TSTP Solution File: ANA086^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA086^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.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 18:40:25 EDT 2024
% Result : Theorem 0.23s 0.41s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 75 ( 2 unt; 12 typ; 0 def)
% Number of atoms : 611 ( 164 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 785 ( 99 ~; 106 |; 33 &; 516 @)
% ( 5 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 114 ( 0 ^ 96 !; 15 ?; 114 :)
% ( 3 !>; 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/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_8,type,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_9,type,
sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_10,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_11,type,
sK3: 'type/realax/real' ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK6: 'type/realax/real' ).
thf(f131,plain,
$false,
inference(avatar_sat_refutation,[],[f75,f80,f85,f99,f104,f115,f130]) ).
thf(f130,plain,
( spl4_5
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f129,f73,f62]) ).
thf(f62,plain,
( spl4_5
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
thf(f73,plain,
( spl4_8
<=> ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
thf(f129,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) )
| ~ spl4_8 ),
inference(superposition,[],[f26,f74]) ).
thf(f74,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f26,plain,
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
!= $true ) )
& ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16]) ).
thf(f16,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
!= $true ) )
& ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f9]) ).
thf(f9,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,negated_conjecture,
~ ! [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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
inference(negated_conjecture,[],[f2]) ).
thf(f2,conjecture,
! [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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_') ).
thf(f115,plain,
( ~ spl4_7
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[],[f114]) ).
thf(f114,plain,
( $false
| ~ spl4_7
| ~ spl4_10 ),
inference(subsumption_resolution,[],[f113,f25]) ).
thf(f25,plain,
( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f113,plain,
( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f112,plain,
( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true )
| ~ spl4_7
| ~ spl4_10 ),
inference(duplicate_literal_removal,[],[f110]) ).
thf(f110,plain,
( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[],[f84,f71]) ).
thf(f71,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f70,plain,
( spl4_7
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
thf(f84,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f83,plain,
( spl4_10
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
!= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
thf(f104,plain,
( ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f103]) ).
thf(f103,plain,
( $false
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f101,plain,
( ( $true != $true )
| ~ spl4_5
| ~ spl4_9 ),
inference(superposition,[],[f79,f63]) ).
thf(f63,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f79,plain,
( ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
!= $true )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f78,plain,
( spl4_9
<=> ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
!= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
thf(f99,plain,
( spl4_9
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f98,f70,f78]) ).
thf(f98,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f97,f24]) ).
thf(f24,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(cnf_transformation,[],[f17]) ).
thf(f97,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true ) )
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f96,f25]) ).
thf(f96,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f95,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f94]) ).
thf(f94,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl4_7 ),
inference(superposition,[],[f21,f71]) ).
thf(f21,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
& ! [X4: 'type/realax/real'] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14,f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $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 )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
= $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 )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,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/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [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'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
=> ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
=> ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,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' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ! [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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(f85,plain,
( spl4_10
| spl4_5 ),
inference(avatar_split_clause,[],[f81,f62,f83]) ).
thf(f81,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
inference(subsumption_resolution,[],[f56,f24]) ).
thf(f56,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f52,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(superposition,[],[f26,f18]) ).
thf(f18,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f80,plain,
( spl4_9
| spl4_7 ),
inference(avatar_split_clause,[],[f76,f70,f78]) ).
thf(f76,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
!= $true ) ),
inference(subsumption_resolution,[],[f57,f24]) ).
thf(f57,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f54,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f26,f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f75,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[],[f68,f73,f70]) ).
thf(f68,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ),
inference(subsumption_resolution,[],[f58,f24]) ).
thf(f58,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f55,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f26,f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 07:58:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH1_THM_EQU_NAR problem
% 0.23/0.37 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/sandbox/benchmark/theBenchmark.p
% 0.23/0.39 % (3317)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)
% 0.23/0.40 % (3315)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.23/0.40 % (3316)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)
% 0.23/0.40 % (3318)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.40 % (3319)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)
% 0.23/0.40 % (3321)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.40 % (3320)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)
% 0.23/0.40 % (3322)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)
% 0.23/0.40 % (3318)Instruction limit reached!
% 0.23/0.40 % (3318)------------------------------
% 0.23/0.40 % (3318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (3318)Termination reason: Unknown
% 0.23/0.40 % (3318)Termination phase: Preprocessing 3
% 0.23/0.40
% 0.23/0.40 % (3318)Memory used [KB]: 895
% 0.23/0.40 % (3318)Time elapsed: 0.004 s
% 0.23/0.40 % (3318)Instructions burned: 2 (million)
% 0.23/0.40 % (3318)------------------------------
% 0.23/0.40 % (3318)------------------------------
% 0.23/0.40 % (3319)Instruction limit reached!
% 0.23/0.40 % (3319)------------------------------
% 0.23/0.40 % (3319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (3319)Termination reason: Unknown
% 0.23/0.40 % (3319)Termination phase: Property scanning
% 0.23/0.40
% 0.23/0.40 % (3319)Memory used [KB]: 895
% 0.23/0.40 % (3319)Time elapsed: 0.004 s
% 0.23/0.40 % (3319)Instructions burned: 2 (million)
% 0.23/0.40 % (3319)------------------------------
% 0.23/0.40 % (3319)------------------------------
% 0.23/0.40 % (3322)Instruction limit reached!
% 0.23/0.40 % (3322)------------------------------
% 0.23/0.40 % (3322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (3322)Termination reason: Unknown
% 0.23/0.40 % (3322)Termination phase: Saturation
% 0.23/0.40
% 0.23/0.40 % (3322)Memory used [KB]: 5500
% 0.23/0.40 % (3322)Time elapsed: 0.005 s
% 0.23/0.40 % (3316)Instruction limit reached!
% 0.23/0.40 % (3316)------------------------------
% 0.23/0.40 % (3316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (3322)Instructions burned: 3 (million)
% 0.23/0.40 % (3322)------------------------------
% 0.23/0.40 % (3322)------------------------------
% 0.23/0.40 % (3316)Termination reason: Unknown
% 0.23/0.40 % (3316)Termination phase: Saturation
% 0.23/0.40
% 0.23/0.40 % (3316)Memory used [KB]: 5500
% 0.23/0.40 % (3316)Time elapsed: 0.007 s
% 0.23/0.40 % (3316)Instructions burned: 5 (million)
% 0.23/0.40 % (3316)------------------------------
% 0.23/0.40 % (3316)------------------------------
% 0.23/0.41 % (3320)First to succeed.
% 0.23/0.41 % (3317)Also succeeded, but the first one will report.
% 0.23/0.41 % (3320)Refutation found. Thanks to Tanya!
% 0.23/0.41 % SZS status Theorem for theBenchmark
% 0.23/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.41 % (3320)------------------------------
% 0.23/0.41 % (3320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41 % (3320)Termination reason: Refutation
% 0.23/0.41
% 0.23/0.41 % (3320)Memory used [KB]: 5628
% 0.23/0.41 % (3320)Time elapsed: 0.017 s
% 0.23/0.41 % (3320)Instructions burned: 12 (million)
% 0.23/0.41 % (3320)------------------------------
% 0.23/0.41 % (3320)------------------------------
% 0.23/0.41 % (3314)Success in time 0.029 s
% 0.23/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------