 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(estii,axiom,
% 0.30/0.45 ! [Xp: nat > $o,Xs: nat] :
% 0.30/0.45 ( ( Xp @ Xs )
% 0.30/0.45 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz1,axiom,
% 0.30/0.45 ! [Xx: nat,Xy: nat] :
% 0.30/0.45 ( ( Xx != Xy )
% 0.30/0.45 => ( ( suc @ Xx )
% 0.30/0.45 != ( suc @ Xy ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz4g,axiom,
% 0.30/0.45 ! [Xx: nat] :
% 0.30/0.45 ( ( suc @ Xx )
% 0.30/0.45 = ( pl @ n_1 @ Xx ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz4h,axiom,
% 0.30/0.45 ! [Xx: nat,Xy: nat] :
% 0.30/0.45 ( ( suc @ ( pl @ Xx @ Xy ) )
% 0.30/0.45 = ( pl @ ( suc @ Xx ) @ Xy ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(satz8,conjecture,
% 0.30/0.45 ( ( pl @ x @ y )
% 0.30/0.45 != ( pl @ x @ z ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 11:08:57 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2DTF22332.p
% See solution above
% 1.47/1.29 ------------------------
% 1.68/1.30 ---- Cleaned THF ---
% 1.68/1.30 thf(nat_type,type,
% 1.68/1.30 nat: $tType ).
% 1.68/1.30
% 1.68/1.30 thf(x,type,
% 1.68/1.30 x: nat ).
% 1.68/1.30
% 1.68/1.30 thf(y,type,
% 1.68/1.30 y: nat ).
% 1.68/1.30
% 1.68/1.30 thf(z,type,
% 1.68/1.30 z: nat ).
% 1.68/1.30
% 1.68/1.30 thf(n,axiom,
% 1.68/1.30 y != z ).
% 1.68/1.30
% 1.68/1.30 thf(pl,type,
% 1.68/1.30 pl: nat > nat > nat ).
% 1.68/1.30
% 1.68/1.30 thf(set_type,type,
% 1.68/1.30 set: $tType ).
% 1.68/1.30
% 1.68/1.30 thf(esti,type,
% 1.68/1.30 esti: nat > set > $o ).
% 1.68/1.30
% 1.68/1.30 thf(setof,type,
% 1.68/1.30 setof: ( nat > $o ) > set ).
% 1.68/1.30
% 1.68/1.30 thf(estie,axiom,
% 1.68/1.30 ! [Xp: nat > $o,Xs: nat] :
% 1.68/1.30 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.68/1.30 => ( Xp @ Xs ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(n_1,type,
% 1.68/1.30 n_1: nat ).
% 1.68/1.30
% 1.68/1.30 thf(suc,type,
% 1.68/1.30 suc: nat > nat ).
% 1.68/1.30
% 1.68/1.30 thf(ax5,axiom,
% 1.68/1.30 ! [Xs: set] :
% 1.68/1.30 ( ( esti @ n_1 @ Xs )
% 1.68/1.30 => ( ! [Xx: nat] :
% 1.68/1.30 ( ( esti @ Xx @ Xs )
% 1.68/1.30 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.68/1.30 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(estii,axiom,
% 1.68/1.30 ! [Xp: nat > $o,Xs: nat] :
% 1.68/1.30 ( ( Xp @ Xs )
% 1.68/1.30 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz1,axiom,
% 1.68/1.30 ! [Xx: nat,Xy: nat] :
% 1.68/1.30 ( ( Xx != Xy )
% 1.68/1.30 => ( ( suc @ Xx )
% 1.68/1.30 != ( suc @ Xy ) ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz4g,axiom,
% 1.68/1.30 ! [Xx: nat] :
% 1.68/1.30 ( ( suc @ Xx )
% 1.68/1.30 = ( pl @ n_1 @ Xx ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz4h,axiom,
% 1.68/1.30 ! [Xx: nat,Xy: nat] :
% 1.68/1.30 ( ( suc @ ( pl @ Xx @ Xy ) )
% 1.68/1.30 = ( pl @ ( suc @ Xx ) @ Xy ) ) ).
% 1.68/1.30
% 1.68/1.30 thf(satz8,conjecture,
% 1.68/1.30 ( ( pl @ x @ y )
% 1.68/1.30 != ( pl @ x @ z ) ) ).
% 1.68/1.30 ------------------------
% 1.68/1.32 % (22553)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/2Mi)
% 1.68/1.32 % (22553)Instruction limit reached!
% 1.68/1.32 % (22553)------------------------------
% 1.68/1.32 % (22553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (22553)Termination reason: Unknown
% 1.68/1.32 % (22553)Termination phase: Preprocessing 3
% 1.68/1.32
% 1.68/1.32 % (22553)Memory used [KB]: 895
% 1.68/1.32 % (22553)Time elapsed: 0.002 s
% 1.68/1.32 % (22553)Instructions burned: 2 (million)
% 1.68/1.32 % (22553)------------------------------
% 1.68/1.32 % (22553)------------------------------
% 1.68/1.32 % (22552)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_22332 for (2999ds/27Mi)
% 1.68/1.32 % (22552)Refutation not found, incomplete strategy
% 1.68/1.32 % (22552)------------------------------
% 1.68/1.32 % (22552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.32 % (22552)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.32
% 1.68/1.32
% 1.68/1.32 % (22552)Memory used [KB]: 5500
% 1.68/1.32 % (22552)Time elapsed: 0.003 s
% 1.68/1.32 % (22552)Instructions burned: 4 (million)
% 1.68/1.32 % (22552)------------------------------
% 1.68/1.32 % (22552)------------------------------
% 1.68/1.32 % (22550)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/183Mi)
% 1.68/1.32 % (22551)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_22332 for (2999ds/4Mi)
% 1.68/1.32 % (22554)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_22332 for (2999ds/2Mi)
% 1.68/1.32 % (22556)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/18Mi)
% 1.68/1.32 % (22555)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_22332 for (2999ds/275Mi)
% 1.68/1.33 % (22554)Instruction limit reached!
% 1.68/1.33 % (22554)------------------------------
% 1.68/1.33 % (22554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (22554)Termination reason: Unknown
% 1.68/1.33 % (22554)Termination phase: Property scanning
% 1.68/1.33
% 1.68/1.33 % (22554)Memory used [KB]: 895
% 1.68/1.33 % (22554)Time elapsed: 0.003 s
% 1.68/1.33 % (22554)Instructions burned: 2 (million)
% 1.68/1.33 % (22554)------------------------------
% 1.68/1.33 % (22554)------------------------------
% 1.68/1.33 % (22555)Refutation not found, incomplete strategy
% 1.68/1.33 % (22555)------------------------------
% 1.68/1.33 % (22555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (22555)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.33
% 1.68/1.33
% 1.68/1.33 % (22555)Memory used [KB]: 5500
% 1.68/1.33 % (22555)Time elapsed: 0.003 s
% 1.68/1.33 % (22555)Instructions burned: 1 (million)
% 1.68/1.33 % (22555)------------------------------
% 1.68/1.33 % (22555)------------------------------
% 1.68/1.33 % (22557)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/3Mi)
% 1.68/1.33 % (22551)Instruction limit reached!
% 1.68/1.33 % (22551)------------------------------
% 1.68/1.33 % (22551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (22551)Termination reason: Unknown
% 1.68/1.33 % (22551)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (22551)Memory used [KB]: 5500
% 1.68/1.33 % (22551)Time elapsed: 0.005 s
% 1.68/1.33 % (22551)Instructions burned: 5 (million)
% 1.68/1.33 % (22551)------------------------------
% 1.68/1.33 % (22551)------------------------------
% 1.68/1.33 % (22557)Instruction limit reached!
% 1.68/1.33 % (22557)------------------------------
% 1.68/1.33 % (22557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.33 % (22557)Termination reason: Unknown
% 1.68/1.33 % (22557)Termination phase: Saturation
% 1.68/1.33
% 1.68/1.33 % (22557)Memory used [KB]: 5500
% 1.68/1.33 % (22557)Time elapsed: 0.003 s
% 1.68/1.33 % (22557)Instructions burned: 5 (million)
% 1.68/1.33 % (22557)------------------------------
% 1.68/1.33 % (22557)------------------------------
% 1.68/1.33 % (22558)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_22332 for (2999ds/37Mi)
% 1.68/1.34 % (22556)Instruction limit reached!
% 1.68/1.34 % (22556)------------------------------
% 1.68/1.34 % (22556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (22556)Termination reason: Unknown
% 1.68/1.34 % (22556)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (22556)Memory used [KB]: 5628
% 1.68/1.34 % (22556)Time elapsed: 0.014 s
% 1.68/1.34 % (22556)Instructions burned: 18 (million)
% 1.68/1.34 % (22556)------------------------------
% 1.68/1.34 % (22556)------------------------------
% 1.68/1.34 % (22562)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/7Mi)
% 1.68/1.34 % (22562)Instruction limit reached!
% 1.68/1.34 % (22562)------------------------------
% 1.68/1.34 % (22562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (22562)Termination reason: Unknown
% 1.68/1.34 % (22562)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (22562)Memory used [KB]: 1023
% 1.68/1.34 % (22562)Time elapsed: 0.004 s
% 1.68/1.34 % (22562)Instructions burned: 7 (million)
% 1.68/1.34 % (22562)------------------------------
% 1.68/1.34 % (22562)------------------------------
% 1.68/1.34 % (22558)Instruction limit reached!
% 1.68/1.34 % (22558)------------------------------
% 1.68/1.34 % (22558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (22558)Termination reason: Unknown
% 1.68/1.34 % (22558)Termination phase: Saturation
% 1.68/1.34
% 1.68/1.34 % (22558)Memory used [KB]: 5884
% 1.68/1.34 % (22558)Time elapsed: 0.014 s
% 1.68/1.34 % (22558)Instructions burned: 37 (million)
% 1.68/1.34 % (22558)------------------------------
% 1.68/1.34 % (22558)------------------------------
% 1.68/1.34 % (22559)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_22332 for (2999ds/15Mi)
% 1.68/1.34 % (22560)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_22332 for (2999ds/3Mi)
% 1.68/1.34 % (22561)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_22332 for (2999ds/1041Mi)
% 1.68/1.34 % (22559)Refutation not found, incomplete strategy
% 1.68/1.34 % (22559)------------------------------
% 1.68/1.34 % (22559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.34 % (22559)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.34
% 1.68/1.34
% 1.68/1.34 % (22559)Memory used [KB]: 5500
% 1.68/1.34 % (22559)Time elapsed: 0.004 s
% 1.68/1.34 % (22559)Instructions burned: 3 (million)
% 1.68/1.34 % (22559)------------------------------
% 1.68/1.34 % (22559)------------------------------
% 1.68/1.35 % (22560)Instruction limit reached!
% 1.68/1.35 % (22560)------------------------------
% 1.68/1.35 % (22560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (22560)Termination reason: Unknown
% 1.68/1.35 % (22560)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (22560)Memory used [KB]: 5500
% 1.68/1.35 % (22560)Time elapsed: 0.004 s
% 1.68/1.35 % (22560)Instructions burned: 3 (million)
% 1.68/1.35 % (22560)------------------------------
% 1.68/1.35 % (22560)------------------------------
% 1.68/1.35 % (22564)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_22332 for (2999ds/3Mi)
% 1.68/1.35 % (22564)Instruction limit reached!
% 1.68/1.35 % (22564)------------------------------
% 1.68/1.35 % (22564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (22564)Termination reason: Unknown
% 1.68/1.35 % (22564)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (22564)Memory used [KB]: 5500
% 1.68/1.35 % (22564)Time elapsed: 0.002 s
% 1.68/1.35 % (22564)Instructions burned: 3 (million)
% 1.68/1.35 % (22564)------------------------------
% 1.68/1.35 % (22564)------------------------------
% 1.68/1.35 % (22565)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_22332 for (2999ds/3Mi)
% 1.68/1.35 % (22565)Instruction limit reached!
% 1.68/1.35 % (22565)------------------------------
% 1.68/1.35 % (22565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.35 % (22565)Termination reason: Unknown
% 1.68/1.35 % (22565)Termination phase: Saturation
% 1.68/1.35
% 1.68/1.35 % (22565)Memory used [KB]: 1023
% 1.68/1.35 % (22565)Time elapsed: 0.003 s
% 1.68/1.35 % (22565)Instructions burned: 4 (million)
% 1.68/1.35 % (22565)------------------------------
% 1.68/1.35 % (22565)------------------------------
% 1.68/1.35 % (22563)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/16Mi)
% 1.68/1.36 % (22568)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/4Mi)
% 1.68/1.36 % (22568)Instruction limit reached!
% 1.68/1.36 % (22568)------------------------------
% 1.68/1.36 % (22568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (22568)Termination reason: Unknown
% 1.68/1.36 % (22568)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (22568)Memory used [KB]: 5500
% 1.68/1.36 % (22568)Time elapsed: 0.003 s
% 1.68/1.36 % (22568)Instructions burned: 5 (million)
% 1.68/1.36 % (22568)------------------------------
% 1.68/1.36 % (22568)------------------------------
% 1.68/1.36 % (22566)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/7Mi)
% 1.68/1.36 % (22569)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/18Mi)
% 1.68/1.36 % (22567)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/3Mi)
% 1.68/1.36 % (22563)Instruction limit reached!
% 1.68/1.36 % (22563)------------------------------
% 1.68/1.36 % (22563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.36 % (22563)Termination reason: Unknown
% 1.68/1.36 % (22563)Termination phase: Saturation
% 1.68/1.36
% 1.68/1.36 % (22563)Memory used [KB]: 5628
% 1.68/1.36 % (22563)Time elapsed: 0.013 s
% 1.68/1.36 % (22563)Instructions burned: 17 (million)
% 1.68/1.36 % (22563)------------------------------
% 1.68/1.36 % (22563)------------------------------
% 1.68/1.37 % (22567)Instruction limit reached!
% 1.68/1.37 % (22567)------------------------------
% 1.68/1.37 % (22567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (22567)Termination reason: Unknown
% 1.68/1.37 % (22567)Termination phase: Saturation
% 1.68/1.37
% 1.68/1.37 % (22567)Memory used [KB]: 5500
% 1.68/1.37 % (22567)Time elapsed: 0.004 s
% 1.68/1.37 % (22567)Instructions burned: 3 (million)
% 1.68/1.37 % (22567)------------------------------
% 1.68/1.37 % (22567)------------------------------
% 1.68/1.37 % (22566)Refutation not found, incomplete strategy
% 1.68/1.37 % (22566)------------------------------
% 1.68/1.37 % (22566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (22566)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.37
% 1.68/1.37
% 1.68/1.37 % (22566)Memory used [KB]: 5500
% 1.68/1.37 % (22566)Time elapsed: 0.005 s
% 1.68/1.37 % (22566)Instructions burned: 4 (million)
% 1.68/1.37 % (22566)------------------------------
% 1.68/1.37 % (22566)------------------------------
% 1.68/1.37 % (22569)Refutation not found, incomplete strategy
% 1.68/1.37 % (22569)------------------------------
% 1.68/1.37 % (22569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.37 % (22569)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.37
% 1.68/1.37
% 1.68/1.37 % (22569)Memory used [KB]: 5500
% 1.68/1.37 % (22569)Time elapsed: 0.005 s
% 1.68/1.37 % (22569)Instructions burned: 9 (million)
% 1.68/1.37 % (22569)------------------------------
% 1.68/1.37 % (22569)------------------------------
% 1.68/1.37 % (22570)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/710Mi)
% 1.68/1.38 % (22574)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/5Mi)
% 1.68/1.38 % (22574)Instruction limit reached!
% 1.68/1.38 % (22574)------------------------------
% 1.68/1.38 % (22574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (22574)Termination reason: Unknown
% 1.68/1.38 % (22574)Termination phase: Saturation
% 1.68/1.38
% 1.68/1.38 % (22574)Memory used [KB]: 5500
% 1.68/1.38 % (22574)Time elapsed: 0.004 s
% 1.68/1.38 % (22574)Instructions burned: 6 (million)
% 1.68/1.38 % (22574)------------------------------
% 1.68/1.38 % (22574)------------------------------
% 1.68/1.38 % (22571)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/6Mi)
% 1.68/1.38 % (22572)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_22332 for (2999ds/902Mi)
% 1.68/1.38 % (22573)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_22332 for (2999ds/21Mi)
% 1.68/1.38 % (22572)Refutation not found, incomplete strategy
% 1.68/1.38 % (22572)------------------------------
% 1.68/1.38 % (22572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.38 % (22572)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.38
% 1.68/1.38
% 1.68/1.38 % (22572)Memory used [KB]: 5500
% 1.68/1.38 % (22572)Time elapsed: 0.003 s
% 1.68/1.38 % (22572)Instructions burned: 2 (million)
% 1.68/1.38 % (22572)------------------------------
% 1.68/1.38 % (22572)------------------------------
% 1.68/1.39 % (22571)Instruction limit reached!
% 1.68/1.39 % (22571)------------------------------
% 1.68/1.39 % (22571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (22571)Termination reason: Unknown
% 1.68/1.39 % (22571)Termination phase: Saturation
% 1.68/1.39
% 1.68/1.39 % (22571)Memory used [KB]: 5500
% 1.68/1.39 % (22571)Time elapsed: 0.006 s
% 1.68/1.39 % (22571)Instructions burned: 6 (million)
% 1.68/1.39 % (22571)------------------------------
% 1.68/1.39 % (22571)------------------------------
% 1.68/1.39 % (22575)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_22332 for (2999ds/6Mi)
% 1.68/1.39 % (22575)Refutation not found, incomplete strategy
% 1.68/1.39 % (22575)------------------------------
% 1.68/1.39 % (22575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.39 % (22575)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.39
% 1.68/1.39
% 1.68/1.39 % (22575)Memory used [KB]: 5500
% 1.68/1.39 % (22575)Time elapsed: 0.003 s
% 1.68/1.39 % (22575)Instructions burned: 4 (million)
% 1.68/1.39 % (22575)------------------------------
% 1.68/1.39 % (22575)------------------------------
% 1.69/1.40 % (22573)Instruction limit reached!
% 1.69/1.40 % (22573)------------------------------
% 1.69/1.40 % (22573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (22573)Termination reason: Unknown
% 1.69/1.40 % (22573)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (22573)Memory used [KB]: 5628
% 1.69/1.40 % (22573)Time elapsed: 0.016 s
% 1.69/1.40 % (22573)Instructions burned: 21 (million)
% 1.69/1.40 % (22573)------------------------------
% 1.69/1.40 % (22573)------------------------------
% 1.69/1.40 % (22578)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_22332 for (2999ds/19Mi)
% 1.69/1.40 % (22576)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/377Mi)
% 1.69/1.40 % (22578)Refutation not found, incomplete strategy
% 1.69/1.40 % (22578)------------------------------
% 1.69/1.40 % (22578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (22578)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.40
% 1.69/1.40
% 1.69/1.40 % (22578)Memory used [KB]: 5500
% 1.69/1.40 % (22578)Time elapsed: 0.003 s
% 1.69/1.40 % (22578)Instructions burned: 4 (million)
% 1.69/1.40 % (22578)------------------------------
% 1.69/1.40 % (22578)------------------------------
% 1.69/1.40 % (22550)Instruction limit reached!
% 1.69/1.40 % (22550)------------------------------
% 1.69/1.40 % (22550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (22550)Termination reason: Unknown
% 1.69/1.40 % (22550)Termination phase: Saturation
% 1.69/1.40
% 1.69/1.40 % (22550)Memory used [KB]: 6396
% 1.69/1.40 % (22550)Time elapsed: 0.082 s
% 1.69/1.40 % (22550)Instructions burned: 186 (million)
% 1.69/1.40 % (22550)------------------------------
% 1.69/1.40 % (22550)------------------------------
% 1.69/1.40 % (22577)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_22332 for (2999ds/779Mi)
% 1.69/1.41 % (22580)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/17Mi)
% 1.69/1.41 % (22581)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/3Mi)
% 1.69/1.42 % (22581)Instruction limit reached!
% 1.69/1.42 % (22581)------------------------------
% 1.69/1.42 % (22581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (22581)Termination reason: Unknown
% 1.69/1.42 % (22581)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (22581)Memory used [KB]: 1023
% 1.69/1.42 % (22581)Time elapsed: 0.003 s
% 1.69/1.42 % (22581)Instructions burned: 4 (million)
% 1.69/1.42 % (22581)------------------------------
% 1.69/1.42 % (22581)------------------------------
% 1.69/1.42 % (22579)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/879Mi)
% 1.69/1.42 % (22580)Instruction limit reached!
% 1.69/1.42 % (22580)------------------------------
% 1.69/1.42 % (22580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (22580)Termination reason: Unknown
% 1.69/1.42 % (22580)Termination phase: Saturation
% 1.69/1.42
% 1.69/1.42 % (22580)Memory used [KB]: 5628
% 1.69/1.42 % (22580)Time elapsed: 0.030 s
% 1.69/1.42 % (22580)Instructions burned: 18 (million)
% 1.69/1.42 % (22580)------------------------------
% 1.69/1.42 % (22580)------------------------------
% 1.69/1.43 % (22582)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22332 for (2999ds/30Mi)
% 1.69/1.43 % (22583)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22332 for (2998ds/127Mi)
% 1.69/1.44 % (22582)Instruction limit reached!
% 1.69/1.44 % (22582)------------------------------
% 1.69/1.44 % (22582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (22582)Termination reason: Unknown
% 1.69/1.44 % (22582)Termination phase: Saturation
% 1.69/1.44
% 1.69/1.44 % (22582)Memory used [KB]: 5628
% 1.69/1.44 % (22582)Time elapsed: 0.035 s
% 1.69/1.44 % (22582)Instructions burned: 32 (million)
% 1.69/1.44 % (22582)------------------------------
% 1.69/1.44 % (22582)------------------------------
% 1.69/1.44 % (22579)Refutation not found, incomplete strategy
% 1.69/1.44 % (22579)------------------------------
% 1.69/1.44 % (22579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.44 % (22579)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.44
% 1.69/1.44
% 1.69/1.44 % (22579)Memory used [KB]: 5628
% 1.69/1.44 % (22579)Time elapsed: 0.048 s
% 1.69/1.44 % (22579)Instructions burned: 39 (million)
% 1.69/1.44 % (22579)------------------------------
% 1.69/1.44 % (22579)------------------------------
% 1.69/1.45 % (22584)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22332 for (2998ds/100Mi)
% 1.69/1.45 % (22585)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_22332 for (2998ds/3Mi)
% 1.69/1.46 % (22585)Instruction limit reached!
% 1.69/1.46 % (22585)------------------------------
% 1.69/1.46 % (22585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (22585)Termination reason: Unknown
% 1.69/1.46 % (22585)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (22585)Memory used [KB]: 5500
% 1.69/1.46 % (22585)Time elapsed: 0.003 s
% 1.69/1.46 % (22585)Instructions burned: 4 (million)
% 1.69/1.46 % (22585)------------------------------
% 1.69/1.46 % (22585)------------------------------
% 1.69/1.47 % (22586)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_22332 for (2998ds/20Mi)
% 1.69/1.47 % (22586)Refutation not found, incomplete strategy
% 1.69/1.47 % (22586)------------------------------
% 1.69/1.47 % (22586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (22586)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.47
% 1.69/1.47
% 1.69/1.47 % (22586)Memory used [KB]: 5500
% 1.69/1.47 % (22586)Time elapsed: 0.002 s
% 1.69/1.47 % (22586)Instructions burned: 1 (million)
% 1.69/1.47 % (22586)------------------------------
% 1.69/1.47 % (22586)------------------------------
% 1.69/1.47 % (22584)First to succeed.
% 1.69/1.47 % (22583)Instruction limit reached!
% 1.69/1.47 % (22583)------------------------------
% 1.69/1.47 % (22583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (22583)Termination reason: Unknown
% 1.69/1.47 % (22583)Termination phase: Saturation
% 1.69/1.47
% 1.69/1.47 % (22583)Memory used [KB]: 6012
% 1.69/1.47 % (22583)Time elapsed: 0.069 s
% 1.69/1.47 % (22583)Instructions burned: 129 (million)
% 1.69/1.47 % (22583)------------------------------
% 1.69/1.47 % (22583)------------------------------
% 1.69/1.48 % (22584)Refutation found. Thanks to Tanya!
% 1.69/1.48 % SZS status Theorem for DTF2THF_22332
% 1.69/1.48 % SZS output start Proof for DTF2THF_22332
% 1.69/1.48 thf(type_def_5, type, nat: $tType).
% 1.69/1.48 thf(type_def_7, type, set: $tType).
% 1.69/1.48 thf(func_def_0, type, nat: $tType).
% 1.69/1.48 thf(func_def_1, type, x: nat).
% 1.69/1.48 thf(func_def_2, type, y: nat).
% 1.69/1.48 thf(func_def_3, type, z: nat).
% 1.69/1.48 thf(func_def_4, type, pl: nat > nat > nat).
% 1.69/1.48 thf(func_def_5, type, set: $tType).
% 1.69/1.48 thf(func_def_6, type, esti: nat > set > $o).
% 1.69/1.48 thf(func_def_7, type, setof: (nat > $o) > set).
% 1.69/1.48 thf(func_def_9, type, n_1: nat).
% 1.69/1.48 thf(func_def_10, type, suc: nat > nat).
% 1.69/1.48 thf(func_def_21, type, sK1: set > nat).
% 1.69/1.48 thf(func_def_22, type, ph2: !>[X0: $tType]:(X0)).
% 1.69/1.48 thf(f442,plain,(
% 1.69/1.48 $false),
% 1.69/1.48 inference(avatar_sat_refutation,[status(thm)],[f302,f345,f376,f429,f441])).
% 1.69/1.48 thf(f441,plain,(
% 1.69/1.48 spl0_12 | ~spl0_15),
% 1.69/1.48 inference(avatar_contradiction_clause,[status(thm)],[f440])).
% 1.69/1.48 thf(f440,plain,(
% 1.69/1.48 $false | (spl0_12 | ~spl0_15)),
% 1.69/1.48 inference(subsumption_resolution,[status(thm)],[f439,f294])).
% 1.69/1.48 thf(f294,plain,(
% 1.69/1.48 ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y) != (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z)) | spl0_12),
% 1.69/1.48 inference(avatar_component_clause,[status(thm)],[f292])).
% 1.69/1.48 thf(f292,definition,(
% 1.69/1.48 spl0_12 <=> ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z))),
% 1.69/1.48 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.69/1.48 thf(f439,plain,(
% 1.69/1.48 ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y) = (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z)) | ~spl0_15),
% 1.69/1.48 inference(equality_resolution,[status(thm)],[f435])).
% 1.69/1.48 thf(f435,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((suc @ X0) != (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y))) | ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z) = X0)) ) | ~spl0_15),
% 1.69/1.48 inference(superposition,[status(thm)],[f108,f433])).
% 1.69/1.48 thf(f433,plain,(
% 1.69/1.48 ((suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y)) = (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z))) | ~spl0_15),
% 1.69/1.48 inference(superposition,[status(thm)],[f72,f336])).
% 1.69/1.48 thf(f336,plain,(
% 1.69/1.48 ((pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ z) = (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y))) | ~spl0_15),
% 1.69/1.48 inference(avatar_component_clause,[status(thm)],[f334])).
% 1.69/1.48 thf(f334,definition,(
% 1.69/1.48 spl0_15 <=> ((pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ z) = (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y)))),
% 1.69/1.48 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.69/1.48 thf(f72,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (((pl @ (suc @ X1) @ X2) = (suc @ (pl @ X1 @ X2)))) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f71])).
% 1.69/1.48 thf(f71,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : ((((suc @ (pl @ X1 @ X2)) = (pl @ (suc @ X1) @ X2)) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.69/1.48 thf(f70,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : ((((^[Y0 : nat]: ((suc @ (pl @ X1 @ Y0)) = (pl @ (suc @ X1) @ Y0))) @ X2) = $true)) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f69])).
% 1.69/1.48 thf(f69,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((suc @ (pl @ X1 @ Y0)) = (pl @ (suc @ X1) @ Y0)))))) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.69/1.48 thf(f68,plain,(
% 1.69/1.48 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1))))) @ X1) = $true)) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f26])).
% 1.69/1.48 thf(f26,plain,(
% 1.69/1.48 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1)))))) = $true)),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f13])).
% 1.69/1.48 thf(f13,plain,(
% 1.69/1.48 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((suc @ (pl @ Y0 @ Y1)) = (pl @ (suc @ Y0) @ Y1)))))) = $true)),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f12])).
% 1.69/1.48 thf(f12,plain,(
% 1.69/1.48 ! [X0 : nat,X1 : nat] : ((suc @ (pl @ X1 @ X0)) = (pl @ (suc @ X1) @ X0))),
% 1.69/1.48 inference(rectify,[status(thm)],[f7])).
% 1.69/1.48 thf(f7,axiom,(
% 1.69/1.48 ! [X3 : nat,X2 : nat] : ((suc @ (pl @ X2 @ X3)) = (pl @ (suc @ X2) @ X3))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz4h)).
% 1.69/1.48 thf(f108,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (((suc @ X2) != (suc @ X1)) | (X1 = X2)) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f107])).
% 1.69/1.48 thf(f107,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (($true = (X2 = X1)) | ((suc @ X2) != (suc @ X1))) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f106])).
% 1.69/1.48 thf(f106,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (($false = ((suc @ X2) = (suc @ X1))) | ($true = (X2 = X1))) )),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f105])).
% 1.69/1.48 thf(f105,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (($true = (~ ((suc @ X2) = (suc @ X1)))) | ($true = (X2 = X1))) )),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f104])).
% 1.69/1.48 thf(f104,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (((~ (X2 = X1)) = $false) | ($true = (~ ((suc @ X2) = (suc @ X1))))) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.69/1.48 thf(f103,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : ((((~ (X2 = X1)) => (~ ((suc @ X2) = (suc @ X1)))) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.69/1.48 thf(f102,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((~ (Y0 = X1)) => (~ ((suc @ Y0) = (suc @ X1))))) @ X2))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f101])).
% 1.69/1.48 thf(f101,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((~ (Y0 = X1)) => (~ ((suc @ Y0) = (suc @ X1)))))))) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.69/1.48 thf(f100,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((~ (Y1 = Y0)) => (~ ((suc @ Y1) = (suc @ Y0))))))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f31])).
% 1.69/1.48 thf(f31,plain,(
% 1.69/1.48 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((~ (Y1 = Y0)) => (~ ((suc @ Y1) = (suc @ Y0)))))))))),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.48 thf(f15,plain,(
% 1.69/1.48 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((~ (Y1 = Y0)) => (~ ((suc @ Y1) = (suc @ Y0)))))))))),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f14])).
% 1.69/1.48 thf(f14,plain,(
% 1.69/1.48 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((suc @ X0) != (suc @ X1)))),
% 1.69/1.48 inference(rectify,[status(thm)],[f5])).
% 1.69/1.48 thf(f5,axiom,(
% 1.69/1.48 ! [X3 : nat,X2 : nat] : ((X2 != X3) => ((suc @ X2) != (suc @ X3)))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz1)).
% 1.69/1.48 thf(f429,plain,(
% 1.69/1.48 ~spl0_14),
% 1.69/1.48 inference(avatar_contradiction_clause,[status(thm)],[f428])).
% 1.69/1.48 thf(f428,plain,(
% 1.69/1.48 $false | ~spl0_14),
% 1.69/1.48 inference(trivial_inequality_removal,[status(thm)],[f426])).
% 1.69/1.48 thf(f426,plain,(
% 1.69/1.48 ((pl @ x @ y) != (pl @ x @ y)) | ~spl0_14),
% 1.69/1.48 inference(superposition,[status(thm)],[f418,f30])).
% 1.69/1.48 thf(f30,plain,(
% 1.69/1.48 ((pl @ x @ y) = (pl @ x @ z))),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.69/1.48 thf(f24,plain,(
% 1.69/1.48 ((pl @ x @ y) = (pl @ x @ z))),
% 1.69/1.48 inference(flattening,[status(thm)],[f9])).
% 1.69/1.48 thf(f9,negated_conjecture,(
% 1.69/1.48 ~((pl @ x @ y) != (pl @ x @ z))),
% 1.69/1.48 inference(negated_conjecture,[status(cth)],[f8])).
% 1.69/1.48 thf(f8,conjecture,(
% 1.69/1.48 ((pl @ x @ y) != (pl @ x @ z))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz8)).
% 1.69/1.48 thf(f418,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((pl @ X0 @ y) != (pl @ X0 @ z))) ) | ~spl0_14),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f417])).
% 1.69/1.48 thf(f417,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($false = ((pl @ X0 @ y) = (pl @ X0 @ z)))) ) | ~spl0_14),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f415])).
% 1.69/1.48 thf(f415,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((~ ((pl @ X0 @ y) = (pl @ X0 @ z))) = $true)) ) | ~spl0_14),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f414])).
% 1.69/1.48 thf(f414,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($true = ((^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))) @ X0))) ) | ~spl0_14),
% 1.69/1.48 inference(trivial_inequality_removal,[status(thm)],[f396])).
% 1.69/1.48 thf(f396,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($true = ((^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))) @ X0)) | ($false = $true)) ) | ~spl0_14),
% 1.69/1.48 inference(superposition,[status(thm)],[f332,f49])).
% 1.69/1.48 thf(f49,plain,(
% 1.69/1.48 ( ! [X2 : nat > $o,X1 : nat] : (($false = (esti @ X1 @ (setof @ X2))) | ($true = (X2 @ X1))) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.69/1.48 thf(f44,plain,(
% 1.69/1.48 ( ! [X2 : nat > $o,X1 : nat] : ((((esti @ X1 @ (setof @ X2)) => (X2 @ X1)) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.69/1.48 thf(f41,plain,(
% 1.69/1.48 ( ! [X2 : nat > $o,X1 : nat] : ((((^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1))) @ X2) = $true)) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f37])).
% 1.69/1.48 thf(f37,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (((!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((esti @ X1 @ (setof @ Y0)) => (Y0 @ X1)))) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.69/1.48 thf(f36,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0))))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f28])).
% 1.69/1.48 thf(f28,plain,(
% 1.69/1.48 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))) = $true)),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.48 thf(f17,plain,(
% 1.69/1.48 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((esti @ Y0 @ (setof @ Y1)) => (Y1 @ Y0)))))) = $true)),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f16])).
% 1.69/1.48 thf(f16,plain,(
% 1.69/1.48 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.69/1.48 inference(rectify,[status(thm)],[f2])).
% 1.69/1.48 thf(f2,axiom,(
% 1.69/1.48 ! [X0 : nat > $o,X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',estie)).
% 1.69/1.48 thf(f332,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)) ) | ~spl0_14),
% 1.69/1.48 inference(avatar_component_clause,[status(thm)],[f331])).
% 1.69/1.48 thf(f331,definition,(
% 1.69/1.48 spl0_14 <=> ! [X0 : nat] : ((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)),
% 1.69/1.48 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.69/1.48 thf(f376,plain,(
% 1.69/1.48 ~spl0_13),
% 1.69/1.48 inference(avatar_contradiction_clause,[status(thm)],[f375])).
% 1.69/1.48 thf(f375,plain,(
% 1.69/1.48 $false | ~spl0_13),
% 1.69/1.48 inference(subsumption_resolution,[status(thm)],[f374,f25])).
% 1.69/1.48 thf(f25,plain,(
% 1.69/1.48 (y != z)),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.48 thf(f11,plain,(
% 1.69/1.48 (y != z)),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f1])).
% 1.69/1.48 thf(f1,axiom,(
% 1.69/1.48 (y != z)),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',n)).
% 1.69/1.48 thf(f374,plain,(
% 1.69/1.48 (y = z) | ~spl0_13),
% 1.69/1.48 inference(equality_resolution,[status(thm)],[f371])).
% 1.69/1.48 thf(f371,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((suc @ X0) != (suc @ y)) | (z = X0)) ) | ~spl0_13),
% 1.69/1.48 inference(superposition,[status(thm)],[f108,f359])).
% 1.69/1.48 thf(f359,plain,(
% 1.69/1.48 ((suc @ y) = (suc @ z)) | ~spl0_13),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f358])).
% 1.69/1.48 thf(f358,plain,(
% 1.69/1.48 ($true = ((suc @ y) = (suc @ z))) | ~spl0_13),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f357])).
% 1.69/1.48 thf(f357,plain,(
% 1.69/1.48 ($false = (~ ((suc @ y) = (suc @ z)))) | ~spl0_13),
% 1.69/1.48 inference(forward_demodulation,[status(thm)],[f356,f35])).
% 1.69/1.48 thf(f35,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (((suc @ X1) = (pl @ n_1 @ X1))) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.69/1.48 thf(f34,plain,(
% 1.69/1.48 ( ! [X1 : nat] : ((((pl @ n_1 @ X1) = (suc @ X1)) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.69/1.48 thf(f33,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f32])).
% 1.69/1.48 thf(f32,plain,(
% 1.69/1.48 ($true = (!! @ nat @ (^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0)))))),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f21])).
% 1.69/1.48 thf(f21,plain,(
% 1.69/1.48 ($true = (!! @ nat @ (^[Y0 : nat]: ((pl @ n_1 @ Y0) = (suc @ Y0)))))),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f20])).
% 1.69/1.48 thf(f20,plain,(
% 1.69/1.48 ! [X0 : nat] : ((pl @ n_1 @ X0) = (suc @ X0))),
% 1.69/1.48 inference(rectify,[status(thm)],[f6])).
% 1.69/1.48 thf(f6,axiom,(
% 1.69/1.48 ! [X2 : nat] : ((suc @ X2) = (pl @ n_1 @ X2))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',satz4g)).
% 1.69/1.48 thf(f356,plain,(
% 1.69/1.48 ($false = (~ ((suc @ y) = (pl @ n_1 @ z)))) | ~spl0_13),
% 1.69/1.48 inference(forward_demodulation,[status(thm)],[f355,f35])).
% 1.69/1.48 thf(f355,plain,(
% 1.69/1.48 ($false = (~ ((pl @ n_1 @ y) = (pl @ n_1 @ z)))) | ~spl0_13),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f354])).
% 1.69/1.48 thf(f354,plain,(
% 1.69/1.48 (((^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))) @ n_1) = $false) | ~spl0_13),
% 1.69/1.48 inference(trivial_inequality_removal,[status(thm)],[f346])).
% 1.69/1.48 thf(f346,plain,(
% 1.69/1.48 ($false = $true) | (((^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))) @ n_1) = $false) | ~spl0_13),
% 1.69/1.48 inference(superposition,[status(thm)],[f298,f88])).
% 1.69/1.48 thf(f88,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat > $o] : (($true = (esti @ X2 @ (setof @ X1))) | ($false = (X1 @ X2))) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.69/1.48 thf(f87,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat > $o] : ((((X1 @ X2) => (esti @ X2 @ (setof @ X1))) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.69/1.48 thf(f86,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((^[Y0 : nat]: ((X1 @ Y0) => (esti @ Y0 @ (setof @ X1)))) @ X2))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f79])).
% 1.69/1.48 thf(f79,plain,(
% 1.69/1.48 ( ! [X1 : nat > $o] : (((!! @ nat @ (^[Y0 : nat]: ((X1 @ Y0) => (esti @ Y0 @ (setof @ X1))))) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f76])).
% 1.69/1.48 thf(f76,plain,(
% 1.69/1.48 ( ! [X1 : nat > $o] : (($true = ((^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0)))))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f27])).
% 1.69/1.48 thf(f27,plain,(
% 1.69/1.48 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0))))))))),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f23])).
% 1.69/1.48 thf(f23,plain,(
% 1.69/1.48 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0))))))))),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f22])).
% 1.69/1.48 thf(f22,plain,(
% 1.69/1.48 ! [X0 : nat,X1 : nat > $o] : ((X1 @ X0) => (esti @ X0 @ (setof @ X1)))),
% 1.69/1.48 inference(rectify,[status(thm)],[f4])).
% 1.69/1.48 thf(f4,axiom,(
% 1.69/1.48 ! [X1 : nat,X0 : nat > $o] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',estii)).
% 1.69/1.48 thf(f298,plain,(
% 1.69/1.48 ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) | ~spl0_13),
% 1.69/1.48 inference(avatar_component_clause,[status(thm)],[f296])).
% 1.69/1.48 thf(f296,definition,(
% 1.69/1.48 spl0_13 <=> ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))))),
% 1.69/1.48 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.69/1.48 thf(f345,plain,(
% 1.69/1.48 spl0_14 | spl0_13 | spl0_15),
% 1.69/1.48 inference(avatar_split_clause,[status(thm)],[f344,f334,f296,f331])).
% 1.69/1.48 thf(f344,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ z) = (suc @ (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y))) | ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)) )),
% 1.69/1.48 inference(forward_demodulation,[status(thm)],[f313,f72])).
% 1.69/1.48 thf(f313,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true) | ((pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ z) = (pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ y)) | ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))))) )),
% 1.69/1.48 inference(trivial_inequality_removal,[status(thm)],[f312])).
% 1.69/1.48 thf(f312,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ z) = (pl @ (suc @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) @ y)) | ($false = $true) | ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)) )),
% 1.69/1.48 inference(superposition,[status(thm)],[f64,f99])).
% 1.69/1.48 thf(f99,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true) | ((pl @ X1 @ z) = (pl @ X1 @ y))) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f98])).
% 1.69/1.48 thf(f98,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = ((pl @ X1 @ y) = (pl @ X1 @ z))) | ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)) )),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f97])).
% 1.69/1.48 thf(f97,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($false = (~ ((pl @ X1 @ y) = (pl @ X1 @ z)))) | ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $true)) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.69/1.48 thf(f96,plain,(
% 1.69/1.48 ( ! [X1 : nat] : ((((~ ((pl @ X1 @ y) = (pl @ X1 @ z))) => (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) = $true)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.69/1.48 thf(f95,plain,(
% 1.69/1.48 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))) => (esti @ Y0 @ (setof @ (^[Y1 : nat]: (~ ((pl @ Y1 @ y) = (pl @ Y1 @ z)))))))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f77])).
% 1.69/1.48 thf(f77,plain,(
% 1.69/1.48 ($true = (!! @ nat @ (^[Y0 : nat]: ((~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))) => (esti @ Y0 @ (setof @ (^[Y1 : nat]: (~ ((pl @ Y1 @ y) = (pl @ Y1 @ z))))))))))),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.69/1.48 thf(f73,plain,(
% 1.69/1.48 ($true = ((^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0)))))) @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))),
% 1.69/1.48 inference(heuristic_instantiation,[status(thm)],[f27])).
% 1.69/1.48 thf(f64,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (($false = (esti @ (suc @ (sK1 @ X1)) @ X1)) | ((esti @ X2 @ X1) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.69/1.48 thf(f63,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ($false = ((esti @ (sK1 @ X1) @ X1) => (esti @ (suc @ (sK1 @ X1)) @ X1))) | ((esti @ n_1 @ X1) = $false)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.69/1.48 thf(f62,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (($false = ((^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))) @ (sK1 @ X1))) | ((esti @ n_1 @ X1) = $false) | ((esti @ X2 @ X1) = $true)) )),
% 1.69/1.48 inference(sigma_clausification,[status(thm)],[f61])).
% 1.69/1.48 thf(f61,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (((esti @ X2 @ X1) = $true) | ($false = (!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))))) | ((esti @ n_1 @ X1) = $false)) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.69/1.48 thf(f60,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (($false = (!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1))))) | ((esti @ n_1 @ X1) = $false) | ($true = ((^[Y0 : nat]: (esti @ Y0 @ X1)) @ X2))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f59])).
% 1.69/1.48 thf(f59,plain,(
% 1.69/1.48 ( ! [X1 : set] : (($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) | ((esti @ n_1 @ X1) = $false) | ($false = (!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))))) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.69/1.48 thf(f58,plain,(
% 1.69/1.48 ( ! [X1 : set] : ((((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1)))) = $true) | ((esti @ n_1 @ X1) = $false)) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.69/1.48 thf(f57,plain,(
% 1.69/1.48 ( ! [X1 : set] : (($true = ((esti @ n_1 @ X1) => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))))))) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.69/1.48 thf(f56,plain,(
% 1.69/1.48 ( ! [X1 : set] : (($true = ((^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0)))))) @ X1))) )),
% 1.69/1.48 inference(pi_clausification,[status(thm)],[f29])).
% 1.69/1.48 thf(f29,plain,(
% 1.69/1.48 ((!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))) = $true)),
% 1.69/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.69/1.48 thf(f19,plain,(
% 1.69/1.48 ((!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))) = $true)),
% 1.69/1.48 inference(fool_elimination,[status(thm)],[f18])).
% 1.69/1.48 thf(f18,plain,(
% 1.69/1.48 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.69/1.48 inference(rectify,[status(thm)],[f3])).
% 1.69/1.48 thf(f3,axiom,(
% 1.69/1.48 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.69/1.48 file('/export/starexec/sandbox2/tmp/tmp.iEVdslmYxZ/DTF2THF_22332.p',ax5)).
% 1.69/1.48 thf(f302,plain,(
% 1.69/1.48 ~spl0_12 | spl0_13),
% 1.69/1.48 inference(avatar_split_clause,[status(thm)],[f287,f296,f292])).
% 1.69/1.48 thf(f287,plain,(
% 1.69/1.48 ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y) != (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z)) | ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))))),
% 1.69/1.48 inference(trivial_inequality_removal,[status(thm)],[f284])).
% 1.69/1.48 thf(f284,plain,(
% 1.69/1.48 ((pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ y) != (pl @ (sK1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) @ z)) | ($false = (esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) | ($false = $true)),
% 1.69/1.48 inference(superposition,[status(thm)],[f66,f48])).
% 1.69/1.48 thf(f48,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $false) | ((pl @ X0 @ y) != (pl @ X0 @ z))) )),
% 1.69/1.48 inference(equality_proxy_clausification,[status(thm)],[f47])).
% 1.69/1.48 thf(f47,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($false = ((pl @ X0 @ y) = (pl @ X0 @ z))) | ((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $false)) )),
% 1.69/1.48 inference(not_proxy_clausification,[status(thm)],[f46])).
% 1.69/1.48 thf(f46,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) = $false) | ((~ ((pl @ X0 @ y) = (pl @ X0 @ z))) = $true)) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.69/1.48 thf(f45,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($true = ((esti @ X0 @ (setof @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z)))))) => (~ ((pl @ X0 @ y) = (pl @ X0 @ z)))))) )),
% 1.69/1.48 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.69/1.48 thf(f38,plain,(
% 1.69/1.48 ( ! [X0 : nat] : (($true = ((^[Y0 : nat > $o]: ((esti @ X0 @ (setof @ Y0)) => (Y0 @ X0))) @ (^[Y0 : nat]: (~ ((pl @ Y0 @ y) = (pl @ Y0 @ z))))))) )),
% 1.69/1.48 inference(heuristic_instantiation,[status(thm)],[f37])).
% 1.69/1.48 thf(f66,plain,(
% 1.69/1.48 ( ! [X0 : set] : (($true = (esti @ (sK1 @ X0) @ X0)) | ((esti @ n_1 @ X0) = $false)) )),
% 1.69/1.48 inference(condensation,[status(thm)],[f65])).
% 1.69/1.48 thf(f65,plain,(
% 1.69/1.48 ( ! [X2 : nat,X1 : set] : (((esti @ n_1 @ X1) = $false) | ((esti @ X2 @ X1) = $true) | ($true = (esti @ (sK1 @ X1) @ X1))) )),
% 1.69/1.48 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.69/1.48 % SZS output end Proof for DTF2THF_22332
% 1.69/1.48 % (22584)------------------------------
% 1.69/1.48 % (22584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.48 % (22584)Termination reason: Refutation
% 1.69/1.48
% 1.69/1.48 % (22584)Memory used [KB]: 5756
% 1.69/1.48 % (22584)Time elapsed: 0.029 s
% 1.69/1.48 % (22584)Instructions burned: 72 (million)
% 1.69/1.48 % (22584)------------------------------
% 1.69/1.48 % (22584)------------------------------
% 1.69/1.48 % (22549)Success in time 0.176 s
%------------------------------------------------------------------------------