%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM636^1 : 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 : n029.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 1.62s 1.51s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 20 unt; 0 typ; 1 def)
% Number of atoms : 392 ( 184 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 553 ( 101 ~; 77 |; 6 &; 351 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 151 ( 38 ^; 109 !; 4 ?; 151 :)
% 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,
suc: nat > nat ).
thf(func_def_3,type,
set: $tType ).
thf(func_def_4,type,
esti: nat > set > $o ).
thf(func_def_5,type,
setof: ( nat > $o ) > set ).
thf(func_def_7,type,
n_1: nat ).
thf(func_def_10,type,
sK0: set > nat ).
thf(func_def_11,type,
sF1: nat ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f346,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f318,f38]) ).
thf(f38,plain,
n_1 != x,
inference(superposition,[status(thm)],[f29,f37]) ).
thf(f37,plain,
( x
= ( suc @ x ) ),
inference(backward_demodulation,[status(thm)],[f35,f36]) ).
thf(f36,plain,
x = sF1,
inference(definition_folding,[status(thm)],[f32,f35]) ).
thf(f32,plain,
( x
= ( suc @ x ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( x
= ( suc @ x ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,negated_conjecture,
~ ( ( x
!= ( suc @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f6,conjecture,
( x
!= ( suc @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',satz2) ).
thf(f35,definition,
( ( suc @ x )
= sF1 ),
introduced(definition,[],[function_definition]) ).
thf(f29,plain,
! [X0: nat] :
( n_1
!= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: nat] :
( n_1
!= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: nat] :
( n_1
!= ( suc @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',ax3) ).
thf(f318,plain,
n_1 = x,
inference(equality_proxy_clausification,[status(thm)],[f317]) ).
thf(f317,plain,
( ( x = n_1 )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f316]) ).
thf(f316,plain,
( $false
= ( x != n_1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f315]) ).
thf(f315,plain,
( ( $false = $true )
| ( $false
= ( x != n_1 ) ) ),
inference(boolean_simplification,[status(thm)],[f314]) ).
thf(f314,plain,
( ( $false
= ( x != n_1 ) )
| ( $true = ( ~ $true ) ) ),
inference(boolean_simplification,[status(thm)],[f313]) ).
thf(f313,plain,
( ( $true
= ( x != x ) )
| ( $false
= ( x != n_1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f304]) ).
thf(f304,plain,
( ( $false
= ( ^ [Y0: nat] : ( x != Y0 )
@ n_1 ) )
| ( ( ^ [Y0: nat] : ( x != Y0 )
@ x )
= $true ) ),
inference(superposition,[status(thm)],[f125,f295]) ).
thf(f295,plain,
( x
= ( sK0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f294,f38]) ).
thf(f294,plain,
( ( x
= ( sK0
@ ( setof
@ ^ [Y0: nat] : ( x != Y0 ) ) ) )
| ( n_1 = x ) ),
inference(equality_resolution,[status(thm)],[f284]) ).
thf(f284,plain,
! [X0: nat] :
( ( x != X0 )
| ( x
= ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X0 != Y0 ) ) ) )
| ( n_1 = X0 ) ),
inference(superposition,[status(thm)],[f39,f260]) ).
thf(f260,plain,
! [X0: nat] :
( ( ( suc
@ ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X0 != Y0 ) ) ) )
= X0 )
| ( n_1 = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
! [X0: nat] :
( ( ( suc
@ ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $true
= ( X0 = n_1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
! [X0: nat] :
( ( ( suc
@ ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $false
= ( X0 != n_1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f229]) ).
thf(f229,plain,
! [X0: nat] :
( ( ( suc
@ ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X0 != Y0 ) ) ) )
= X0 )
| ( $false
= ( ^ [Y0: nat] : ( X0 != Y0 )
@ n_1 ) ) ),
inference(leibniz_equality_elimination,[status(thm)],[f227]) ).
thf(f227,plain,
! [X0: nat,X1: nat > $o] :
( ( $false
= ( X1 @ ( suc @ ( sK0 @ ( setof @ X1 ) ) ) ) )
| ( ( X1 @ X0 )
= $true )
| ( $false
= ( X1 @ n_1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
! [X0: nat,X1: nat > $o] :
( ( $false
= ( X1 @ ( suc @ ( sK0 @ ( setof @ X1 ) ) ) ) )
| ( $true != $true )
| ( ( X1 @ X0 )
= $true )
| ( $false
= ( X1 @ n_1 ) ) ),
inference(superposition,[status(thm)],[f34,f194]) ).
thf(f194,plain,
! [X0: nat > $o,X1: nat] :
( ( $false
= ( X0 @ ( suc @ ( sK0 @ ( setof @ X0 ) ) ) ) )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true )
| ( $false
= ( X0 @ n_1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f193]) ).
thf(f193,plain,
! [X0: nat > $o,X1: nat] :
( ( $false
= ( X0 @ n_1 ) )
| ( $false
= ( X0 @ ( suc @ ( sK0 @ ( setof @ X0 ) ) ) ) )
| ( $true != $true )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f109,f98]) ).
thf(f98,plain,
! [X0: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X0 ) )
= $true )
| ( ( X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: nat > $o,X1: nat] :
( ( ( esti @ X1 @ ( setof @ X0 ) )
= $true )
| ( ( X0 @ X1 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28,f75]) ).
thf(f75,plain,
! [X0: nat,X1: nat > $o] :
( ( ( X1 @ X0 )
= $true )
| ( $false
= ( X1 @ X0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: nat,X1: nat > $o] :
( ( ( X1 @ X0 )
= $true )
| ( $true
= ( ~ ( X1 @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: nat,X1: nat > $o] :
( ( ( X1 @ X0 )
= $true )
| ( $true
= ( ^ [Y0: nat] :
~ ( X1 @ Y0 )
@ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: nat,X1: nat > $o] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: nat] :
~ ( X1 @ Y0 )
@ X0 ) )
| ( ( X1 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f34,f49]) ).
thf(f49,plain,
! [X1: nat,X4: nat > $o] :
( ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
= ( X4 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: nat,X4: nat > $o] :
( ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X4 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: nat,X4: nat > $o] :
( ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X4 @ Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: nat] :
~ ( X4 @ Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: nat > $o,X1: nat] :
( ( ( X0 @ X1 )
!= $true )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat > $o,X1: nat] :
( ( ( X0 @ X1 )
!= $true )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: nat > $o,X0: nat] :
( ( ( X1 @ X0 )
!= $true )
| ( $true
= ( esti @ X0 @ ( setof @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: nat > $o,X0: nat] :
( ( ( X1 @ X0 )
= $true )
=> ( $true
= ( esti @ X0 @ ( setof @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: nat,X1: nat > $o] :
( ( X1 @ X0 )
=> ( esti @ X0 @ ( setof @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: nat,X0: nat > $o] :
( ( X0 @ X1 )
=> ( esti @ X1 @ ( setof @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',estii) ).
thf(f109,plain,
! [X0: nat > $o,X1: nat] :
( ( $true
!= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( $false
= ( X0 @ ( suc @ ( sK0 @ ( setof @ X0 ) ) ) ) )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true
!= ( esti @ n_1 @ ( setof @ X0 ) ) )
| ( ( esti @ X1 @ ( setof @ X0 ) )
= $true )
| ( $false
= ( X0 @ ( suc @ ( sK0 @ ( setof @ X0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f31,f98]) ).
thf(f31,plain,
! [X0: set,X1: nat] :
( ( $true
!= ( esti @ ( suc @ ( sK0 @ X0 ) ) @ X0 ) )
| ( ( esti @ n_1 @ X0 )
!= $true )
| ( ( esti @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: set] :
( ( ( esti @ n_1 @ X0 )
!= $true )
| ! [X1: nat] :
( ( esti @ X1 @ X0 )
= $true )
| ( ( $true
!= ( esti @ ( suc @ ( sK0 @ X0 ) ) @ X0 ) )
& ( ( esti @ ( sK0 @ X0 ) @ X0 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25]) ).
thf(f25,plain,
! [X0: set] :
( ? [X2: nat] :
( ( $true
!= ( esti @ ( suc @ X2 ) @ X0 ) )
& ( $true
= ( esti @ X2 @ X0 ) ) )
=> ( ( $true
!= ( esti @ ( suc @ ( sK0 @ X0 ) ) @ X0 ) )
& ( ( esti @ ( sK0 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
! [X0: set] :
( ( ( esti @ n_1 @ X0 )
!= $true )
| ! [X1: nat] :
( ( esti @ X1 @ X0 )
= $true )
| ? [X2: nat] :
( ( $true
!= ( esti @ ( suc @ X2 ) @ X0 ) )
& ( $true
= ( esti @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: set] :
( ( ( esti @ n_1 @ X0 )
!= $true )
| ! [X2: nat] :
( $true
= ( esti @ X2 @ X0 ) )
| ? [X1: nat] :
( ( ( esti @ ( suc @ X1 ) @ X0 )
!= $true )
& ( ( esti @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: set] :
( ! [X2: nat] :
( $true
= ( esti @ X2 @ X0 ) )
| ? [X1: nat] :
( ( ( esti @ ( suc @ X1 ) @ X0 )
!= $true )
& ( ( esti @ X1 @ X0 )
= $true ) )
| ( ( esti @ n_1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: set] :
( ( ( esti @ n_1 @ X0 )
= $true )
=> ( ! [X1: nat] :
( ( ( esti @ X1 @ X0 )
= $true )
=> ( ( esti @ ( suc @ X1 ) @ X0 )
= $true ) )
=> ! [X2: nat] :
( $true
= ( esti @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: set] :
( ( esti @ n_1 @ X0 )
=> ( ! [X1: nat] :
( ( esti @ X1 @ X0 )
=> ( esti @ ( suc @ X1 ) @ X0 ) )
=> ! [X2: nat] : ( esti @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: set] :
( ( esti @ n_1 @ X1 )
=> ( ! [X2: nat] :
( ( esti @ X2 @ X1 )
=> ( esti @ ( suc @ X2 ) @ X1 ) )
=> ! [X2: nat] : ( esti @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',ax5) ).
thf(f34,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
!= ( esti @ X0 @ ( setof @ X1 ) ) )
| ( ( X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: nat > $o] :
( ( $true
!= ( esti @ X0 @ ( setof @ X1 ) ) )
| ( ( X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: nat > $o,X0: nat] :
( ( $true
= ( esti @ X0 @ ( setof @ X1 ) ) )
=> ( ( X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: nat,X1: nat > $o] :
( ( esti @ X0 @ ( setof @ X1 ) )
=> ( X1 @ X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X0: nat > $o] :
( ( esti @ X1 @ ( setof @ X0 ) )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',estie) ).
thf(f39,plain,
! [X0: nat] :
( ( x
!= ( suc @ X0 ) )
| ( x = X0 ) ),
inference(superposition,[status(thm)],[f33,f37]) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: nat,X0: nat] :
( ( ( suc @ X0 )
!= ( suc @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( suc @ X0 )
!= ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: nat,X3: nat] :
( ( X2 != X3 )
=> ( ( suc @ X2 )
!= ( suc @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',satz1) ).
thf(f125,plain,
! [X3: nat > $o] :
( ( $true
= ( X3 @ ( sK0 @ ( setof @ X3 ) ) ) )
| ( $false
= ( X3 @ n_1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X3: nat > $o] :
( ( $true
= ( ~ ( X3 @ n_1 ) ) )
| ( $true
= ( X3 @ ( sK0 @ ( setof @ X3 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X3: nat > $o] :
( ( ( ~ ( X3 @ ( sK0 @ ( setof @ X3 ) ) ) )
= $false )
| ( $true
= ( ~ ( X3 @ n_1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f122]) ).
thf(f122,plain,
! [X3: nat > $o] :
( ( $true
= ( ~ ( X3 @ n_1 ) ) )
| ( $false
= ( ~ ( X3
@ ( sK0
@ ( setof
@ ^ [Y0: nat] : ( X3 @ Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X3: nat > $o] :
( ( $true
= ( ~ ( X3 @ n_1 ) ) )
| ( $false
= ( ~ ( X3
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ~ ( X3 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
! [X3: nat > $o] :
( ( $false
= ( ^ [Y0: nat] :
~ ( X3 @ Y0 )
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( ^ [Y1: nat] :
~ ( X3 @ Y1 )
@ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: nat] :
~ ( X3 @ Y0 )
@ n_1 ) ) ),
inference(primitive_instantiation,[status(thm)],[f80]) ).
thf(f80,plain,
! [X0: nat > $o] :
( ( $false
= ( X0
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: nat > $o] :
( ( $true
= ( ~ ( X0
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) ) ) )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X0: nat > $o] :
( ( $true
= ( X0 @ n_1 ) )
| ( $true
= ( ^ [Y0: nat] :
~ ( X0 @ Y0 )
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: nat > $o] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: nat] :
~ ( X0 @ Y0 )
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(superposition,[status(thm)],[f34,f65]) ).
thf(f65,plain,
! [X0: nat > $o] :
( ( $true
= ( esti
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) )
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: nat > $o] :
( ( $true
= ( esti
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) )
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(equality_factoring,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: nat > $o,X1: nat] :
( ( $true
= ( esti
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) )
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: nat > $o,X1: nat] :
( ( $true
= ( esti @ X1
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true
= ( esti
@ ( sK0
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) )
@ ( setof
@ ^ [Y0: nat] :
~ ( X0 @ Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( X0 @ n_1 ) ) ),
inference(superposition,[status(thm)],[f30,f49]) ).
thf(f30,plain,
! [X0: set,X1: nat] :
( ( ( esti @ n_1 @ X0 )
!= $true )
| ( ( esti @ ( sK0 @ X0 ) @ X0 )
= $true )
| ( ( esti @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM636^1 : 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
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:09:14 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : NUM636^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Number Theory
% 0.31/0.46 % Problem : Landau theorem 2
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : ~(suc x = x)
% 0.31/0.46
% 0.31/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.31/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : satz2 [Lan30]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % : Without extensionality : Theorem
% 0.31/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 13 ( 4 unt; 7 typ; 0 def)
% 0.31/0.46 % Number of atoms : 10 ( 4 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.31/0.46 % Number of connectives : 31 ( 4 ~; 0 |; 0 &; 21 @)
% 0.31/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.31/0.46 % Number of types : 3 ( 2 usr)
% 0.31/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(nat_type,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(x,type,
% 0.31/0.46 x: nat ).
% 0.31/0.46
% 0.31/0.46 thf(suc,type,
% 0.31/0.46 suc: nat > nat ).
% 0.31/0.46
% 0.31/0.46 thf(set_type,type,
% 0.31/0.46 set: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(esti,type,
% 0.31/0.46 esti: nat > set > $o ).
% 0.31/0.46
% 0.31/0.46 thf(setof,type,
% 0.31/0.46 setof: ( nat > $o ) > set ).
% 0.31/0.46
% 0.31/0.46 thf(estie,axiom,
% 0.31/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.31/0.46 ( ( esti @ Xs @ ( setof @ Xp ) )
% 0.31/0.46 => ( Xp @ Xs ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(n_1,type,
% 0.31/0.46 n_1: nat ).
% 0.31/0.46
% 0.31/0.46 thf(ax5,axiom,
% 0.31/0.46 ! [Xs: set] :
% 0.31/0.46 ( ( esti @ n_1 @ Xs )
% 0.31/0.46 => ( ! [Xx: nat] :
% 0.31/0.46 ( ( esti @ Xx @ Xs )
% 0.31/0.46 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 0.31/0.46 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(estii,axiom,
% 0.31/0.46 ! [Xp: nat > $o,Xs: nat] :
% 0.31/0.46 ( ( Xp @ Xs )
% 0.31/0.46 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(ax3,axiom,
% 0.31/0.46 ! [Xx: nat] :
% 0.31/0.46 ( ( suc @ Xx )
% 0.31/0.46 != n_1 ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz1,axiom,
% 0.31/0.46 ! [Xx: nat,Xy: nat] :
% 0.31/0.46 ( ( Xx != Xy )
% 0.31/0.46 => ( ( suc @ Xx )
% 0.31/0.46 != ( suc @ Xy ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(satz2,conjecture,
% 0.31/0.46 ( ( suc @ x )
% 0.31/0.46 != x ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 11:09:15 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2DTF26748.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(nat_type,type,
% 1.46/1.28 nat: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(x,type,
% 1.46/1.28 x: nat ).
% 1.46/1.28
% 1.46/1.28 thf(suc,type,
% 1.46/1.28 suc: nat > nat ).
% 1.46/1.28
% 1.46/1.28 thf(set_type,type,
% 1.46/1.28 set: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(esti,type,
% 1.46/1.28 esti: nat > set > $o ).
% 1.46/1.28
% 1.46/1.28 thf(setof,type,
% 1.46/1.28 setof: ( nat > $o ) > set ).
% 1.46/1.28
% 1.46/1.28 thf(estie,axiom,
% 1.46/1.28 ! [Xp: nat > $o,Xs: nat] :
% 1.46/1.28 ( ( esti @ Xs @ ( setof @ Xp ) )
% 1.46/1.28 => ( Xp @ Xs ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(n_1,type,
% 1.46/1.28 n_1: nat ).
% 1.46/1.28
% 1.46/1.28 thf(ax5,axiom,
% 1.46/1.28 ! [Xs: set] :
% 1.46/1.28 ( ( esti @ n_1 @ Xs )
% 1.46/1.28 => ( ! [Xx: nat] :
% 1.46/1.28 ( ( esti @ Xx @ Xs )
% 1.46/1.28 => ( esti @ ( suc @ Xx ) @ Xs ) )
% 1.46/1.28 => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(estii,axiom,
% 1.46/1.28 ! [Xp: nat > $o,Xs: nat] :
% 1.46/1.28 ( ( Xp @ Xs )
% 1.46/1.28 => ( esti @ Xs @ ( setof @ Xp ) ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(ax3,axiom,
% 1.46/1.28 ! [Xx: nat] :
% 1.46/1.28 ( ( suc @ Xx )
% 1.46/1.28 != n_1 ) ).
% 1.46/1.28
% 1.46/1.28 thf(satz1,axiom,
% 1.46/1.28 ! [Xx: nat,Xy: nat] :
% 1.46/1.28 ( ( Xx != Xy )
% 1.46/1.28 => ( ( suc @ Xx )
% 1.46/1.28 != ( suc @ Xy ) ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(satz2,conjecture,
% 1.46/1.28 ( ( suc @ x )
% 1.46/1.28 != x ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (27026)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_26748 for (2999ds/4Mi)
% 1.46/1.30 % (27027)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_26748 for (2999ds/27Mi)
% 1.62/1.30 % (27026)Instruction limit reached!
% 1.62/1.30 % (27026)------------------------------
% 1.62/1.30 % (27026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27026)Termination reason: Unknown
% 1.62/1.30 % (27026)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (27026)Memory used [KB]: 5500
% 1.62/1.30 % (27026)Time elapsed: 0.003 s
% 1.62/1.30 % (27026)Instructions burned: 5 (million)
% 1.62/1.30 % (27026)------------------------------
% 1.62/1.30 % (27026)------------------------------
% 1.62/1.30 % (27027)Refutation not found, incomplete strategy
% 1.62/1.30 % (27027)------------------------------
% 1.62/1.30 % (27027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27027)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (27027)Memory used [KB]: 5500
% 1.62/1.30 % (27027)Time elapsed: 0.002 s
% 1.62/1.30 % (27027)Instructions burned: 2 (million)
% 1.62/1.30 % (27027)------------------------------
% 1.62/1.30 % (27027)------------------------------
% 1.62/1.30 % (27025)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/183Mi)
% 1.62/1.30 % (27028)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/2Mi)
% 1.62/1.30 % (27029)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_26748 for (2999ds/2Mi)
% 1.62/1.30 % (27030)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_26748 for (2999ds/275Mi)
% 1.62/1.30 % (27031)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/18Mi)
% 1.62/1.30 % (27029)Instruction limit reached!
% 1.62/1.30 % (27029)------------------------------
% 1.62/1.30 % (27029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27029)Termination reason: Unknown
% 1.62/1.30 % (27029)Termination phase: shuffling
% 1.62/1.30
% 1.62/1.30 % (27029)Memory used [KB]: 895
% 1.62/1.30 % (27029)Time elapsed: 0.003 s
% 1.62/1.30 % (27029)Instructions burned: 2 (million)
% 1.62/1.30 % (27029)------------------------------
% 1.62/1.30 % (27029)------------------------------
% 1.62/1.30 % (27028)Instruction limit reached!
% 1.62/1.30 % (27028)------------------------------
% 1.62/1.30 % (27028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27028)Termination reason: Unknown
% 1.62/1.30 % (27028)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (27028)Memory used [KB]: 5500
% 1.62/1.30 % (27028)Time elapsed: 0.004 s
% 1.62/1.30 % (27030)Refutation not found, incomplete strategy
% 1.62/1.30 % (27030)------------------------------
% 1.62/1.30 % (27030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27028)Instructions burned: 2 (million)
% 1.62/1.30 % (27028)------------------------------
% 1.62/1.30 % (27028)------------------------------
% 1.62/1.30 % (27030)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.30
% 1.62/1.30
% 1.62/1.30 % (27030)Memory used [KB]: 5500
% 1.62/1.30 % (27030)Time elapsed: 0.003 s
% 1.62/1.30 % (27030)Instructions burned: 1 (million)
% 1.62/1.30 % (27030)------------------------------
% 1.62/1.30 % (27030)------------------------------
% 1.62/1.31 % (27032)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/3Mi)
% 1.62/1.31 % (27032)Instruction limit reached!
% 1.62/1.31 % (27032)------------------------------
% 1.62/1.31 % (27032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (27032)Termination reason: Unknown
% 1.62/1.31 % (27033)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_26748 for (2999ds/37Mi)
% 1.62/1.31 % (27032)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (27032)Memory used [KB]: 5500
% 1.62/1.31 % (27032)Time elapsed: 0.003 s
% 1.62/1.31 % (27032)Instructions burned: 5 (million)
% 1.62/1.31 % (27032)------------------------------
% 1.62/1.31 % (27032)------------------------------
% 1.62/1.32 % (27031)Instruction limit reached!
% 1.62/1.32 % (27031)------------------------------
% 1.62/1.32 % (27031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27031)Termination reason: Unknown
% 1.62/1.32 % (27031)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (27031)Memory used [KB]: 5628
% 1.62/1.32 % (27031)Time elapsed: 0.014 s
% 1.62/1.32 % (27031)Instructions burned: 19 (million)
% 1.62/1.32 % (27031)------------------------------
% 1.62/1.32 % (27031)------------------------------
% 1.62/1.32 % (27037)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/7Mi)
% 1.62/1.32 % (27033)Instruction limit reached!
% 1.62/1.32 % (27033)------------------------------
% 1.62/1.32 % (27033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27033)Termination reason: Unknown
% 1.62/1.32 % (27033)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (27033)Memory used [KB]: 5884
% 1.62/1.32 % (27033)Time elapsed: 0.014 s
% 1.62/1.32 % (27033)Instructions burned: 37 (million)
% 1.62/1.32 % (27033)------------------------------
% 1.62/1.32 % (27033)------------------------------
% 1.62/1.32 % (27037)Instruction limit reached!
% 1.62/1.32 % (27037)------------------------------
% 1.62/1.32 % (27037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27037)Termination reason: Unknown
% 1.62/1.32 % (27037)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (27037)Memory used [KB]: 1023
% 1.62/1.32 % (27037)Time elapsed: 0.004 s
% 1.62/1.32 % (27037)Instructions burned: 8 (million)
% 1.62/1.32 % (27037)------------------------------
% 1.62/1.32 % (27037)------------------------------
% 1.62/1.32 % (27034)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_26748 for (2999ds/15Mi)
% 1.62/1.32 % (27035)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_26748 for (2999ds/3Mi)
% 1.62/1.32 % (27036)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_26748 for (2999ds/1041Mi)
% 1.62/1.32 % (27034)Refutation not found, incomplete strategy
% 1.62/1.32 % (27034)------------------------------
% 1.62/1.32 % (27034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (27034)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.32
% 1.62/1.32
% 1.62/1.32 % (27034)Memory used [KB]: 5500
% 1.62/1.32 % (27034)Time elapsed: 0.004 s
% 1.62/1.32 % (27034)Instructions burned: 2 (million)
% 1.62/1.32 % (27034)------------------------------
% 1.62/1.32 % (27034)------------------------------
% 1.62/1.33 % (27035)Instruction limit reached!
% 1.62/1.33 % (27035)------------------------------
% 1.62/1.33 % (27035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (27035)Termination reason: Unknown
% 1.62/1.33 % (27035)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (27035)Memory used [KB]: 5500
% 1.62/1.33 % (27035)Time elapsed: 0.005 s
% 1.62/1.33 % (27035)Instructions burned: 4 (million)
% 1.62/1.33 % (27035)------------------------------
% 1.62/1.33 % (27035)------------------------------
% 1.62/1.33 % (27040)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_26748 for (2999ds/3Mi)
% 1.62/1.33 % (27040)Instruction limit reached!
% 1.62/1.33 % (27040)------------------------------
% 1.62/1.33 % (27040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (27040)Termination reason: Unknown
% 1.62/1.33 % (27040)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (27040)Memory used [KB]: 1023
% 1.62/1.33 % (27040)Time elapsed: 0.002 s
% 1.62/1.33 % (27040)Instructions burned: 3 (million)
% 1.62/1.33 % (27040)------------------------------
% 1.62/1.33 % (27040)------------------------------
% 1.62/1.33 % (27038)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/16Mi)
% 1.62/1.34 % (27039)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_26748 for (2999ds/3Mi)
% 1.62/1.34 % (27039)Instruction limit reached!
% 1.62/1.34 % (27039)------------------------------
% 1.62/1.34 % (27039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (27039)Termination reason: Unknown
% 1.62/1.34 % (27039)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (27039)Memory used [KB]: 5500
% 1.62/1.34 % (27039)Time elapsed: 0.004 s
% 1.62/1.34 % (27039)Instructions burned: 3 (million)
% 1.62/1.34 % (27039)------------------------------
% 1.62/1.34 % (27039)------------------------------
% 1.62/1.34 % (27043)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/4Mi)
% 1.62/1.34 % (27043)Instruction limit reached!
% 1.62/1.34 % (27043)------------------------------
% 1.62/1.34 % (27043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (27043)Termination reason: Unknown
% 1.62/1.34 % (27043)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (27043)Memory used [KB]: 5500
% 1.62/1.34 % (27043)Time elapsed: 0.003 s
% 1.62/1.34 % (27043)Instructions burned: 5 (million)
% 1.62/1.34 % (27043)------------------------------
% 1.62/1.34 % (27043)------------------------------
% 1.62/1.34 % (27041)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/7Mi)
% 1.62/1.34 % (27042)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/3Mi)
% 1.62/1.34 % (27038)Instruction limit reached!
% 1.62/1.34 % (27038)------------------------------
% 1.62/1.34 % (27038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (27038)Termination reason: Unknown
% 1.62/1.34 % (27038)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (27038)Memory used [KB]: 5628
% 1.62/1.34 % (27038)Time elapsed: 0.013 s
% 1.62/1.34 % (27038)Instructions burned: 17 (million)
% 1.62/1.34 % (27038)------------------------------
% 1.62/1.34 % (27038)------------------------------
% 1.62/1.34 % (27042)Instruction limit reached!
% 1.62/1.34 % (27042)------------------------------
% 1.62/1.34 % (27042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (27042)Termination reason: Unknown
% 1.62/1.34 % (27042)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (27042)Memory used [KB]: 5500
% 1.62/1.34 % (27042)Time elapsed: 0.004 s
% 1.62/1.34 % (27042)Instructions burned: 3 (million)
% 1.62/1.34 % (27042)------------------------------
% 1.62/1.34 % (27042)------------------------------
% 1.62/1.34 % (27041)Refutation not found, incomplete strategy
% 1.62/1.34 % (27041)------------------------------
% 1.62/1.34 % (27041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (27041)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.34
% 1.62/1.34
% 1.62/1.34 % (27041)Memory used [KB]: 5500
% 1.62/1.34 % (27041)Time elapsed: 0.005 s
% 1.62/1.34 % (27041)Instructions burned: 4 (million)
% 1.62/1.34 % (27041)------------------------------
% 1.62/1.34 % (27041)------------------------------
% 1.62/1.35 % (27045)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/710Mi)
% 1.62/1.36 % (27044)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/18Mi)
% 1.62/1.36 % (27046)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/6Mi)
% 1.62/1.36 % (27047)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_26748 for (2999ds/902Mi)
% 1.62/1.36 % (27044)Refutation not found, incomplete strategy
% 1.62/1.36 % (27044)------------------------------
% 1.62/1.36 % (27044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (27044)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.36
% 1.62/1.36
% 1.62/1.36 % (27044)Memory used [KB]: 5500
% 1.62/1.36 % (27044)Time elapsed: 0.007 s
% 1.62/1.36 % (27044)Instructions burned: 7 (million)
% 1.62/1.36 % (27044)------------------------------
% 1.62/1.36 % (27044)------------------------------
% 1.62/1.36 % (27048)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_26748 for (2999ds/21Mi)
% 1.62/1.36 % (27047)Refutation not found, incomplete strategy
% 1.62/1.36 % (27047)------------------------------
% 1.62/1.36 % (27047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (27047)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.36
% 1.62/1.36
% 1.62/1.36 % (27047)Memory used [KB]: 5500
% 1.62/1.36 % (27047)Time elapsed: 0.003 s
% 1.62/1.36 % (27047)Instructions burned: 2 (million)
% 1.62/1.36 % (27047)------------------------------
% 1.62/1.36 % (27047)------------------------------
% 1.62/1.36 % (27046)Instruction limit reached!
% 1.62/1.36 % (27046)------------------------------
% 1.62/1.36 % (27046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (27046)Termination reason: Unknown
% 1.62/1.36 % (27046)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (27046)Memory used [KB]: 5500
% 1.62/1.36 % (27046)Time elapsed: 0.006 s
% 1.62/1.36 % (27046)Instructions burned: 7 (million)
% 1.62/1.36 % (27046)------------------------------
% 1.62/1.36 % (27046)------------------------------
% 1.62/1.38 % (27051)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/377Mi)
% 1.62/1.38 % (27048)Instruction limit reached!
% 1.62/1.38 % (27048)------------------------------
% 1.62/1.38 % (27048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (27048)Termination reason: Unknown
% 1.62/1.38 % (27048)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (27048)Memory used [KB]: 5628
% 1.62/1.38 % (27048)Time elapsed: 0.016 s
% 1.62/1.38 % (27048)Instructions burned: 21 (million)
% 1.62/1.38 % (27048)------------------------------
% 1.62/1.38 % (27048)------------------------------
% 1.62/1.38 % (27049)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/5Mi)
% 1.62/1.38 % (27050)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_26748 for (2999ds/6Mi)
% 1.62/1.38 % (27049)Instruction limit reached!
% 1.62/1.38 % (27049)------------------------------
% 1.62/1.38 % (27049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (27049)Termination reason: Unknown
% 1.62/1.38 % (27049)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (27049)Memory used [KB]: 5500
% 1.62/1.38 % (27049)Time elapsed: 0.005 s
% 1.62/1.38 % (27049)Instructions burned: 5 (million)
% 1.62/1.38 % (27049)------------------------------
% 1.62/1.38 % (27049)------------------------------
% 1.62/1.39 % (27050)Refutation not found, incomplete strategy
% 1.62/1.39 % (27050)------------------------------
% 1.62/1.39 % (27050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (27050)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.39
% 1.62/1.39
% 1.62/1.39 % (27050)Memory used [KB]: 5500
% 1.62/1.39 % (27050)Time elapsed: 0.005 s
% 1.62/1.39 % (27050)Instructions burned: 5 (million)
% 1.62/1.39 % (27050)------------------------------
% 1.62/1.39 % (27050)------------------------------
% 1.62/1.39 % (27025)Instruction limit reached!
% 1.62/1.39 % (27025)------------------------------
% 1.62/1.39 % (27025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (27025)Termination reason: Unknown
% 1.62/1.39 % (27025)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (27025)Memory used [KB]: 6524
% 1.62/1.39 % (27025)Time elapsed: 0.090 s
% 1.62/1.39 % (27025)Instructions burned: 184 (million)
% 1.62/1.39 % (27025)------------------------------
% 1.62/1.39 % (27025)------------------------------
% 1.62/1.39 % (27052)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_26748 for (2999ds/779Mi)
% 1.62/1.39 % (27053)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_26748 for (2999ds/19Mi)
% 1.62/1.40 % (27053)Refutation not found, incomplete strategy
% 1.62/1.40 % (27053)------------------------------
% 1.62/1.40 % (27053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (27053)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.40
% 1.62/1.40
% 1.62/1.40 % (27053)Memory used [KB]: 5500
% 1.62/1.40 % (27053)Time elapsed: 0.002 s
% 1.62/1.40 % (27053)Instructions burned: 3 (million)
% 1.62/1.40 % (27053)------------------------------
% 1.62/1.40 % (27053)------------------------------
% 1.62/1.40 % (27055)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/17Mi)
% 1.62/1.40 % (27054)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/879Mi)
% 1.62/1.41 % (27056)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26748 for (2999ds/3Mi)
% 1.62/1.41 % (27055)Instruction limit reached!
% 1.62/1.41 % (27055)------------------------------
% 1.62/1.41 % (27055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (27055)Termination reason: Unknown
% 1.62/1.41 % (27055)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (27055)Memory used [KB]: 5628
% 1.62/1.41 % (27055)Time elapsed: 0.008 s
% 1.62/1.41 % (27055)Instructions burned: 17 (million)
% 1.62/1.41 % (27055)------------------------------
% 1.62/1.41 % (27055)------------------------------
% 1.62/1.41 % (27056)Instruction limit reached!
% 1.62/1.41 % (27056)------------------------------
% 1.62/1.41 % (27056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (27056)Termination reason: Unknown
% 1.62/1.41 % (27056)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (27056)Memory used [KB]: 1023
% 1.62/1.41 % (27056)Time elapsed: 0.003 s
% 1.62/1.41 % (27056)Instructions burned: 4 (million)
% 1.62/1.41 % (27056)------------------------------
% 1.62/1.41 % (27056)------------------------------
% 1.62/1.42 % (27057)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/30Mi)
% 1.62/1.42 % (27058)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/127Mi)
% 1.62/1.42 % (27054)Refutation not found, incomplete strategy
% 1.62/1.42 % (27054)------------------------------
% 1.62/1.42 % (27054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.42 % (27054)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.42
% 1.62/1.42
% 1.62/1.42 % (27054)Memory used [KB]: 5628
% 1.62/1.42 % (27054)Time elapsed: 0.019 s
% 1.62/1.42 % (27054)Instructions burned: 38 (million)
% 1.62/1.42 % (27054)------------------------------
% 1.62/1.42 % (27054)------------------------------
% 1.62/1.43 % (27057)Instruction limit reached!
% 1.62/1.43 % (27057)------------------------------
% 1.62/1.43 % (27057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (27057)Termination reason: Unknown
% 1.62/1.43 % (27057)Termination phase: Saturation
% 1.62/1.43
% 1.62/1.43 % (27057)Memory used [KB]: 5628
% 1.62/1.43 % (27057)Time elapsed: 0.013 s
% 1.62/1.43 % (27057)Instructions burned: 32 (million)
% 1.62/1.43 % (27057)------------------------------
% 1.62/1.43 % (27057)------------------------------
% 1.62/1.43 % (27059)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/100Mi)
% 1.62/1.43 % (27059)Refutation not found, incomplete strategy
% 1.62/1.43 % (27059)------------------------------
% 1.62/1.43 % (27059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (27059)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.43
% 1.62/1.43
% 1.62/1.43 % (27059)Memory used [KB]: 5500
% 1.62/1.43 % (27059)Time elapsed: 0.005 s
% 1.62/1.43 % (27059)Instructions burned: 9 (million)
% 1.62/1.43 % (27059)------------------------------
% 1.62/1.43 % (27059)------------------------------
% 1.62/1.44 % (27060)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_26748 for (2998ds/3Mi)
% 1.62/1.44 % (27060)Instruction limit reached!
% 1.62/1.44 % (27060)------------------------------
% 1.62/1.44 % (27060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (27060)Termination reason: Unknown
% 1.62/1.44 % (27060)Termination phase: Saturation
% 1.62/1.44
% 1.62/1.44 % (27060)Memory used [KB]: 5500
% 1.62/1.44 % (27060)Time elapsed: 0.003 s
% 1.62/1.44 % (27060)Instructions burned: 3 (million)
% 1.62/1.44 % (27060)------------------------------
% 1.62/1.44 % (27060)------------------------------
% 1.62/1.44 % (27061)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_26748 for (2998ds/20Mi)
% 1.62/1.45 % (27061)Refutation not found, incomplete strategy
% 1.62/1.45 % (27061)------------------------------
% 1.62/1.45 % (27061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (27061)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.45
% 1.62/1.45
% 1.62/1.45 % (27061)Memory used [KB]: 5500
% 1.62/1.45 % (27061)Time elapsed: 0.002 s
% 1.62/1.45 % (27061)Instructions burned: 1 (million)
% 1.62/1.45 % (27061)------------------------------
% 1.62/1.45 % (27061)------------------------------
% 1.62/1.45 % (27062)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/86Mi)
% 1.62/1.46 % (27063)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/107Mi)
% 1.62/1.46 % (27063)Refutation not found, incomplete strategy
% 1.62/1.46 % (27063)------------------------------
% 1.62/1.46 % (27063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (27063)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.46
% 1.62/1.46
% 1.62/1.46 % (27063)Memory used [KB]: 5500
% 1.62/1.46 % (27063)Time elapsed: 0.003 s
% 1.62/1.46 % (27063)Instructions burned: 3 (million)
% 1.62/1.46 % (27063)------------------------------
% 1.62/1.46 % (27063)------------------------------
% 1.62/1.46 % (27058)Instruction limit reached!
% 1.62/1.46 % (27058)------------------------------
% 1.62/1.46 % (27058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (27058)Termination reason: Unknown
% 1.62/1.46 % (27058)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (27058)Memory used [KB]: 6140
% 1.62/1.46 % (27058)Time elapsed: 0.044 s
% 1.62/1.46 % (27058)Instructions burned: 127 (million)
% 1.62/1.46 % (27058)------------------------------
% 1.62/1.46 % (27058)------------------------------
% 1.62/1.47 % (27064)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/39Mi)
% 1.62/1.47 % (27065)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/448Mi)
% 1.62/1.48 % (27062)Instruction limit reached!
% 1.62/1.48 % (27062)------------------------------
% 1.62/1.48 % (27062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (27062)Termination reason: Unknown
% 1.62/1.48 % (27062)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (27062)Memory used [KB]: 5884
% 1.62/1.48 % (27062)Time elapsed: 0.052 s
% 1.62/1.48 % (27062)Instructions burned: 89 (million)
% 1.62/1.48 % (27062)------------------------------
% 1.62/1.48 % (27062)------------------------------
% 1.62/1.48 % (27064)Instruction limit reached!
% 1.62/1.48 % (27064)------------------------------
% 1.62/1.48 % (27064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (27064)Termination reason: Unknown
% 1.62/1.48 % (27064)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (27064)Memory used [KB]: 5756
% 1.62/1.48 % (27064)Time elapsed: 0.015 s
% 1.62/1.48 % (27064)Instructions burned: 39 (million)
% 1.62/1.48 % (27064)------------------------------
% 1.62/1.48 % (27064)------------------------------
% 1.62/1.49 % (27066)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/46Mi)
% 1.62/1.49 % (27067)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_26748 for (2998ds/98Mi)
% 1.62/1.50 % (27051)Instruction limit reached!
% 1.62/1.50 % (27051)------------------------------
% 1.62/1.50 % (27051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.50 % (27051)Termination reason: Unknown
% 1.62/1.50 % (27051)Termination phase: Saturation
% 1.62/1.50
% 1.62/1.50 % (27051)Memory used [KB]: 6268
% 1.62/1.50 % (27051)Time elapsed: 0.121 s
% 1.62/1.50 % (27051)Instructions burned: 378 (million)
% 1.62/1.50 % (27051)------------------------------
% 1.62/1.50 % (27051)------------------------------
% 1.62/1.50 % (27066)First to succeed.
% 1.62/1.51 % (27068)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_26748 for (2997ds/507Mi)
% 1.62/1.51 % (27066)Refutation found. Thanks to Tanya!
% 1.62/1.51 % SZS status Theorem for DTF2THF_26748
% 1.62/1.51 % SZS output start Proof for DTF2THF_26748
% 1.62/1.51 thf(type_def_5, type, nat: $tType).
% 1.62/1.51 thf(type_def_7, type, set: $tType).
% 1.62/1.51 thf(func_def_0, type, nat: $tType).
% 1.62/1.51 thf(func_def_1, type, x: nat).
% 1.62/1.51 thf(func_def_2, type, suc: nat > nat).
% 1.62/1.51 thf(func_def_3, type, set: $tType).
% 1.62/1.51 thf(func_def_4, type, esti: nat > set > $o).
% 1.62/1.51 thf(func_def_5, type, setof: (nat > $o) > set).
% 1.62/1.51 thf(func_def_7, type, n_1: nat).
% 1.62/1.51 thf(func_def_10, type, sK0: set > nat).
% 1.62/1.51 thf(func_def_11, type, sF1: nat).
% 1.62/1.51 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 1.62/1.51 thf(f346,plain,(
% 1.62/1.51 $false),
% 1.62/1.51 inference(subsumption_resolution,[status(thm)],[f318,f38])).
% 1.62/1.51 thf(f38,plain,(
% 1.62/1.51 (n_1 != x)),
% 1.62/1.51 inference(superposition,[status(thm)],[f29,f37])).
% 1.62/1.51 thf(f37,plain,(
% 1.62/1.51 (x = (suc @ x))),
% 1.62/1.51 inference(backward_demodulation,[status(thm)],[f35,f36])).
% 1.62/1.51 thf(f36,plain,(
% 1.62/1.51 (x = sF1)),
% 1.62/1.51 inference(definition_folding,[status(thm)],[f32,f35])).
% 1.62/1.51 thf(f32,plain,(
% 1.62/1.51 (x = (suc @ x))),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.51 thf(f15,plain,(
% 1.62/1.51 (x = (suc @ x))),
% 1.62/1.51 inference(flattening,[status(thm)],[f7])).
% 1.62/1.51 thf(f7,negated_conjecture,(
% 1.62/1.51 ~(x != (suc @ x))),
% 1.62/1.51 inference(negated_conjecture,[status(cth)],[f6])).
% 1.62/1.51 thf(f6,conjecture,(
% 1.62/1.51 (x != (suc @ x))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',satz2)).
% 1.62/1.51 thf(f35,definition,(
% 1.62/1.51 ((suc @ x) = sF1)),
% 1.62/1.51 introduced(definition,[],[function_definition])).
% 1.62/1.51 thf(f29,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((n_1 != (suc @ X0))) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f17])).
% 1.62/1.51 thf(f17,plain,(
% 1.62/1.51 ! [X0 : nat] : (n_1 != (suc @ X0))),
% 1.62/1.51 inference(rectify,[status(thm)],[f4])).
% 1.62/1.51 thf(f4,axiom,(
% 1.62/1.51 ! [X2 : nat] : (n_1 != (suc @ X2))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',ax3)).
% 1.62/1.51 thf(f318,plain,(
% 1.62/1.51 (n_1 = x)),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f317])).
% 1.62/1.51 thf(f317,plain,(
% 1.62/1.51 ((x = n_1) = $true)),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f316])).
% 1.62/1.51 thf(f316,plain,(
% 1.62/1.51 ($false = (~ (x = n_1)))),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f315])).
% 1.62/1.51 thf(f315,plain,(
% 1.62/1.51 ($false = $true) | ($false = (~ (x = n_1)))),
% 1.62/1.51 inference(boolean_simplification,[status(thm)],[f314])).
% 1.62/1.51 thf(f314,plain,(
% 1.62/1.51 ($false = (~ (x = n_1))) | ($true = (~ $true))),
% 1.62/1.51 inference(boolean_simplification,[status(thm)],[f313])).
% 1.62/1.51 thf(f313,plain,(
% 1.62/1.51 ($true = (~ (x = x))) | ($false = (~ (x = n_1)))),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f304])).
% 1.62/1.51 thf(f304,plain,(
% 1.62/1.51 ($false = ((^[Y0 : nat]: (~ (x = Y0))) @ n_1)) | (((^[Y0 : nat]: (~ (x = Y0))) @ x) = $true)),
% 1.62/1.51 inference(superposition,[status(thm)],[f125,f295])).
% 1.62/1.51 thf(f295,plain,(
% 1.62/1.51 (x = (sK0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0))))))),
% 1.62/1.51 inference(subsumption_resolution,[status(thm)],[f294,f38])).
% 1.62/1.51 thf(f294,plain,(
% 1.62/1.51 (x = (sK0 @ (setof @ (^[Y0 : nat]: (~ (x = Y0)))))) | (n_1 = x)),
% 1.62/1.51 inference(equality_resolution,[status(thm)],[f284])).
% 1.62/1.51 thf(f284,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((x != X0) | (x = (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0)))))) | (n_1 = X0)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f39,f260])).
% 1.62/1.51 thf(f260,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0)))))) = X0) | (n_1 = X0)) )),
% 1.62/1.51 inference(equality_proxy_clausification,[status(thm)],[f259])).
% 1.62/1.51 thf(f259,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0)))))) = X0) | ($true = (X0 = n_1))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f258])).
% 1.62/1.51 thf(f258,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0)))))) = X0) | ($false = (~ (X0 = n_1)))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f229])).
% 1.62/1.51 thf(f229,plain,(
% 1.62/1.51 ( ! [X0 : nat] : (((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0)))))) = X0) | ($false = ((^[Y0 : nat]: (~ (X0 = Y0))) @ n_1))) )),
% 1.62/1.51 inference(leibniz_equality_elimination,[status(thm)],[f227])).
% 1.62/1.51 thf(f227,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (($false = (X1 @ (suc @ (sK0 @ (setof @ X1))))) | ((X1 @ X0) = $true) | ($false = (X1 @ n_1))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.62/1.51 thf(f212,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (($false = (X1 @ (suc @ (sK0 @ (setof @ X1))))) | ($true != $true) | ((X1 @ X0) = $true) | ($false = (X1 @ n_1))) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f34,f194])).
% 1.62/1.51 thf(f194,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($false = (X0 @ (suc @ (sK0 @ (setof @ X0))))) | ((esti @ X1 @ (setof @ X0)) = $true) | ($false = (X0 @ n_1))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f193])).
% 1.62/1.51 thf(f193,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($false = (X0 @ n_1)) | ($false = (X0 @ (suc @ (sK0 @ (setof @ X0))))) | ($true != $true) | ((esti @ X1 @ (setof @ X0)) = $true)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f109,f98])).
% 1.62/1.51 thf(f98,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (((esti @ X1 @ (setof @ X0)) = $true) | ((X0 @ X1) = $false)) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.62/1.51 thf(f92,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (((esti @ X1 @ (setof @ X0)) = $true) | ((X0 @ X1) = $false) | ($true != $true)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f28,f75])).
% 1.62/1.51 thf(f75,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (((X1 @ X0) = $true) | ($false = (X1 @ X0))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f74])).
% 1.62/1.51 thf(f74,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (((X1 @ X0) = $true) | ($true = (~ (X1 @ X0)))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.62/1.51 thf(f73,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (((X1 @ X0) = $true) | ($true = ((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.62/1.51 thf(f70,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = ((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0)) | ((X1 @ X0) = $true)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f34,f49])).
% 1.62/1.51 thf(f49,plain,(
% 1.62/1.51 ( ! [X1 : nat,X4 : nat > $o] : (($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0)))))) | ($true = (X4 @ X1))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f48])).
% 1.62/1.51 thf(f48,plain,(
% 1.62/1.51 ( ! [X1 : nat,X4 : nat > $o] : (($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0)))))) | ($true != (~ (X4 @ X1)))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.62/1.51 thf(f45,plain,(
% 1.62/1.51 ( ! [X1 : nat,X4 : nat > $o] : (($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X4 @ Y0)))))) | ($true != ((^[Y0 : nat]: (~ (X4 @ Y0))) @ X1))) )),
% 1.62/1.51 inference(primitive_instantiation,[status(thm)],[f28])).
% 1.62/1.51 thf(f28,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (((X0 @ X1) != $true) | ((esti @ X1 @ (setof @ X0)) = $true)) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f23])).
% 1.62/1.51 thf(f23,plain,(
% 1.62/1.51 ! [X0 : nat > $o,X1 : nat] : (((X0 @ X1) != $true) | ((esti @ X1 @ (setof @ X0)) = $true))),
% 1.62/1.51 inference(rectify,[status(thm)],[f20])).
% 1.62/1.51 thf(f20,plain,(
% 1.62/1.51 ! [X1 : nat > $o,X0 : nat] : (((X1 @ X0) != $true) | ($true = (esti @ X0 @ (setof @ X1))))),
% 1.62/1.51 inference(ennf_transformation,[status(thm)],[f14])).
% 1.62/1.51 thf(f14,plain,(
% 1.62/1.51 ! [X1 : nat > $o,X0 : nat] : (((X1 @ X0) = $true) => ($true = (esti @ X0 @ (setof @ X1))))),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f13])).
% 1.62/1.51 thf(f13,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat > $o] : ((X1 @ X0) => (esti @ X0 @ (setof @ X1)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f3])).
% 1.62/1.51 thf(f3,axiom,(
% 1.62/1.51 ! [X1 : nat,X0 : nat > $o] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',estii)).
% 1.62/1.51 thf(f109,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($true != (esti @ n_1 @ (setof @ X0))) | ($false = (X0 @ (suc @ (sK0 @ (setof @ X0))))) | ((esti @ X1 @ (setof @ X0)) = $true)) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.62/1.51 thf(f108,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true != (esti @ n_1 @ (setof @ X0))) | ((esti @ X1 @ (setof @ X0)) = $true) | ($false = (X0 @ (suc @ (sK0 @ (setof @ X0)))))) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f31,f98])).
% 1.62/1.51 thf(f31,plain,(
% 1.62/1.51 ( ! [X0 : set,X1 : nat] : (($true != (esti @ (suc @ (sK0 @ X0)) @ X0)) | ((esti @ n_1 @ X0) != $true) | ((esti @ X1 @ X0) = $true)) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.51 thf(f26,plain,(
% 1.62/1.51 ! [X0 : set] : (((esti @ n_1 @ X0) != $true) | ! [X1 : nat] : ((esti @ X1 @ X0) = $true) | (($true != (esti @ (suc @ (sK0 @ X0)) @ X0)) & ((esti @ (sK0 @ X0) @ X0) = $true)))),
% 1.62/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25])).
% 1.62/1.51 thf(f25,plain,(
% 1.62/1.51 ! [X0 : set] : (? [X2 : nat] : (($true != (esti @ (suc @ X2) @ X0)) & ($true = (esti @ X2 @ X0))) => (($true != (esti @ (suc @ (sK0 @ X0)) @ X0)) & ((esti @ (sK0 @ X0) @ X0) = $true)))),
% 1.62/1.51 introduced(definition,[],[choice_axiom])).
% 1.62/1.51 thf(f24,plain,(
% 1.62/1.51 ! [X0 : set] : (((esti @ n_1 @ X0) != $true) | ! [X1 : nat] : ((esti @ X1 @ X0) = $true) | ? [X2 : nat] : (($true != (esti @ (suc @ X2) @ X0)) & ($true = (esti @ X2 @ X0))))),
% 1.62/1.51 inference(rectify,[status(thm)],[f19])).
% 1.62/1.51 thf(f19,plain,(
% 1.62/1.51 ! [X0 : set] : (((esti @ n_1 @ X0) != $true) | ! [X2 : nat] : ($true = (esti @ X2 @ X0)) | ? [X1 : nat] : (((esti @ (suc @ X1) @ X0) != $true) & ((esti @ X1 @ X0) = $true)))),
% 1.62/1.51 inference(flattening,[status(thm)],[f18])).
% 1.62/1.51 thf(f18,plain,(
% 1.62/1.51 ! [X0 : set] : ((! [X2 : nat] : ($true = (esti @ X2 @ X0)) | ? [X1 : nat] : (((esti @ (suc @ X1) @ X0) != $true) & ((esti @ X1 @ X0) = $true))) | ((esti @ n_1 @ X0) != $true))),
% 1.62/1.51 inference(ennf_transformation,[status(thm)],[f12])).
% 1.62/1.51 thf(f12,plain,(
% 1.62/1.51 ! [X0 : set] : (((esti @ n_1 @ X0) = $true) => (! [X1 : nat] : (((esti @ X1 @ X0) = $true) => ((esti @ (suc @ X1) @ X0) = $true)) => ! [X2 : nat] : ($true = (esti @ X2 @ X0))))),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.51 thf(f11,plain,(
% 1.62/1.51 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f2])).
% 1.62/1.51 thf(f2,axiom,(
% 1.62/1.51 ! [X1 : set] : ((esti @ n_1 @ X1) => (! [X2 : nat] : ((esti @ X2 @ X1) => (esti @ (suc @ X2) @ X1)) => ! [X2 : nat] : (esti @ X2 @ X1)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',ax5)).
% 1.62/1.51 thf(f34,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat > $o] : (($true != (esti @ X0 @ (setof @ X1))) | ((X1 @ X0) = $true)) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f21])).
% 1.62/1.51 thf(f21,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat > $o] : (($true != (esti @ X0 @ (setof @ X1))) | ((X1 @ X0) = $true))),
% 1.62/1.51 inference(ennf_transformation,[status(thm)],[f10])).
% 1.62/1.51 thf(f10,plain,(
% 1.62/1.51 ! [X1 : nat > $o,X0 : nat] : (($true = (esti @ X0 @ (setof @ X1))) => ((X1 @ X0) = $true))),
% 1.62/1.51 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.51 thf(f9,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat > $o] : ((esti @ X0 @ (setof @ X1)) => (X1 @ X0))),
% 1.62/1.51 inference(rectify,[status(thm)],[f1])).
% 1.62/1.51 thf(f1,axiom,(
% 1.62/1.51 ! [X1 : nat,X0 : nat > $o] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',estie)).
% 1.62/1.51 thf(f39,plain,(
% 1.62/1.51 ( ! [X0 : nat] : ((x != (suc @ X0)) | (x = X0)) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f33,f37])).
% 1.62/1.51 thf(f33,plain,(
% 1.62/1.51 ( ! [X0 : nat,X1 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1)) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f27])).
% 1.62/1.51 thf(f27,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1))),
% 1.62/1.51 inference(rectify,[status(thm)],[f22])).
% 1.62/1.51 thf(f22,plain,(
% 1.62/1.51 ! [X1 : nat,X0 : nat] : (((suc @ X0) != (suc @ X1)) | (X0 = X1))),
% 1.62/1.51 inference(ennf_transformation,[status(thm)],[f16])).
% 1.62/1.51 thf(f16,plain,(
% 1.62/1.51 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((suc @ X0) != (suc @ X1)))),
% 1.62/1.51 inference(rectify,[status(thm)],[f5])).
% 1.62/1.51 thf(f5,axiom,(
% 1.62/1.51 ! [X2 : nat,X3 : nat] : ((X2 != X3) => ((suc @ X2) != (suc @ X3)))),
% 1.62/1.51 file('/export/starexec/sandbox/tmp/tmp.yNPbA9UUZp/DTF2THF_26748.p',satz1)).
% 1.62/1.51 thf(f125,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (($true = (X3 @ (sK0 @ (setof @ X3)))) | ($false = (X3 @ n_1))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f124])).
% 1.62/1.51 thf(f124,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (($true = (~ (X3 @ n_1))) | ($true = (X3 @ (sK0 @ (setof @ X3))))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f123])).
% 1.62/1.51 thf(f123,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (((~ (X3 @ (sK0 @ (setof @ X3)))) = $false) | ($true = (~ (X3 @ n_1)))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f122])).
% 1.62/1.51 thf(f122,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (($true = (~ (X3 @ n_1))) | ($false = (~ (X3 @ (sK0 @ (setof @ (^[Y0 : nat]: (X3 @ Y0)))))))) )),
% 1.62/1.51 inference(boolean_simplification,[status(thm)],[f121])).
% 1.62/1.51 thf(f121,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (($true = (~ (X3 @ n_1))) | ($false = (~ (X3 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (~ (X3 @ Y0)))))))))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.62/1.51 thf(f115,plain,(
% 1.62/1.51 ( ! [X3 : nat > $o] : (($false = ((^[Y0 : nat]: (~ (X3 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ ((^[Y1 : nat]: (~ (X3 @ Y1))) @ Y0))))))) | ($true = ((^[Y0 : nat]: (~ (X3 @ Y0))) @ n_1))) )),
% 1.62/1.51 inference(primitive_instantiation,[status(thm)],[f80])).
% 1.62/1.51 thf(f80,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($false = (X0 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(not_proxy_clausification,[status(thm)],[f79])).
% 1.62/1.51 thf(f79,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($true = (~ (X0 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.62/1.51 thf(f78,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($true = (X0 @ n_1)) | ($true = ((^[Y0 : nat]: (~ (X0 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.62/1.51 thf(f71,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($true != $true) | ($true = ((^[Y0 : nat]: (~ (X0 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f34,f65])).
% 1.62/1.51 thf(f65,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($true = (esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.62/1.51 thf(f63,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o] : (($true = (esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true != $true) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(equality_factoring,[status(thm)],[f60])).
% 1.62/1.51 thf(f60,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($true = (esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.62/1.51 thf(f59,plain,(
% 1.62/1.51 ( ! [X0 : nat > $o,X1 : nat] : (($true = (esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true = (esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))) | ($true != $true) | ($true = (X0 @ n_1))) )),
% 1.62/1.51 inference(superposition,[status(thm)],[f30,f49])).
% 1.62/1.51 thf(f30,plain,(
% 1.62/1.51 ( ! [X0 : set,X1 : nat] : (((esti @ n_1 @ X0) != $true) | ((esti @ (sK0 @ X0) @ X0) = $true) | ((esti @ X1 @ X0) = $true)) )),
% 1.62/1.51 inference(cnf_transformation,[status(thm)],[f26])).
% 1.62/1.51 % SZS output end Proof for DTF2THF_26748
% 1.62/1.51 % (27066)------------------------------
% 1.62/1.51 % (27066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (27066)Termination reason: Refutation
% 1.62/1.51
% 1.62/1.51 % (27066)Memory used [KB]: 5628
% 1.62/1.51 % (27066)Time elapsed: 0.041 s
% 1.62/1.51 % (27066)Instructions burned: 44 (million)
% 1.62/1.51 % (27066)------------------------------
% 1.62/1.51 % (27066)------------------------------
% 1.62/1.51 % (27024)Success in time 0.225 s
%------------------------------------------------------------------------------