%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM637^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:24:01 AM UTC 2026
% Result : Theorem 1.67s 1.43s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 35 unt; 0 typ; 2 def)
% Number of atoms : 360 ( 126 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 566 ( 61 ~; 54 |; 0 &; 368 @)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 7 con; 0-2 aty)
% ( 36 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 131 ( 57 ^; 74 !; 0 ?; 131 :)
% 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,
n_1: nat ).
thf(func_def_3,type,
suc: 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_18,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK2: set > nat ).
thf(f1735,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1507,f1534,f1734]) ).
thf(f1734,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f1733]) ).
thf(f1733,plain,
( $false
| ~ spl0_12 ),
inference(equality_resolution,[status(thm)],[f1676]) ).
thf(f1676,plain,
( ! [X0: nat] : ( x != X0 )
| ~ spl0_12 ),
inference(equality_proxy_clausification,[status(thm)],[f1668]) ).
thf(f1668,plain,
( ! [X0: nat] :
( $false
= ( x = X0 ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1667]) ).
thf(f1667,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( $false
= ( x = X0 ) ) )
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f1636]) ).
thf(f1636,plain,
( ! [X0: nat] :
( ( $false
= ( x = X0 ) )
| ( $true = ( ~ $true ) ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f1627,f82]) ).
thf(f82,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
= ( X1 @ X0 ) )
| ( ( X1 @ X0 )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
= ( $true
=> ( X1 @ X0 ) ) )
| ( ( X1 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f40,f53]) ).
thf(f53,plain,
! [X2: nat,X1: nat > $o] :
( ( $true
= ( esti @ X2 @ ( setof @ X1 ) ) )
| ( $false
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ( X1 @ X2 )
=> ( esti @ X2 @ ( setof @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ^ [Y0: nat] :
( ( X1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: nat > $o] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( X1 @ Y0 )
=> ( esti @ Y0 @ ( setof @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: nat > $o] :
( $true
= ( ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( Y0 @ Y1 )
=> ( esti @ Y1 @ ( setof @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,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/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',estii) ).
thf(f40,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ( esti @ X2 @ ( setof @ X1 ) )
=> ( X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: nat,X1: nat > $o] :
( $true
= ( ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X1 ) )
=> ( X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: nat > $o] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X1 ) )
=> ( X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: nat > $o] :
( $true
= ( ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( !! @ nat
@ ^ [Y1: nat] :
( ( esti @ Y1 @ ( setof @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat,X1: nat > $o] :
( ( esti @ X0 @ ( setof @ X1 ) )
=> ( X1 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: nat,X0: nat > $o] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',estie) ).
thf(f1627,plain,
( ! [X0: nat] :
( $true
= ( x != X0 ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1626]) ).
thf(f1626,plain,
( ! [X0: nat] :
( ( ^ [Y0: nat] : ( x != Y0 )
@ X0 )
= $true )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1543]) ).
thf(f1543,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( ( ^ [Y0: nat] : ( x != Y0 )
@ X0 )
= $true ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f41,f1506]) ).
thf(f1506,plain,
( ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f1505]) ).
thf(f1505,definition,
( spl0_12
<=> ! [X0: nat] :
( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f41,plain,
! [X2: nat,X1: nat > $o] :
( ( $false
= ( esti @ X2 @ ( setof @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f1534,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[status(thm)],[f1533]) ).
thf(f1533,plain,
( $false
| ~ spl0_11 ),
inference(subsumption_resolution,[status(thm)],[f1522,f25]) ).
thf(f25,plain,
x != n_1,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
x != n_1,
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
x != n_1,
file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',n) ).
thf(f1522,plain,
( ( x = n_1 )
| ~ spl0_11 ),
inference(equality_proxy_clausification,[status(thm)],[f1517]) ).
thf(f1517,plain,
( ( $true
= ( x = n_1 ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1510]) ).
thf(f1510,plain,
( ( $true
= ( x = n_1 ) )
| ( $true = $false )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f1503,f68]) ).
thf(f68,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
= ( ~ ( X1 @ X0 ) ) )
| ( $true
= ( X1 @ X0 ) ) ),
inference(boolean_simplification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
= ( ( X1 @ X0 )
=> $false ) )
| ( $true
= ( X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f52,f41]) ).
thf(f1503,plain,
( ( ( x != n_1 )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f1502]) ).
thf(f1502,definition,
( spl0_11
<=> ( ( x != n_1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f1507,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f1497,f1505,f1502]) ).
thf(f1497,plain,
! [X0: nat] :
( ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) )
| ( ( x != n_1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f1496]) ).
thf(f1496,plain,
! [X0: nat] :
( ( $true = $false )
| ( ( x != n_1 )
= $false )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1489]) ).
thf(f1489,plain,
! [X0: nat] :
( ( ( x != n_1 )
= $false )
| ( $true
= ( esti @ X0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) )
| ( ( ~ $false ) = $false ) ),
inference(superposition,[status(thm)],[f1087,f33]) ).
thf(f33,plain,
! [X1: nat] :
( ( x
= ( suc @ X1 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: nat] :
( $true
= ( x
!= ( suc @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( x
!= ( suc @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( x
!= ( suc @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( ~ ~ ( !! @ nat
@ ^ [Y0: nat] :
( x
!= ( suc @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ~ ~ ( !! @ nat
@ ^ [Y0: nat] :
( x
!= ( suc @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ~ ! [X0: nat] :
( x
!= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ~ ! [X4: nat] :
( x
!= ( suc @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
~ ! [X4: nat] :
( x
!= ( suc @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',satz3) ).
thf(f1087,plain,
! [X1: nat,X4: nat > $o] :
( ( ( ~ ( X4
@ ( suc
@ ( sK2
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) ) ) )
= $false )
| ( ( ~ ( X4 @ n_1 ) )
= $false )
| ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1068]) ).
thf(f1068,plain,
! [X1: nat,X4: nat > $o] :
( ( ( ^ [Y0: nat] :
~ ( X4 @ Y0 )
@ n_1 )
= $false )
| ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) )
| ( ( ^ [Y0: nat] :
~ ( X4 @ Y0 )
@ ( suc
@ ( sK2
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) ) )
= $false ) ),
inference(primitive_instantiation,[status(thm)],[f1064]) ).
thf(f1064,plain,
! [X0: nat > $o,X1: nat] :
( ( $false
= ( X0 @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) ) )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1056]) ).
thf(f1056,plain,
! [X0: nat > $o,X1: nat] :
( ( $true
= ( ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) )
@ X1 ) )
| ( $false
= ( X0 @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) ) )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(pi_clausification,[status(thm)],[f971]) ).
thf(f971,plain,
! [X0: nat > $o] :
( ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) )
| ( $false
= ( X0 @ n_1 ) )
| ( $false
= ( X0 @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f970]) ).
thf(f970,plain,
! [X0: nat > $o] :
( ( $false
= ( X0 @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) ) )
| ( $false
= ( X0 @ n_1 ) )
| ( $true = $false )
| ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f951]) ).
thf(f951,plain,
! [X0: nat > $o] :
( ( ( ( esti @ ( sK2 @ ( setof @ X0 ) ) @ ( setof @ X0 ) )
=> $true )
= $false )
| ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) )
| ( $false
= ( X0 @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) ) )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(superposition,[status(thm)],[f937,f53]) ).
thf(f937,plain,
! [X0: nat > $o] :
( ( $false
= ( ( esti @ ( sK2 @ ( setof @ X0 ) ) @ ( setof @ X0 ) )
=> ( esti @ ( suc @ ( sK2 @ ( setof @ X0 ) ) ) @ ( setof @ X0 ) ) ) )
| ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f928]) ).
thf(f928,plain,
! [X0: nat > $o] :
( ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) )
| ( $false
= ( X0 @ n_1 ) )
| ( ( ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X0 ) )
=> ( esti @ ( suc @ Y0 ) @ ( setof @ X0 ) ) )
@ ( sK2 @ ( setof @ X0 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f889]) ).
thf(f889,plain,
! [X0: nat > $o] :
( ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X0 ) )
=> ( esti @ ( suc @ Y0 ) @ ( setof @ X0 ) ) ) )
= $false )
| ( $false
= ( X0 @ n_1 ) )
| ( $true
= ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: nat > $o] :
( ( $true
= ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X0 ) )
=> ( esti @ ( suc @ Y0 ) @ ( setof @ X0 ) ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) ) )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(boolean_simplification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X0: nat > $o] :
( ( $true
= ( $true
=> ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ ( setof @ X0 ) )
=> ( esti @ ( suc @ Y0 ) @ ( setof @ X0 ) ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ ( setof @ X0 ) ) ) ) ) )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(superposition,[status(thm)],[f61,f53]) ).
thf(f61,plain,
! [X1: set] :
( ( ( esti @ n_1 @ X1 )
=> ( ( !! @ nat
@ ^ [Y0: nat] :
( ( esti @ Y0 @ X1 )
=> ( esti @ ( suc @ Y0 ) @ X1 ) ) )
=> ( !! @ nat
@ ^ [Y0: nat] : ( esti @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,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)],[f22]) ).
thf(f22,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)],[f16]) ).
thf(f16,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)],[f15]) ).
thf(f15,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/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',ax5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM637^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 11:08:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : NUM637^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Number Theory
% 0.30/0.46 % Problem : Landau theorem 3
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : ~(forall x_0:nat.~(x = suc x_0))
% 0.30/0.46
% 0.30/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : satz3 [Lan30]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % : Without extensionality : Theorem
% 0.30/0.46 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 13 ( 4 unt; 7 typ; 0 def)
% 0.30/0.46 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.30/0.46 % Number of connectives : 29 ( 5 ~; 0 |; 0 &; 18 @)
% 0.30/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.30/0.46 % Number of types : 3 ( 2 usr)
% 0.30/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(nat_type,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(x,type,
% 0.30/0.46 x: nat ).
% 0.30/0.46
% 0.30/0.46 thf(n_1,type,
% 0.30/0.46 n_1: nat ).
% 0.30/0.46
% 0.30/0.46 thf(n,axiom,
% 0.30/0.46 x != n_1 ).
% 0.30/0.46
% 0.30/0.46 thf(suc,type,
% 0.30/0.46 suc: nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(set_type,type,
% 0.30/0.46 set: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(esti,type,
% 0.30/0.46 esti: nat > set > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setof,type,
% 0.30/0.46 setof: ( nat > $o ) > set ).
% 0.30/0.46
% 0.30/0.46 thf(estie,axiom,
% 0.30/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.30/0.46 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.30/0.46 => ( Xp @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ax5,axiom,
% 0.30/0.46 ! [Xs: set] :
% 0.30/0.46 ( ( esti @ n_1 @ Xs )
% 0.30/0.46 => ( ! [Xx: nat] :
% 0.30/0.46 ( ( esti @ Xx @ Xs )
% 0.30/0.46 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.30/0.46 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(estii,axiom,
% 0.30/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.30/0.46 ( ( Xp @ Xs )
% 0.30/0.46 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(et,axiom,
% 0.30/0.46 ! [Xa: $o] :
% 0.30/0.46 ( ~ ~ Xa
% 0.30/0.46 => Xa ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz3,conjecture,
% 0.30/0.46 ~ ! [Xx_0: nat] :
% 0.30/0.46 ( x
% 0.30/0.46 != ( suc @ Xx_0 ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 11:08:26 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2DTF32159.p
% See solution above
% 1.49/1.29 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.66/1.30 thf(nat_type,type,
% 1.66/1.30 nat: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(x,type,
% 1.66/1.30 x: nat ).
% 1.66/1.30
% 1.66/1.30 thf(n_1,type,
% 1.66/1.30 n_1: nat ).
% 1.66/1.30
% 1.66/1.30 thf(n,axiom,
% 1.66/1.30 x != n_1 ).
% 1.66/1.30
% 1.66/1.30 thf(suc,type,
% 1.66/1.30 suc: nat > nat ).
% 1.66/1.30
% 1.66/1.30 thf(set_type,type,
% 1.66/1.30 set: $tType ).
% 1.66/1.30
% 1.66/1.30 thf(esti,type,
% 1.66/1.30 esti: nat > set > $o ).
% 1.66/1.30
% 1.66/1.30 thf(setof,type,
% 1.66/1.30 setof: ( nat > $o ) > set ).
% 1.66/1.30
% 1.66/1.30 thf(estie,axiom,
% 1.66/1.30 ! [Xp: nat > $o,Xs: nat] :
% 1.66/1.30 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.66/1.30 => ( Xp @ Xs ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(ax5,axiom,
% 1.66/1.30 ! [Xs: set] :
% 1.66/1.30 ( ( esti @ n_1 @ Xs )
% 1.66/1.30 => ( ! [Xx: nat] :
% 1.66/1.30 ( ( esti @ Xx @ Xs )
% 1.66/1.30 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.66/1.30 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(estii,axiom,
% 1.66/1.30 ! [Xp: nat > $o,Xs: nat] :
% 1.66/1.30 ( ( Xp @ Xs )
% 1.66/1.30 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(et,axiom,
% 1.66/1.30 ! [Xa: $o] :
% 1.66/1.30 ( ~ ~ Xa
% 1.66/1.30 => Xa ) ).
% 1.66/1.30
% 1.66/1.30 thf(satz3,conjecture,
% 1.66/1.30 ~ ! [Xx_0: nat] :
% 1.66/1.30 ( x
% 1.66/1.30 != ( suc @ Xx_0 ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.31 % (32266)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/183Mi)
% 1.66/1.31 % (32267)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_32159 for (2999ds/4Mi)
% 1.66/1.31 % (32267)Instruction limit reached!
% 1.66/1.31 % (32267)------------------------------
% 1.66/1.31 % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (32267)Termination reason: Unknown
% 1.66/1.31 % (32267)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (32267)Memory used [KB]: 5500
% 1.66/1.31 % (32267)Time elapsed: 0.003 s
% 1.66/1.31 % (32267)Instructions burned: 4 (million)
% 1.66/1.31 % (32267)------------------------------
% 1.66/1.31 % (32267)------------------------------
% 1.66/1.32 % (32268)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_32159 for (2999ds/27Mi)
% 1.66/1.32 % (32269)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/2Mi)
% 1.66/1.32 % (32270)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_32159 for (2999ds/2Mi)
% 1.66/1.32 % (32271)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_32159 for (2999ds/275Mi)
% 1.66/1.32 % (32272)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/18Mi)
% 1.66/1.32 % (32270)Instruction limit reached!
% 1.66/1.32 % (32270)------------------------------
% 1.66/1.32 % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (32270)Termination reason: Unknown
% 1.66/1.32 % (32270)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (32270)Memory used [KB]: 895
% 1.66/1.32 % (32270)Time elapsed: 0.003 s
% 1.66/1.32 % (32270)Instructions burned: 2 (million)
% 1.66/1.32 % (32270)------------------------------
% 1.66/1.32 % (32270)------------------------------
% 1.66/1.32 % (32269)Instruction limit reached!
% 1.66/1.32 % (32269)------------------------------
% 1.66/1.32 % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (32269)Termination reason: Unknown
% 1.66/1.32 % (32269)Termination phase: Saturation
% 1.66/1.32 % (32271)Refutation not found, incomplete strategy
% 1.66/1.32 % (32271)------------------------------
% 1.66/1.32 % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32
% 1.66/1.32 % (32271)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 % (32269)Memory used [KB]: 5500
% 1.66/1.32 % (32269)Time elapsed: 0.004 s
% 1.66/1.32 % (32271)Memory used [KB]: 5500
% 1.66/1.32 % (32269)Instructions burned: 2 (million)
% 1.66/1.32 % (32271)Time elapsed: 0.003 s
% 1.66/1.32 % (32269)------------------------------
% 1.66/1.32 % (32269)------------------------------
% 1.66/1.32 % (32271)Instructions burned: 1 (million)
% 1.66/1.32 % (32271)------------------------------
% 1.66/1.32 % (32271)------------------------------
% 1.66/1.32 % (32268)Refutation not found, incomplete strategy
% 1.66/1.32 % (32268)------------------------------
% 1.66/1.32 % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (32268)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 % (32268)Memory used [KB]: 5500
% 1.66/1.32 % (32268)Time elapsed: 0.004 s
% 1.66/1.32 % (32268)Instructions burned: 2 (million)
% 1.66/1.32 % (32268)------------------------------
% 1.66/1.32 % (32268)------------------------------
% 1.66/1.32 % (32273)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/3Mi)
% 1.66/1.32 % (32273)Instruction limit reached!
% 1.66/1.32 % (32273)------------------------------
% 1.66/1.32 % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (32273)Termination reason: Unknown
% 1.66/1.32 % (32273)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (32273)Memory used [KB]: 5500
% 1.66/1.32 % (32273)Time elapsed: 0.003 s
% 1.66/1.32 % (32273)Instructions burned: 3 (million)
% 1.66/1.32 % (32273)------------------------------
% 1.66/1.32 % (32273)------------------------------
% 1.66/1.33 % (32272)Instruction limit reached!
% 1.66/1.33 % (32272)------------------------------
% 1.66/1.33 % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (32272)Termination reason: Unknown
% 1.66/1.33 % (32272)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (32272)Memory used [KB]: 5628
% 1.66/1.33 % (32272)Time elapsed: 0.014 s
% 1.66/1.33 % (32272)Instructions burned: 18 (million)
% 1.66/1.33 % (32272)------------------------------
% 1.66/1.33 % (32272)------------------------------
% 1.66/1.34 % (32278)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/7Mi)
% 1.66/1.34 % (32274)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_32159 for (2999ds/37Mi)
% 1.66/1.34 % (32278)Instruction limit reached!
% 1.66/1.34 % (32278)------------------------------
% 1.66/1.34 % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (32278)Termination reason: Unknown
% 1.66/1.34 % (32278)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (32278)Memory used [KB]: 1023
% 1.66/1.34 % (32278)Time elapsed: 0.005 s
% 1.66/1.34 % (32278)Instructions burned: 8 (million)
% 1.66/1.34 % (32278)------------------------------
% 1.66/1.34 % (32278)------------------------------
% 1.66/1.34 % (32277)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_32159 for (2999ds/1041Mi)
% 1.66/1.34 % (32275)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_32159 for (2999ds/15Mi)
% 1.66/1.34 % (32276)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_32159 for (2999ds/3Mi)
% 1.66/1.34 % (32275)Refutation not found, incomplete strategy
% 1.66/1.34 % (32275)------------------------------
% 1.66/1.34 % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (32275)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.34
% 1.66/1.34
% 1.66/1.34 % (32275)Memory used [KB]: 5500
% 1.66/1.34 % (32275)Time elapsed: 0.003 s
% 1.66/1.34 % (32275)Instructions burned: 2 (million)
% 1.66/1.34 % (32275)------------------------------
% 1.66/1.34 % (32275)------------------------------
% 1.66/1.34 % (32276)Instruction limit reached!
% 1.66/1.34 % (32276)------------------------------
% 1.66/1.34 % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (32276)Termination reason: Unknown
% 1.66/1.34 % (32276)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (32276)Memory used [KB]: 5500
% 1.66/1.34 % (32276)Time elapsed: 0.004 s
% 1.66/1.34 % (32276)Instructions burned: 3 (million)
% 1.66/1.34 % (32276)------------------------------
% 1.66/1.34 % (32276)------------------------------
% 1.66/1.35 % (32280)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_32159 for (2999ds/3Mi)
% 1.66/1.35 % (32279)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/16Mi)
% 1.66/1.35 % (32280)Instruction limit reached!
% 1.66/1.35 % (32280)------------------------------
% 1.66/1.35 % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (32280)Termination reason: Unknown
% 1.66/1.35 % (32280)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (32280)Memory used [KB]: 5500
% 1.66/1.35 % (32280)Time elapsed: 0.003 s
% 1.66/1.35 % (32280)Instructions burned: 3 (million)
% 1.66/1.35 % (32280)------------------------------
% 1.66/1.35 % (32280)------------------------------
% 1.66/1.36 % (32282)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/7Mi)
% 1.66/1.36 % (32281)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_32159 for (2999ds/3Mi)
% 1.66/1.36 % (32274)Instruction limit reached!
% 1.66/1.36 % (32274)------------------------------
% 1.66/1.36 % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (32274)Termination reason: Unknown
% 1.66/1.36 % (32274)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (32274)Memory used [KB]: 5884
% 1.66/1.36 % (32274)Time elapsed: 0.024 s
% 1.66/1.36 % (32274)Instructions burned: 38 (million)
% 1.66/1.36 % (32274)------------------------------
% 1.66/1.36 % (32274)------------------------------
% 1.66/1.36 % (32279)Instruction limit reached!
% 1.66/1.36 % (32279)------------------------------
% 1.66/1.36 % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (32279)Termination reason: Unknown
% 1.66/1.36 % (32279)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (32279)Memory used [KB]: 5628
% 1.66/1.36 % (32279)Time elapsed: 0.013 s
% 1.66/1.36 % (32279)Instructions burned: 17 (million)
% 1.66/1.36 % (32279)------------------------------
% 1.66/1.36 % (32279)------------------------------
% 1.66/1.36 % (32283)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/3Mi)
% 1.66/1.36 % (32281)Instruction limit reached!
% 1.66/1.36 % (32281)------------------------------
% 1.66/1.36 % (32281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (32281)Termination reason: Unknown
% 1.66/1.36 % (32281)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (32281)Memory used [KB]: 1023
% 1.66/1.36 % (32281)Time elapsed: 0.004 s
% 1.66/1.36 % (32281)Instructions burned: 3 (million)
% 1.66/1.36 % (32281)------------------------------
% 1.66/1.36 % (32281)------------------------------
% 1.66/1.36 % (32283)Instruction limit reached!
% 1.66/1.36 % (32283)------------------------------
% 1.66/1.36 % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (32283)Termination reason: Unknown
% 1.66/1.36 % (32283)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (32283)Memory used [KB]: 5500
% 1.66/1.36 % (32283)Time elapsed: 0.003 s
% 1.66/1.36 % (32283)Instructions burned: 3 (million)
% 1.66/1.36 % (32283)------------------------------
% 1.66/1.36 % (32283)------------------------------
% 1.66/1.36 % (32282)Refutation not found, incomplete strategy
% 1.66/1.36 % (32282)------------------------------
% 1.66/1.36 % (32282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (32282)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.36
% 1.66/1.36
% 1.66/1.36 % (32282)Memory used [KB]: 5500
% 1.66/1.36 % (32282)Time elapsed: 0.004 s
% 1.66/1.36 % (32282)Instructions burned: 3 (million)
% 1.66/1.36 % (32282)------------------------------
% 1.66/1.36 % (32282)------------------------------
% 1.66/1.37 % (32266)Instruction limit reached!
% 1.66/1.37 % (32266)------------------------------
% 1.66/1.37 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (32266)Termination reason: Unknown
% 1.66/1.37 % (32266)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (32266)Memory used [KB]: 6524
% 1.66/1.37 % (32266)Time elapsed: 0.059 s
% 1.66/1.37 % (32266)Instructions burned: 183 (million)
% 1.66/1.37 % (32266)------------------------------
% 1.66/1.37 % (32266)------------------------------
% 1.66/1.37 % (32287)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/6Mi)
% 1.66/1.37 % (32287)Instruction limit reached!
% 1.66/1.37 % (32287)------------------------------
% 1.66/1.37 % (32287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (32287)Termination reason: Unknown
% 1.66/1.37 % (32287)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (32287)Memory used [KB]: 5500
% 1.66/1.37 % (32287)Time elapsed: 0.004 s
% 1.66/1.37 % (32287)Instructions burned: 6 (million)
% 1.66/1.37 % (32287)------------------------------
% 1.66/1.37 % (32287)------------------------------
% 1.66/1.38 % (32284)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/4Mi)
% 1.66/1.38 % (32285)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/18Mi)
% 1.66/1.38 % (32286)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/710Mi)
% 1.66/1.38 % (32288)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_32159 for (2999ds/902Mi)
% 1.66/1.38 % (32289)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_32159 for (2999ds/21Mi)
% 1.66/1.38 % (32284)Instruction limit reached!
% 1.66/1.38 % (32284)------------------------------
% 1.66/1.38 % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (32284)Termination reason: Unknown
% 1.66/1.38 % (32284)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (32284)Memory used [KB]: 5500
% 1.66/1.38 % (32284)Time elapsed: 0.005 s
% 1.66/1.38 % (32284)Instructions burned: 4 (million)
% 1.66/1.38 % (32284)------------------------------
% 1.66/1.38 % (32284)------------------------------
% 1.66/1.38 % (32288)Refutation not found, incomplete strategy
% 1.66/1.38 % (32288)------------------------------
% 1.66/1.38 % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (32288)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (32288)Memory used [KB]: 5500
% 1.66/1.38 % (32288)Time elapsed: 0.003 s
% 1.66/1.38 % (32288)Instructions burned: 2 (million)
% 1.66/1.38 % (32288)------------------------------
% 1.66/1.38 % (32288)------------------------------
% 1.66/1.38 % (32285)Refutation not found, incomplete strategy
% 1.66/1.38 % (32285)------------------------------
% 1.66/1.38 % (32285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (32285)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (32285)Memory used [KB]: 5500
% 1.66/1.38 % (32285)Time elapsed: 0.006 s
% 1.66/1.38 % (32285)Instructions burned: 6 (million)
% 1.66/1.38 % (32285)------------------------------
% 1.66/1.38 % (32285)------------------------------
% 1.66/1.38 % (32290)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/5Mi)
% 1.66/1.39 % (32290)Instruction limit reached!
% 1.66/1.39 % (32290)------------------------------
% 1.66/1.39 % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (32290)Termination reason: Unknown
% 1.66/1.39 % (32290)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (32290)Memory used [KB]: 5500
% 1.66/1.39 % (32290)Time elapsed: 0.004 s
% 1.66/1.39 % (32290)Instructions burned: 6 (million)
% 1.66/1.39 % (32290)------------------------------
% 1.66/1.39 % (32290)------------------------------
% 1.66/1.39 % (32289)Instruction limit reached!
% 1.66/1.39 % (32289)------------------------------
% 1.66/1.39 % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (32289)Termination reason: Unknown
% 1.66/1.39 % (32289)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (32289)Memory used [KB]: 5628
% 1.66/1.39 % (32289)Time elapsed: 0.010 s
% 1.66/1.39 % (32289)Instructions burned: 22 (million)
% 1.66/1.39 % (32289)------------------------------
% 1.66/1.39 % (32289)------------------------------
% 1.66/1.40 % (32294)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_32159 for (2999ds/19Mi)
% 1.67/1.40 % (32291)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_32159 for (2999ds/6Mi)
% 1.67/1.40 % (32294)Refutation not found, incomplete strategy
% 1.67/1.40 % (32294)------------------------------
% 1.67/1.40 % (32294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (32294)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.40
% 1.67/1.40
% 1.67/1.40 % (32294)Memory used [KB]: 5500
% 1.67/1.40 % (32294)Time elapsed: 0.003 s
% 1.67/1.40 % (32294)Instructions burned: 4 (million)
% 1.67/1.40 % (32294)------------------------------
% 1.67/1.40 % (32294)------------------------------
% 1.67/1.40 % (32295)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/879Mi)
% 1.67/1.40 % (32292)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/377Mi)
% 1.67/1.40 % (32293)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_32159 for (2999ds/779Mi)
% 1.67/1.40 % (32291)Instruction limit reached!
% 1.67/1.40 % (32291)------------------------------
% 1.67/1.40 % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.40 % (32291)Termination reason: Unknown
% 1.67/1.40 % (32291)Termination phase: Saturation
% 1.67/1.40
% 1.67/1.40 % (32291)Memory used [KB]: 5500
% 1.67/1.40 % (32291)Time elapsed: 0.006 s
% 1.67/1.40 % (32291)Instructions burned: 7 (million)
% 1.67/1.40 % (32291)------------------------------
% 1.67/1.40 % (32291)------------------------------
% 1.67/1.41 % (32295)Refutation not found, incomplete strategy
% 1.67/1.41 % (32295)------------------------------
% 1.67/1.41 % (32295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (32295)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.41
% 1.67/1.41
% 1.67/1.41 % (32295)Memory used [KB]: 5628
% 1.67/1.41 % (32295)Time elapsed: 0.011 s
% 1.67/1.41 % (32295)Instructions burned: 25 (million)
% 1.67/1.41 % (32295)------------------------------
% 1.67/1.41 % (32295)------------------------------
% 1.67/1.41 % (32299)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/17Mi)
% 1.67/1.41 % (32299)Instruction limit reached!
% 1.67/1.41 % (32299)------------------------------
% 1.67/1.41 % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (32299)Termination reason: Unknown
% 1.67/1.41 % (32299)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (32299)Memory used [KB]: 5628
% 1.67/1.41 % (32299)Time elapsed: 0.007 s
% 1.67/1.41 % (32299)Instructions burned: 17 (million)
% 1.67/1.41 % (32299)------------------------------
% 1.67/1.41 % (32299)------------------------------
% 1.67/1.42 % (32301)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/30Mi)
% 1.67/1.42 % (32300)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32159 for (2999ds/3Mi)
% 1.67/1.42 % (32300)Instruction limit reached!
% 1.67/1.42 % (32300)------------------------------
% 1.67/1.42 % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (32300)Termination reason: Unknown
% 1.67/1.42 % (32300)Termination phase: Saturation
% 1.67/1.42
% 1.67/1.42 % (32300)Memory used [KB]: 1023
% 1.67/1.42 % (32300)Time elapsed: 0.004 s
% 1.67/1.42 % (32300)Instructions burned: 4 (million)
% 1.67/1.42 % (32300)------------------------------
% 1.67/1.42 % (32300)------------------------------
% 1.67/1.42 % (32302)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32159 for (2998ds/127Mi)
% 1.67/1.43 % (32301)Instruction limit reached!
% 1.67/1.43 % (32301)------------------------------
% 1.67/1.43 % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (32301)Termination reason: Unknown
% 1.67/1.43 % (32301)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (32301)Memory used [KB]: 5628
% 1.67/1.43 % (32301)Time elapsed: 0.013 s
% 1.67/1.43 % (32301)Instructions burned: 31 (million)
% 1.67/1.43 % (32301)------------------------------
% 1.67/1.43 % (32301)------------------------------
% 1.67/1.43 % (32277)First to succeed.
% 1.67/1.43 % (32277)Refutation found. Thanks to Tanya!
% 1.67/1.43 % SZS status Theorem for DTF2THF_32159
% 1.67/1.43 % SZS output start Proof for DTF2THF_32159
% 1.67/1.43 thf(type_def_5, type, nat: $tType).
% 1.67/1.43 thf(type_def_7, type, set: $tType).
% 1.67/1.43 thf(func_def_0, type, nat: $tType).
% 1.67/1.43 thf(func_def_1, type, x: nat).
% 1.67/1.43 thf(func_def_2, type, n_1: nat).
% 1.67/1.43 thf(func_def_3, type, suc: nat > nat).
% 1.67/1.43 thf(func_def_4, type, set: $tType).
% 1.67/1.43 thf(func_def_5, type, esti: nat > set > $o).
% 1.67/1.43 thf(func_def_6, type, setof: (nat > $o) > set).
% 1.67/1.43 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.43 thf(func_def_19, type, sK2: set > nat).
% 1.67/1.43 thf(f1735,plain,(
% 1.67/1.43 $false),
% 1.67/1.43 inference(avatar_sat_refutation,[status(thm)],[f1507,f1534,f1734])).
% 1.67/1.43 thf(f1734,plain,(
% 1.67/1.43 ~spl0_12),
% 1.67/1.43 inference(avatar_contradiction_clause,[status(thm)],[f1733])).
% 1.67/1.43 thf(f1733,plain,(
% 1.67/1.43 $false | ~spl0_12),
% 1.67/1.43 inference(equality_resolution,[status(thm)],[f1676])).
% 1.67/1.43 thf(f1676,plain,(
% 1.67/1.43 ( ! [X0 : nat] : ((x != X0)) ) | ~spl0_12),
% 1.67/1.43 inference(equality_proxy_clausification,[status(thm)],[f1668])).
% 1.67/1.43 thf(f1668,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($false = (x = X0))) ) | ~spl0_12),
% 1.67/1.43 inference(trivial_inequality_removal,[status(thm)],[f1667])).
% 1.67/1.43 thf(f1667,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = $false) | ($false = (x = X0))) ) | ~spl0_12),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f1636])).
% 1.67/1.43 thf(f1636,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($false = (x = X0)) | ($true = (~ $true))) ) | ~spl0_12),
% 1.67/1.43 inference(superposition,[status(thm)],[f1627,f82])).
% 1.67/1.43 thf(f82,plain,(
% 1.67/1.43 ( ! [X0 : nat,X1 : nat > $o] : (($true = (X1 @ X0)) | ((X1 @ X0) = $false)) )),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f73])).
% 1.67/1.43 thf(f73,plain,(
% 1.67/1.43 ( ! [X0 : nat,X1 : nat > $o] : (($true = ($true => (X1 @ X0))) | ((X1 @ X0) = $false)) )),
% 1.67/1.43 inference(superposition,[status(thm)],[f40,f53])).
% 1.67/1.43 thf(f53,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($true = (esti @ X2 @ (setof @ X1))) | ($false = (X1 @ X2))) )),
% 1.67/1.43 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.67/1.43 thf(f52,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((X1 @ X2) => (esti @ X2 @ (setof @ X1))))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.67/1.43 thf(f51,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((^[Y0 : nat]: ((X1 @ Y0) => (esti @ Y0 @ (setof @ X1)))) @ X2))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f48])).
% 1.67/1.43 thf(f48,plain,(
% 1.67/1.43 ( ! [X1 : nat > $o] : (($true = (!! @ nat @ (^[Y0 : nat]: ((X1 @ Y0) => (esti @ Y0 @ (setof @ X1))))))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.67/1.43 thf(f47,plain,(
% 1.67/1.43 ( ! [X1 : nat > $o] : (($true = ((^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0)))))) @ X1))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f24])).
% 1.67/1.43 thf(f24,plain,(
% 1.67/1.43 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0))))))))),
% 1.67/1.43 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.43 thf(f12,plain,(
% 1.67/1.43 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((Y0 @ Y1) => (esti @ Y1 @ (setof @ Y0))))))))),
% 1.67/1.43 inference(fool_elimination,[status(thm)],[f11])).
% 1.67/1.43 thf(f11,plain,(
% 1.67/1.43 ! [X0 : nat,X1 : nat > $o] : ((X1 @ X0) => (esti @ X0 @ (setof @ X1)))),
% 1.67/1.43 inference(rectify,[status(thm)],[f4])).
% 1.67/1.43 thf(f4,axiom,(
% 1.67/1.43 ! [X1 : nat,X0 : nat > $o] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.67/1.43 file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',estii)).
% 1.67/1.43 thf(f40,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((esti @ X2 @ (setof @ X1)) => (X1 @ X2)))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.67/1.43 thf(f39,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($true = ((^[Y0 : nat]: ((esti @ Y0 @ (setof @ X1)) => (X1 @ Y0))) @ X2))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f38])).
% 1.67/1.43 thf(f38,plain,(
% 1.67/1.43 ( ! [X1 : nat > $o] : (($true = (!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ (setof @ X1)) => (X1 @ Y0)))))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.67/1.43 thf(f37,plain,(
% 1.67/1.43 ( ! [X1 : nat > $o] : (($true = ((^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1))))) @ X1))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f21])).
% 1.67/1.43 thf(f21,plain,(
% 1.67/1.43 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1)))))))),
% 1.67/1.43 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.43 thf(f18,plain,(
% 1.67/1.43 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: (!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ (setof @ Y0)) => (Y0 @ Y1)))))))),
% 1.67/1.43 inference(fool_elimination,[status(thm)],[f17])).
% 1.67/1.43 thf(f17,plain,(
% 1.67/1.43 ! [X0 : nat,X1 : nat > $o] : ((esti @ X0 @ (setof @ X1)) => (X1 @ X0))),
% 1.67/1.43 inference(rectify,[status(thm)],[f2])).
% 1.67/1.43 thf(f2,axiom,(
% 1.67/1.43 ! [X1 : nat,X0 : nat > $o] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.67/1.43 file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',estie)).
% 1.67/1.43 thf(f1627,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = (~ (x = X0)))) ) | ~spl0_12),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f1626])).
% 1.67/1.43 thf(f1626,plain,(
% 1.67/1.43 ( ! [X0 : nat] : ((((^[Y0 : nat]: (~ (x = Y0))) @ X0) = $true)) ) | ~spl0_12),
% 1.67/1.43 inference(trivial_inequality_removal,[status(thm)],[f1543])).
% 1.67/1.43 thf(f1543,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = $false) | (((^[Y0 : nat]: (~ (x = Y0))) @ X0) = $true)) ) | ~spl0_12),
% 1.67/1.43 inference(superposition,[status(thm)],[f41,f1506])).
% 1.67/1.43 thf(f1506,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0))))))) ) | ~spl0_12),
% 1.67/1.43 inference(avatar_component_clause,[status(thm)],[f1505])).
% 1.67/1.43 thf(f1505,definition,(
% 1.67/1.43 spl0_12 <=> ! [X0 : nat] : ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0))))))),
% 1.67/1.43 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.67/1.43 thf(f41,plain,(
% 1.67/1.43 ( ! [X2 : nat,X1 : nat > $o] : (($false = (esti @ X2 @ (setof @ X1))) | ($true = (X1 @ X2))) )),
% 1.67/1.43 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.67/1.43 thf(f1534,plain,(
% 1.67/1.43 ~spl0_11),
% 1.67/1.43 inference(avatar_contradiction_clause,[status(thm)],[f1533])).
% 1.67/1.43 thf(f1533,plain,(
% 1.67/1.43 $false | ~spl0_11),
% 1.67/1.43 inference(subsumption_resolution,[status(thm)],[f1522,f25])).
% 1.67/1.43 thf(f25,plain,(
% 1.67/1.43 (x != n_1)),
% 1.67/1.43 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.43 thf(f19,plain,(
% 1.67/1.43 (x != n_1)),
% 1.67/1.43 inference(fool_elimination,[status(thm)],[f1])).
% 1.67/1.43 thf(f1,axiom,(
% 1.67/1.43 (x != n_1)),
% 1.67/1.43 file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',n)).
% 1.67/1.43 thf(f1522,plain,(
% 1.67/1.43 (x = n_1) | ~spl0_11),
% 1.67/1.43 inference(equality_proxy_clausification,[status(thm)],[f1517])).
% 1.67/1.43 thf(f1517,plain,(
% 1.67/1.43 ($true = (x = n_1)) | ~spl0_11),
% 1.67/1.43 inference(trivial_inequality_removal,[status(thm)],[f1510])).
% 1.67/1.43 thf(f1510,plain,(
% 1.67/1.43 ($true = (x = n_1)) | ($true = $false) | ~spl0_11),
% 1.67/1.43 inference(superposition,[status(thm)],[f1503,f68])).
% 1.67/1.43 thf(f68,plain,(
% 1.67/1.43 ( ! [X0 : nat,X1 : nat > $o] : (($true = (~ (X1 @ X0))) | ($true = (X1 @ X0))) )),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f63])).
% 1.67/1.43 thf(f63,plain,(
% 1.67/1.43 ( ! [X0 : nat,X1 : nat > $o] : (($true = ((X1 @ X0) => $false)) | ($true = (X1 @ X0))) )),
% 1.67/1.43 inference(superposition,[status(thm)],[f52,f41])).
% 1.67/1.43 thf(f1503,plain,(
% 1.67/1.43 ((~ (x = n_1)) = $false) | ~spl0_11),
% 1.67/1.43 inference(avatar_component_clause,[status(thm)],[f1502])).
% 1.67/1.43 thf(f1502,definition,(
% 1.67/1.43 spl0_11 <=> ((~ (x = n_1)) = $false)),
% 1.67/1.43 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.67/1.43 thf(f1507,plain,(
% 1.67/1.43 spl0_11 | spl0_12),
% 1.67/1.43 inference(avatar_split_clause,[status(thm)],[f1497,f1505,f1502])).
% 1.67/1.43 thf(f1497,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0)))))) | ((~ (x = n_1)) = $false)) )),
% 1.67/1.43 inference(trivial_inequality_removal,[status(thm)],[f1496])).
% 1.67/1.43 thf(f1496,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (($true = $false) | ((~ (x = n_1)) = $false) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0))))))) )),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f1489])).
% 1.67/1.43 thf(f1489,plain,(
% 1.67/1.43 ( ! [X0 : nat] : (((~ (x = n_1)) = $false) | ($true = (esti @ X0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0)))))) | ((~ $false) = $false)) )),
% 1.67/1.43 inference(superposition,[status(thm)],[f1087,f33])).
% 1.67/1.43 thf(f33,plain,(
% 1.67/1.43 ( ! [X1 : nat] : (((x = (suc @ X1)) = $false)) )),
% 1.67/1.43 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.67/1.43 thf(f32,plain,(
% 1.67/1.43 ( ! [X1 : nat] : (($true = (~ (x = (suc @ X1))))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.67/1.43 thf(f31,plain,(
% 1.67/1.43 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (~ (x = (suc @ Y0)))) @ X1))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f26])).
% 1.67/1.43 thf(f26,plain,(
% 1.67/1.43 ($true = (!! @ nat @ (^[Y0 : nat]: (~ (x = (suc @ Y0))))))),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f23])).
% 1.67/1.43 thf(f23,plain,(
% 1.67/1.43 ($true = (~ (~ (!! @ nat @ (^[Y0 : nat]: (~ (x = (suc @ Y0))))))))),
% 1.67/1.43 inference(cnf_transformation,[status(thm)],[f14])).
% 1.67/1.43 thf(f14,plain,(
% 1.67/1.43 ($true = (~ (~ (!! @ nat @ (^[Y0 : nat]: (~ (x = (suc @ Y0))))))))),
% 1.67/1.43 inference(fool_elimination,[status(thm)],[f13])).
% 1.67/1.43 thf(f13,plain,(
% 1.67/1.43 ~~! [X0 : nat] : (x != (suc @ X0))),
% 1.67/1.43 inference(rectify,[status(thm)],[f7])).
% 1.67/1.43 thf(f7,negated_conjecture,(
% 1.67/1.43 ~~! [X4 : nat] : (x != (suc @ X4))),
% 1.67/1.43 inference(negated_conjecture,[status(cth)],[f6])).
% 1.67/1.43 thf(f6,conjecture,(
% 1.67/1.43 ~! [X4 : nat] : (x != (suc @ X4))),
% 1.67/1.43 file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',satz3)).
% 1.67/1.43 thf(f1087,plain,(
% 1.67/1.43 ( ! [X1 : nat,X4 : nat > $o] : (((~ (X4 @ (suc @ (sK2 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0)))))))) = $false) | ((~ (X4 @ n_1)) = $false) | ($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0))))))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f1068])).
% 1.67/1.43 thf(f1068,plain,(
% 1.67/1.43 ( ! [X1 : nat,X4 : nat > $o] : ((((^[Y0 : nat]: (~ (X4 @ Y0))) @ n_1) = $false) | ($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0)))))) | (((^[Y0 : nat]: (~ (X4 @ Y0))) @ (suc @ (sK2 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0))))))) = $false)) )),
% 1.67/1.43 inference(primitive_instantiation,[status(thm)],[f1064])).
% 1.67/1.43 thf(f1064,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o,X1 : nat] : (($false = (X0 @ (suc @ (sK2 @ (setof @ X0))))) | ((esti @ X1 @ (setof @ X0)) = $true) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f1056])).
% 1.67/1.43 thf(f1056,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))) @ X1)) | ($false = (X0 @ (suc @ (sK2 @ (setof @ X0))))) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f971])).
% 1.67/1.43 thf(f971,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))))) | ($false = (X0 @ n_1)) | ($false = (X0 @ (suc @ (sK2 @ (setof @ X0)))))) )),
% 1.67/1.43 inference(trivial_inequality_removal,[status(thm)],[f970])).
% 1.67/1.43 thf(f970,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($false = (X0 @ (suc @ (sK2 @ (setof @ X0))))) | ($false = (X0 @ n_1)) | ($true = $false) | ($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0)))))) )),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f951])).
% 1.67/1.43 thf(f951,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : ((((esti @ (sK2 @ (setof @ X0)) @ (setof @ X0)) => $true) = $false) | ($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))))) | ($false = (X0 @ (suc @ (sK2 @ (setof @ X0))))) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(superposition,[status(thm)],[f937,f53])).
% 1.67/1.43 thf(f937,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($false = ((esti @ (sK2 @ (setof @ X0)) @ (setof @ X0)) => (esti @ (suc @ (sK2 @ (setof @ X0))) @ (setof @ X0)))) | ($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))))) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f928])).
% 1.67/1.43 thf(f928,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))))) | ($false = (X0 @ n_1)) | (((^[Y0 : nat]: ((esti @ Y0 @ (setof @ X0)) => (esti @ (suc @ Y0) @ (setof @ X0)))) @ (sK2 @ (setof @ X0))) = $false)) )),
% 1.67/1.43 inference(sigma_clausification,[status(thm)],[f889])).
% 1.67/1.43 thf(f889,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ (setof @ X0)) => (esti @ (suc @ Y0) @ (setof @ X0))))) = $false) | ($false = (X0 @ n_1)) | ($true = (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0)))))) )),
% 1.67/1.43 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.67/1.43 thf(f79,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($true = ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ (setof @ X0)) => (esti @ (suc @ Y0) @ (setof @ X0))))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0)))))) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(boolean_simplification,[status(thm)],[f75])).
% 1.67/1.43 thf(f75,plain,(
% 1.67/1.43 ( ! [X0 : nat > $o] : (($true = ($true => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ (setof @ X0)) => (esti @ (suc @ Y0) @ (setof @ X0))))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ (setof @ X0))))))) | ($false = (X0 @ n_1))) )),
% 1.67/1.43 inference(superposition,[status(thm)],[f61,f53])).
% 1.67/1.43 thf(f61,plain,(
% 1.67/1.43 ( ! [X1 : set] : ((((esti @ n_1 @ X1) => ((!! @ nat @ (^[Y0 : nat]: ((esti @ Y0 @ X1) => (esti @ (suc @ Y0) @ X1)))) => (!! @ nat @ (^[Y0 : nat]: (esti @ Y0 @ X1))))) = $true)) )),
% 1.67/1.43 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.67/1.43 thf(f60,plain,(
% 1.67/1.43 ( ! [X1 : set] : (($true = ((^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0)))))) @ X1))) )),
% 1.67/1.43 inference(pi_clausification,[status(thm)],[f22])).
% 1.67/1.43 thf(f22,plain,(
% 1.67/1.43 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.67/1.43 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.43 thf(f16,plain,(
% 1.67/1.43 ($true = (!! @ set @ (^[Y0 : set]: ((esti @ n_1 @ Y0) => ((!! @ nat @ (^[Y1 : nat]: ((esti @ Y1 @ Y0) => (esti @ (suc @ Y1) @ Y0)))) => (!! @ nat @ (^[Y1 : nat]: (esti @ Y1 @ Y0))))))))),
% 1.67/1.43 inference(fool_elimination,[status(thm)],[f15])).
% 1.67/1.43 thf(f15,plain,(
% 1.67/1.43 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.67/1.43 inference(rectify,[status(thm)],[f3])).
% 1.67/1.43 thf(f3,axiom,(
% 1.67/1.43 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.67/1.43 file('/export/starexec/sandbox/tmp/tmp.hjfrc3vaog/DTF2THF_32159.p',ax5)).
% 1.67/1.43 % SZS output end Proof for DTF2THF_32159
% 1.67/1.43 % (32277)------------------------------
% 1.67/1.43 % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (32277)Termination reason: Refutation
% 1.67/1.43
% 1.67/1.43 % (32277)Memory used [KB]: 6012
% 1.67/1.43 % (32277)Time elapsed: 0.095 s
% 1.67/1.43 % (32277)Instructions burned: 247 (million)
% 1.67/1.43 % (32277)------------------------------
% 1.67/1.43 % (32277)------------------------------
% 1.67/1.43 % (32265)Success in time 0.117 s
%------------------------------------------------------------------------------