%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ANA091^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 08:38:51 AM UTC 2026
% Result : Theorem 1.72s 1.45s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 573 ( 168 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 758 ( 88 ~; 76 |; 48 &; 510 @)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-3 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 153 ( 6 ^; 122 !; 25 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_13,type,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_14,type,
sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_16,type,
sK3: 'type/realax/real' ).
thf(func_def_17,type,
sK4: 'type/realax/real' ).
thf(func_def_18,type,
sK5: 'type/realax/real' ).
thf(func_def_20,type,
sK7:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK9: 'type/realax/real' ).
thf(f136,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f110,f114,f135]) ).
thf(f135,plain,
~ spl6_6,
inference(avatar_contradiction_clause,[status(thm)],[f134]) ).
thf(f134,plain,
( $false
| ~ spl6_6 ),
inference(subsumption_resolution,[status(thm)],[f130,f36]) ).
thf(f36,plain,
( ( 'const/realax/real_le' @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X4 )
= $true ) )
& ( ( 'const/realax/real_le' @ sK5 @ sK4 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f20,f25]) ).
thf(f25,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true ) )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true ) )
=> ( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X4 )
= $true ) )
& ( ( 'const/realax/real_le' @ sK5 @ sK4 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true ) )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/realax/real_le' @ X3 @ X2 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/realax/real_le' @ X3 @ X2 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/realax/real_le' @ X3 @ X2 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/REAL_INF_LE_') ).
thf(f130,plain,
( ( ( 'const/realax/real_le' @ sK5 @ sK4 )
!= $true )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK5 @ sK4 )
!= $true )
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f124,f35]) ).
thf(f35,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f124,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( $true != $true ) )
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f90,f109]) ).
thf(f109,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl6_6
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition]) ).
thf(f90,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f34,f27]) ).
thf(f27,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/realax/REAL_LE_TRANS_') ).
thf(f34,plain,
( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f114,plain,
( spl6_6
| ~ spl6_5 ),
inference(avatar_split_clause,[status(thm)],[f113,f105,f108]) ).
thf(f105,definition,
( spl6_5
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f113,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 )
= $true ) )
| ~ spl6_5 ),
inference(subsumption_resolution,[status(thm)],[f112,f52]) ).
thf(f52,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $false = $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
inference(superposition,[status(thm)],[f44,f35]) ).
thf(f44,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ( $false
= ( ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $false
= ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
| ( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
= $true )
| ( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f112,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 )
= $true ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 )
!= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 )
= $true ) )
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f30,f106]) ).
thf(f106,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f30,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23,f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) )
| ( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X4 )
!= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X4 )
!= $true ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X3 @ X4 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X4 ) )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/INF_') ).
thf(f110,plain,
( spl6_5
| spl6_6 ),
inference(avatar_split_clause,[status(thm)],[f103,f108,f105]) ).
thf(f103,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f102,f52]) ).
thf(f102,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) ),
inference(superposition,[status(thm)],[f37,f33]) ).
thf(f33,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f37,plain,
! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA091^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 03:51:57 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : ANA091^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.48 % Domain : Analysis
% 0.19/0.48 % Problem : REAL_INF_LE
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Kal16]
% 0.19/0.48 % Names : REAL_INF_LE_.p [Kal16]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.00 v7.1.0
% 0.19/0.48 % Syntax : Number of formulae : 9 ( 1 unt; 5 typ; 0 def)
% 0.19/0.48 % Number of atoms : 21 ( 3 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 8 ( 5 avg)
% 0.19/0.48 % Number of connectives : 58 ( 2 ~; 0 |; 5 &; 43 @)
% 0.19/0.48 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 13 ( 9 avg)
% 0.19/0.48 % Number of types : 2 ( 1 usr)
% 0.19/0.48 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.19/0.48 % Number of variables : 19 ( 0 ^; 15 !; 2 ?; 19 :)
% 0.19/0.48 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.48 % SPC : TH1_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : Exported from core HOL Light.
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf('thf_type_type/realax/real',type,
% 0.19/0.48 'type/realax/real': $tType ).
% 0.19/0.48
% 0.19/0.48 thf('thf_const_const/sets/inf',type,
% 0.19/0.48 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.19/0.48
% 0.19/0.48 thf('thf_const_const/sets/IN',type,
% 0.19/0.48 'const/sets/IN':
% 0.19/0.48 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.19/0.48
% 0.19/0.48 thf('thf_const_const/sets/EMPTY',type,
% 0.19/0.48 'const/sets/EMPTY':
% 0.19/0.48 !>[A: $tType] : ( A > $o ) ).
% 0.19/0.48
% 0.19/0.48 thf('thf_const_const/realax/real_le',type,
% 0.19/0.48 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.19/0.48
% 0.19/0.48 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 0.19/0.48 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 0.19/0.48 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.19/0.48 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.19/0.48 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 0.19/0.48
% 0.19/0.48 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 0.19/0.48 ! [A: $tType,A0: A > $o] :
% 0.19/0.48 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 0.19/0.48 = ( A0
% 0.19/0.48 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf('thm/sets/INF_',axiom,
% 0.19/0.48 ! [A: 'type/realax/real' > $o] :
% 0.19/0.48 ( ( ( A
% 0.19/0.48 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.19/0.48 & ? [A0: 'type/realax/real'] :
% 0.19/0.48 ! [A1: 'type/realax/real'] :
% 0.19/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.19/0.48 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.19/0.48 => ( ! [A0: 'type/realax/real'] :
% 0.19/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.19/0.48 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.19/0.48 & ! [A0: 'type/realax/real'] :
% 0.19/0.48 ( ! [A1: 'type/realax/real'] :
% 0.19/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.19/0.48 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.19/0.48 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf('thm/sets/REAL_INF_LE_',conjecture,
% 0.19/0.48 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real',A2: 'type/realax/real'] :
% 0.19/0.48 ( ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 0.19/0.48 & ( 'const/realax/real_le' @ A2 @ A1 )
% 0.19/0.48 & ! [A3: 'type/realax/real'] :
% 0.19/0.48 ( ( 'const/sets/IN' @ 'type/realax/real' @ A3 @ A )
% 0.19/0.48 => ( 'const/realax/real_le' @ A0 @ A3 ) ) )
% 0.19/0.48 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.72/1.41 ---- Embedded in THF ---
% 1.72/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.41 %%% Generated on Tue Feb 24 03:51:58 EST 2026
% 1.72/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.41 %%% Logic specification used:
% 1.72/1.41 %%% thf(spec, logic, $$dhol).
% 1.72/1.41
% 1.72/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2DTF25885.p
% See solution above
% 1.72/1.41 ------------------------
% 1.72/1.42 ---- Cleaned THF ---
% 1.72/1.42 thf('thf_type_type/realax/real',type,
% 1.72/1.42 'type/realax/real': $tType ).
% 1.72/1.42
% 1.72/1.42 thf('thf_const_const/sets/inf',type,
% 1.72/1.42 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.72/1.42
% 1.72/1.42 thf('thf_const_const/sets/IN',type,
% 1.72/1.42 'const/sets/IN':
% 1.72/1.42 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.72/1.42
% 1.72/1.42 thf('thf_const_const/sets/EMPTY',type,
% 1.72/1.42 'const/sets/EMPTY':
% 1.72/1.42 !>[A: $tType] : ( A > $o ) ).
% 1.72/1.42
% 1.72/1.42 thf('thf_const_const/realax/real_le',type,
% 1.72/1.42 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.72/1.42
% 1.72/1.42 thf('thm/realax/REAL_LE_TRANS_',axiom,
% 1.72/1.42 ! [A: 'type/realax/real',A0: 'type/realax/real',A1: 'type/realax/real'] :
% 1.72/1.42 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.72/1.42 & ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.72/1.42 => ( 'const/realax/real_le' @ A @ A1 ) ) ).
% 1.72/1.42
% 1.72/1.42 thf('thm/sets/MEMBER_NOT_EMPTY_',axiom,
% 1.72/1.42 ! [A: $tType,A0: A > $o] :
% 1.72/1.42 ( ( ? [A1: A] : ( 'const/sets/IN' @ A @ A1 @ A0 ) )
% 1.72/1.42 = ( A0
% 1.72/1.42 != ( 'const/sets/EMPTY' @ A ) ) ) ).
% 1.72/1.42
% 1.72/1.42 thf('thm/sets/INF_',axiom,
% 1.72/1.42 ! [A: 'type/realax/real' > $o] :
% 1.72/1.42 ( ( ( A
% 1.72/1.42 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.72/1.42 & ? [A0: 'type/realax/real'] :
% 1.72/1.42 ! [A1: 'type/realax/real'] :
% 1.72/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.72/1.42 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.72/1.42 => ( ! [A0: 'type/realax/real'] :
% 1.72/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.72/1.42 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.72/1.42 & ! [A0: 'type/realax/real'] :
% 1.72/1.42 ( ! [A1: 'type/realax/real'] :
% 1.72/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.72/1.42 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.72/1.42 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.72/1.42
% 1.72/1.42 thf('thm/sets/REAL_INF_LE_',conjecture,
% 1.72/1.42 ! [A: 'type/realax/real' > $o,A0: 'type/realax/real',A1: 'type/realax/real',A2: 'type/realax/real'] :
% 1.72/1.42 ( ( ( 'const/sets/IN' @ 'type/realax/real' @ A2 @ A )
% 1.72/1.42 & ( 'const/realax/real_le' @ A2 @ A1 )
% 1.72/1.42 & ! [A3: 'type/realax/real'] :
% 1.72/1.42 ( ( 'const/sets/IN' @ 'type/realax/real' @ A3 @ A )
% 1.72/1.42 => ( 'const/realax/real_le' @ A0 @ A3 ) ) )
% 1.72/1.42 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A1 ) ) ).
% 1.72/1.42 ------------------------
% 1.72/1.44 % (25983)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_25885 for (2999ds/4Mi)
% 1.72/1.44 % (25986)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_25885 for (2999ds/2Mi)
% 1.72/1.44 % (25982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25885 for (2999ds/183Mi)
% 1.72/1.44 % (25988)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25885 for (2999ds/18Mi)
% 1.72/1.44 % (25987)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_25885 for (2999ds/275Mi)
% 1.72/1.44 % (25985)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25885 for (2999ds/2Mi)
% 1.72/1.44 % (25984)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_25885 for (2999ds/27Mi)
% 1.72/1.44 % (25985)Instruction limit reached!
% 1.72/1.44 % (25985)------------------------------
% 1.72/1.44 % (25985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (25985)Termination reason: Unknown
% 1.72/1.44 % (25985)Termination phase: Property scanning
% 1.72/1.44 % (25986)Instruction limit reached!
% 1.72/1.44 % (25986)------------------------------
% 1.72/1.44 % (25986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (25986)Termination reason: Unknown
% 1.72/1.44 % (25986)Termination phase: Property scanning
% 1.72/1.44
% 1.72/1.44 % (25986)Memory used [KB]: 1023
% 1.72/1.44 % (25986)Time elapsed: 0.003 s
% 1.72/1.44 % (25986)Instructions burned: 3 (million)
% 1.72/1.44 % (25986)------------------------------
% 1.72/1.44 % (25986)------------------------------
% 1.72/1.44
% 1.72/1.44 % (25985)Memory used [KB]: 1023
% 1.72/1.44 % (25985)Time elapsed: 0.003 s
% 1.72/1.44 % (25985)Instructions burned: 2 (million)
% 1.72/1.44 % (25985)------------------------------
% 1.72/1.44 % (25985)------------------------------
% 1.72/1.44 % (25983)Instruction limit reached!
% 1.72/1.44 % (25983)------------------------------
% 1.72/1.44 % (25983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (25983)Termination reason: Unknown
% 1.72/1.44 % (25983)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (25983)Memory used [KB]: 5500
% 1.72/1.44 % (25983)Time elapsed: 0.004 s
% 1.72/1.44 % (25983)Instructions burned: 4 (million)
% 1.72/1.44 % (25983)------------------------------
% 1.72/1.44 % (25983)------------------------------
% 1.72/1.45 % (25988)Instruction limit reached!
% 1.72/1.45 % (25988)------------------------------
% 1.72/1.45 % (25988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (25988)Termination reason: Unknown
% 1.72/1.45 % (25988)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (25988)Memory used [KB]: 5628
% 1.72/1.45 % (25982)First to succeed.
% 1.72/1.45 % (25988)Time elapsed: 0.012 s
% 1.72/1.45 % (25988)Instructions burned: 19 (million)
% 1.72/1.45 % (25988)------------------------------
% 1.72/1.45 % (25988)------------------------------
% 1.72/1.45 % (25987)Also succeeded, but the first one will report.
% 1.72/1.45 % (25982)Refutation found. Thanks to Tanya!
% 1.72/1.45 % SZS status Theorem for DTF2THF_25885
% 1.72/1.45 % SZS output start Proof for DTF2THF_25885
% 1.72/1.45 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.72/1.45 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.72/1.45 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.72/1.45 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.72/1.45 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.72/1.45 thf(func_def_4, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.72/1.45 thf(func_def_13, type, sK0: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.72/1.45 thf(func_def_14, type, sK1: 'type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real').
% 1.72/1.45 thf(func_def_15, type, sK2: 'type/realax/real' > $o).
% 1.72/1.45 thf(func_def_16, type, sK3: 'type/realax/real').
% 1.72/1.45 thf(func_def_17, type, sK4: 'type/realax/real').
% 1.72/1.45 thf(func_def_18, type, sK5: 'type/realax/real').
% 1.72/1.45 thf(func_def_20, type, sK7: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.72/1.45 thf(func_def_21, type, ph8: !>[X0: $tType]:(X0)).
% 1.72/1.45 thf(func_def_22, type, sK9: 'type/realax/real').
% 1.72/1.45 thf(f136,plain,(
% 1.72/1.45 $false),
% 1.72/1.45 inference(avatar_sat_refutation,[status(thm)],[f110,f114,f135])).
% 1.72/1.45 thf(f135,plain,(
% 1.72/1.45 ~spl6_6),
% 1.72/1.45 inference(avatar_contradiction_clause,[status(thm)],[f134])).
% 1.72/1.45 thf(f134,plain,(
% 1.72/1.45 $false | ~spl6_6),
% 1.72/1.45 inference(subsumption_resolution,[status(thm)],[f130,f36])).
% 1.72/1.45 thf(f36,plain,(
% 1.72/1.45 (('const/realax/real_le' @ sK5 @ sK4) = $true)),
% 1.72/1.45 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.45 thf(f26,plain,(
% 1.72/1.45 ! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2) != $true) | (('const/realax/real_le' @ sK3 @ X4) = $true)) & (('const/realax/real_le' @ sK5 @ sK4) = $true) & (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4) != $true)),
% 1.72/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f20,f25])).
% 1.72/1.45 thf(f25,plain,(
% 1.72/1.45 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X4) = $true)) & (('const/realax/real_le' @ X3 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $true)) => (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2) != $true) | (('const/realax/real_le' @ sK3 @ X4) = $true)) & (('const/realax/real_le' @ sK5 @ sK4) = $true) & (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4) != $true))),
% 1.72/1.45 introduced(definition,[],[choice_axiom])).
% 1.72/1.45 thf(f20,plain,(
% 1.72/1.45 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X4) = $true)) & (('const/realax/real_le' @ X3 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $true))),
% 1.72/1.45 inference(flattening,[status(thm)],[f19])).
% 1.72/1.45 thf(f19,plain,(
% 1.72/1.45 ? [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) != $true) & ((('const/realax/real_le' @ X3 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) != $true) | (('const/realax/real_le' @ X1 @ X4) = $true))))),
% 1.72/1.45 inference(ennf_transformation,[status(thm)],[f8])).
% 1.72/1.45 thf(f8,plain,(
% 1.72/1.45 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X2) = $true) & (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) = $true) & ! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) => (('const/realax/real_le' @ X1 @ X4) = $true))) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2) = $true))),
% 1.72/1.45 inference(fool_elimination,[status(thm)],[f7])).
% 1.72/1.45 thf(f7,plain,(
% 1.72/1.45 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 1.72/1.45 inference(rectify,[status(thm)],[f5])).
% 1.72/1.45 thf(f5,negated_conjecture,(
% 1.72/1.45 ~! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 1.72/1.45 inference(negated_conjecture,[status(cth)],[f4])).
% 1.72/1.45 thf(f4,conjecture,(
% 1.72/1.45 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real',X2 : 'type/realax/real',X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) & ! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X1 @ X4)) & ('const/realax/real_le' @ X3 @ X2)) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X2))),
% 1.72/1.45 file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/REAL_INF_LE_')).
% 1.72/1.45 thf(f130,plain,(
% 1.72/1.45 (('const/realax/real_le' @ sK5 @ sK4) != $true) | ~spl6_6),
% 1.72/1.45 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.72/1.45 thf(f127,plain,(
% 1.72/1.45 ($true != $true) | (('const/realax/real_le' @ sK5 @ sK4) != $true) | ~spl6_6),
% 1.72/1.45 inference(superposition,[status(thm)],[f124,f35])).
% 1.72/1.45 thf(f35,plain,(
% 1.72/1.45 (('const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2) = $true)),
% 1.72/1.45 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.45 thf(f124,plain,(
% 1.72/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | (('const/realax/real_le' @ X0 @ sK4) != $true)) ) | ~spl6_6),
% 1.72/1.45 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.72/1.45 thf(f118,plain,(
% 1.72/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ sK4) != $true) | (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | ($true != $true)) ) | ~spl6_6),
% 1.72/1.45 inference(superposition,[status(thm)],[f90,f109])).
% 1.72/1.45 thf(f109,plain,(
% 1.72/1.45 ( ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true)) ) | ~spl6_6),
% 1.72/1.45 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.72/1.45 thf(f108,definition,(
% 1.72/1.45 spl6_6 <=> ! [X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true))),
% 1.72/1.45 introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition])).
% 1.72/1.45 thf(f90,plain,(
% 1.72/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0) != $true) | (('const/realax/real_le' @ X0 @ sK4) != $true)) )),
% 1.72/1.45 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.72/1.45 thf(f89,plain,(
% 1.72/1.45 ( ! [X0 : 'type/realax/real'] : (($true != $true) | (('const/realax/real_le' @ X0 @ sK4) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0) != $true)) )),
% 1.72/1.45 inference(superposition,[status(thm)],[f34,f27])).
% 1.72/1.45 thf(f27,plain,(
% 1.72/1.45 ( ! [X2 : 'type/realax/real',X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | (('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)) )),
% 1.72/1.45 inference(cnf_transformation,[status(thm)],[f18])).
% 1.72/1.45 thf(f18,plain,(
% 1.72/1.45 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true) | (('const/realax/real_le' @ X0 @ X2) = $true))),
% 1.72/1.45 inference(flattening,[status(thm)],[f17])).
% 1.72/1.45 thf(f17,plain,(
% 1.72/1.45 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X0 @ X2) = $true) | ((('const/realax/real_le' @ X1 @ X2) != $true) | (('const/realax/real_le' @ X0 @ X1) != $true)))),
% 1.72/1.45 inference(ennf_transformation,[status(thm)],[f10])).
% 1.72/1.45 thf(f10,plain,(
% 1.72/1.45 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2) = $true) & (('const/realax/real_le' @ X0 @ X1) = $true)) => (('const/realax/real_le' @ X0 @ X2) = $true))),
% 1.72/1.45 inference(fool_elimination,[status(thm)],[f9])).
% 1.72/1.45 thf(f9,plain,(
% 1.72/1.45 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.72/1.45 inference(rectify,[status(thm)],[f1])).
% 1.72/1.45 thf(f1,axiom,(
% 1.72/1.45 ! [X0 : 'type/realax/real',X1 : 'type/realax/real',X2 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ X2) & ('const/realax/real_le' @ X0 @ X1)) => ('const/realax/real_le' @ X0 @ X2))),
% 1.72/1.45 file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/realax/REAL_LE_TRANS_')).
% 1.72/1.45 thf(f34,plain,(
% 1.72/1.45 (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK4) != $true)),
% 1.72/1.45 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.45 thf(f114,plain,(
% 1.72/1.45 spl6_6 | ~spl6_5),
% 1.72/1.45 inference(avatar_split_clause,[status(thm)],[f113,f105,f108])).
% 1.72/1.45 thf(f105,definition,(
% 1.72/1.45 spl6_5 <=> ! [X0 : 'type/realax/real'] : (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)) = $true)),
% 1.72/1.45 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.72/1.45 thf(f113,plain,(
% 1.72/1.45 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0) = $true)) ) | ~spl6_5),
% 1.72/1.45 inference(subsumption_resolution,[status(thm)],[f112,f52])).
% 1.72/1.45 thf(f52,plain,(
% 1.72/1.45 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 1.72/1.45 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.72/1.45 thf(f49,plain,(
% 1.72/1.45 ($false = $true) | ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 1.72/1.46 inference(superposition,[status(thm)],[f44,f35])).
% 1.72/1.46 thf(f44,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $false) | ('const/sets/EMPTY' @ X0 != X1)) )),
% 1.72/1.46 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.72/1.46 thf(f43,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) | ($false = ((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ X2))) )),
% 1.72/1.46 inference(pi_clausification,[status(thm)],[f42])).
% 1.72/1.46 thf(f42,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) | ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))) = $false)) )),
% 1.72/1.46 inference(equality_proxy_clausification,[status(thm)],[f41])).
% 1.72/1.46 thf(f41,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = ('const/sets/EMPTY' @ X0 = X1)) | ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))) = $false)) )),
% 1.72/1.46 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.72/1.46 thf(f40,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X1 : X0 > $o] : (((~ ('const/sets/EMPTY' @ X0 = X1)) = $true) | ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))) = $false)) )),
% 1.72/1.46 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.72/1.46 thf(f38,plain,(
% 1.72/1.46 ( ! [X0 : $tType,X1 : X0 > $o] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))) = (~ ('const/sets/EMPTY' @ X0 = X1)))) )),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f12])).
% 1.72/1.46 thf(f12,plain,(
% 1.72/1.46 ! [X0 : $tType,X1 : X0 > $o] : ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))) = (~ ('const/sets/EMPTY' @ X0 = X1)))),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f11])).
% 1.72/1.46 thf(f11,plain,(
% 1.72/1.46 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.72/1.46 inference(rectify,[status(thm)],[f2])).
% 1.72/1.46 thf(f2,axiom,(
% 1.72/1.46 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/EMPTY' @ X0 != X1) = ? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1))),
% 1.72/1.46 file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 1.72/1.46 thf(f112,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0) = $true)) ) | ~spl6_5),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.72/1.46 thf(f111,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2) != $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X0) = $true)) ) | ~spl6_5),
% 1.72/1.46 inference(superposition,[status(thm)],[f30,f106])).
% 1.72/1.46 thf(f106,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real'] : ((('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)) = $true)) ) | ~spl6_5),
% 1.72/1.46 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.72/1.46 thf(f30,plain,(
% 1.72/1.46 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.46 thf(f24,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) != $true)) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true)) & ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0) = $true) & ($true != ('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))))))),
% 1.72/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23,f22])).
% 1.72/1.46 thf(f22,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : (? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true) & (('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0)) != $true)))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f23,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o,X4 : 'type/realax/real'] : (? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)) => ((('const/sets/IN' @ 'type/realax/real' @ (sK1 @ X4 @ X0) @ X0) = $true) & ($true != ('const/realax/real_le' @ X4 @ (sK1 @ X4 @ X0)))))),
% 1.72/1.46 introduced(definition,[],[choice_axiom])).
% 1.72/1.46 thf(f21,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) | (! [X3 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true)) & ! [X4 : 'type/realax/real'] : ((('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)) = $true) | ? [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) & (('const/realax/real_le' @ X4 @ X5) != $true)))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f16])).
% 1.72/1.46 thf(f16,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true)) | (! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5) = $true)) & ! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)) = $true) | ? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & (('const/realax/real_le' @ X3 @ X4) != $true)))))),
% 1.72/1.46 inference(flattening,[status(thm)],[f15])).
% 1.72/1.46 thf(f15,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : ((! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) != $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5) = $true)) & ! [X3 : 'type/realax/real'] : ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)) = $true) | ? [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) & (('const/realax/real_le' @ X3 @ X4) != $true)))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) & (('const/realax/real_le' @ X1 @ X2) != $true))))),
% 1.72/1.46 inference(ennf_transformation,[status(thm)],[f14])).
% 1.72/1.46 thf(f14,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) = $true) => (('const/realax/real_le' @ X1 @ X2) = $true))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) = $true) => (('const/realax/real_le' @ X3 @ X4) = $true)) => (('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0)) = $true)) & ! [X5 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) = $true) => (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5) = $true))))),
% 1.72/1.46 inference(fool_elimination,[status(thm)],[f13])).
% 1.72/1.46 thf(f13,plain,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 1.72/1.46 inference(rectify,[status(thm)],[f3])).
% 1.72/1.46 thf(f3,axiom,(
% 1.72/1.46 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 1.72/1.46 file('/export/starexec/sandbox/tmp/tmp.tP5NRIhp6R/DTF2THF_25885.p','thm/sets/INF_')).
% 1.72/1.46 thf(f110,plain,(
% 1.72/1.46 spl6_5 | spl6_6),
% 1.72/1.46 inference(avatar_split_clause,[status(thm)],[f103,f108,f105])).
% 1.72/1.46 thf(f103,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true)) )),
% 1.72/1.46 inference(subsumption_resolution,[status(thm)],[f102,f52])).
% 1.72/1.46 thf(f102,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1) = $true) | (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) )),
% 1.72/1.46 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.72/1.46 thf(f100,plain,(
% 1.72/1.46 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : ((('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1) = $true) | (('const/realax/real_le' @ sK3 @ (sK0 @ X0 @ sK2)) = $true) | ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) != $true)) )),
% 1.72/1.46 inference(superposition,[status(thm)],[f37,f33])).
% 1.72/1.46 thf(f33,plain,(
% 1.72/1.46 ( ! [X3 : 'type/realax/real',X0 : 'type/realax/real' > $o,X1 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0) = $true) | (('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3) = $true) | (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f24])).
% 1.72/1.46 thf(f37,plain,(
% 1.72/1.46 ( ! [X4 : 'type/realax/real'] : ((('const/sets/IN' @ 'type/realax/real' @ X4 @ sK2) != $true) | (('const/realax/real_le' @ sK3 @ X4) = $true)) )),
% 1.72/1.46 inference(cnf_transformation,[status(thm)],[f26])).
% 1.72/1.46 % SZS output end Proof for DTF2THF_25885
% 1.72/1.46 % (25982)------------------------------
% 1.72/1.46 % (25982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (25982)Termination reason: Refutation
% 1.72/1.46
% 1.72/1.46 % (25982)Memory used [KB]: 5628
% 1.72/1.46 % (25982)Time elapsed: 0.014 s
% 1.72/1.46 % (25982)Instructions burned: 18 (million)
% 1.72/1.46 % (25982)------------------------------
% 1.72/1.46 % (25982)------------------------------
% 1.72/1.46 % (25981)Success in time 0.028 s
%------------------------------------------------------------------------------