TSTP Solution File: ANA079^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:40:24 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 80 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 587 ( 170 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 776 ( 97 ~; 83 |; 51 &; 511 @)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 156 ( 0 ^ 123 !; 29 ?; 156 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 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/sup': ( '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_8,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_9,type,
sK1: 'type/realax/real' ).
thf(func_def_10,type,
sK2: 'type/realax/real' ).
thf(func_def_11,type,
sK3: 'type/realax/real' ).
thf(func_def_12,type,
sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
sK5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_14,type,
sK6:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK9: 'type/realax/real' ).
thf(f188,plain,
$false,
inference(avatar_sat_refutation,[],[f77,f109,f141,f181]) ).
thf(f181,plain,
~ spl7_5,
inference(avatar_contradiction_clause,[],[f180]) ).
thf(f180,plain,
( $false
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f173,f32]) ).
thf(f32,plain,
( ( 'const/realax/real_le' @ sK1 @ sK3 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
( ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ sK2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ sK3 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f21]) ).
thf(f21,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
=> ( ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ sK2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ sK3 )
= $true )
& ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true ) ) ),
introduced(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/realax/real_le' @ X4 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) ),
inference(flattening,[],[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' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X2 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X3 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X2 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X3 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X2 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X3 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X2 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_') ).
thf(f173,plain,
( ( ( 'const/realax/real_le' @ sK1 @ sK3 )
!= $true )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f168,plain,
( ( ( 'const/realax/real_le' @ sK1 @ sK3 )
!= $true )
| ( $true != $true )
| ~ spl7_5 ),
inference(superposition,[],[f147,f33]) ).
thf(f33,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f147,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f142]) ).
thf(f142,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( $true != $true ) )
| ~ spl7_5 ),
inference(superposition,[],[f46,f76]) ).
thf(f76,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
!= $true ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f75,plain,
( spl7_5
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
thf(f46,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f45,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ X0 )
!= $true ) ),
inference(superposition,[],[f31,f43]) ).
thf(f43,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[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,[],[f8]) ).
thf(f8,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,[],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f31,plain,
( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f141,plain,
( spl7_5
| ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f140,f63,f60,f75]) ).
thf(f60,plain,
( spl7_1
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
thf(f63,plain,
( spl7_2
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
thf(f140,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true ) )
| ~ spl7_1
| spl7_2 ),
inference(subsumption_resolution,[],[f136,f64]) ).
thf(f64,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
| spl7_2 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f136,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f134,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( $true != $true ) )
| ~ spl7_1 ),
inference(superposition,[],[f39,f61]) ).
thf(f61,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
= $true )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f39,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ( ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true ) ) ) )
| ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f23,f25,f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f25,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' @ X5 @ X4 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true )
| ? [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) ) ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
= $true )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
= $true )
| ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true ) ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,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' @ X2 @ X1 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X5 @ X4 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X5 @ X4 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_') ).
thf(f109,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f108]) ).
thf(f108,plain,
( $false
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f105,plain,
( ( $true != $true )
| ~ spl7_2 ),
inference(superposition,[],[f91,f33]) ).
thf(f91,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ~ spl7_2 ),
inference(superposition,[],[f44,f65]) ).
thf(f65,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f44,plain,
! [X0: $tType,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(equality_resolution,[],[f41]) ).
thf(f41,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f28,f29]) ).
thf(f29,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
=> ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
= $true ) ),
introduced(choice_axiom,[]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
<=> ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f77,plain,
( spl7_1
| spl7_5
| spl7_2 ),
inference(avatar_split_clause,[],[f56,f63,f75,f60]) ).
thf(f56,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f49,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
!= $true ) ),
inference(superposition,[],[f34,f40]) ).
thf(f40,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f34,plain,
! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 07:42:37 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH1_THM_EQU_NAR problem
% 0.14/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % (4314)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.36 % (4312)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 theBenchmark for (2999ds/27Mi)
% 0.14/0.36 % (4317)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.36 % (4311)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 theBenchmark for (2999ds/4Mi)
% 0.14/0.36 % (4314)Instruction limit reached!
% 0.14/0.36 % (4314)------------------------------
% 0.14/0.36 % (4314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (4314)Termination reason: Unknown
% 0.14/0.36 % (4314)Termination phase: Property scanning
% 0.14/0.36
% 0.14/0.36 % (4314)Memory used [KB]: 895
% 0.14/0.36 % (4314)Time elapsed: 0.003 s
% 0.14/0.36 % (4314)Instructions burned: 3 (million)
% 0.14/0.36 % (4314)------------------------------
% 0.14/0.36 % (4314)------------------------------
% 0.14/0.36 % (4317)Instruction limit reached!
% 0.14/0.36 % (4317)------------------------------
% 0.14/0.36 % (4317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (4317)Termination reason: Unknown
% 0.14/0.36 % (4317)Termination phase: Saturation
% 0.14/0.36
% 0.14/0.36 % (4317)Memory used [KB]: 1023
% 0.14/0.36 % (4317)Time elapsed: 0.003 s
% 0.14/0.36 % (4317)Instructions burned: 3 (million)
% 0.14/0.36 % (4317)------------------------------
% 0.14/0.36 % (4317)------------------------------
% 0.14/0.36 % (4315)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37 % (4310)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (4311)Instruction limit reached!
% 0.14/0.37 % (4311)------------------------------
% 0.14/0.37 % (4311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (4311)Termination reason: Unknown
% 0.14/0.37 % (4311)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (4311)Memory used [KB]: 5500
% 0.14/0.37 % (4311)Time elapsed: 0.005 s
% 0.14/0.37 % (4311)Instructions burned: 5 (million)
% 0.14/0.37 % (4311)------------------------------
% 0.14/0.37 % (4311)------------------------------
% 0.14/0.37 % (4313)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (4313)Instruction limit reached!
% 0.14/0.37 % (4313)------------------------------
% 0.14/0.37 % (4313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (4313)Termination reason: Unknown
% 0.14/0.37 % (4313)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (4313)Memory used [KB]: 895
% 0.14/0.37 % (4313)Time elapsed: 0.003 s
% 0.14/0.37 % (4313)Instructions burned: 2 (million)
% 0.14/0.37 % (4313)------------------------------
% 0.14/0.37 % (4313)------------------------------
% 0.14/0.37 % (4316)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (4315)First to succeed.
% 0.14/0.38 % (4318)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 theBenchmark for (2999ds/37Mi)
% 0.14/0.38 % (4310)Also succeeded, but the first one will report.
% 0.14/0.38 % (4315)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (4315)------------------------------
% 0.14/0.38 % (4315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4315)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (4315)Memory used [KB]: 5628
% 0.14/0.38 % (4315)Time elapsed: 0.014 s
% 0.14/0.38 % (4315)Instructions burned: 19 (million)
% 0.14/0.38 % (4315)------------------------------
% 0.14/0.38 % (4315)------------------------------
% 0.14/0.38 % (4309)Success in time 0.028 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------