TSTP Solution File: ANA071^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA071^1 : 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 : 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 : Mon May 20 18:40:21 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 91 ( 4 unt; 14 typ; 0 def)
% Number of atoms : 543 ( 131 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 664 ( 88 ~; 90 |; 41 &; 414 @)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 14 con; 0-3 aty)
% ( 0 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 71 ( 11 ^ 46 !; 9 ?; 71 :)
% ( 5 !>; 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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_6,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_16,type,
sK1: 'type/realax/real' ).
thf(func_def_18,type,
sK3: 'type/realax/real' ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK5: 'type/realax/real' ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[],[f43,f48,f56,f98,f103,f106,f125,f133,f146]) ).
thf(f146,plain,
( spl2_4
| ~ spl2_5
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f142,f89,f54,f50]) ).
thf(f50,plain,
( spl2_4
<=> ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f54,plain,
( spl2_5
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X1 )
= $false )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f89,plain,
( spl2_11
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
thf(f142,plain,
( ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_5
| ~ spl2_11 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f136,plain,
( ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true = $false )
| ~ spl2_5
| ~ spl2_11 ),
inference(superposition,[],[f55,f91]) ).
thf(f91,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f55,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false )
| ( ( 'const/realax/real_lt' @ sK1 @ X1 )
= $false ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f133,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_13 ),
inference(avatar_contradiction_clause,[],[f132]) ).
thf(f132,plain,
( $false
| ~ spl2_1
| ~ spl2_4
| ~ spl2_13 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f131,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4
| ~ spl2_13 ),
inference(forward_demodulation,[],[f130,f52]) ).
thf(f52,plain,
( ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f130,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_1
| ~ spl2_13 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f129,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_1
| ~ spl2_13 ),
inference(superposition,[],[f127,f38]) ).
thf(f38,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ sK3 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f36,plain,
( spl2_1
<=> ( $true
= ( 'const/realax/real_lt' @ sK1 @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f127,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ X0 @ sK3 ) )
| ( $true
= ( 'const/realax/real_lt' @ X0 @ ( 'const/sets/sup' @ sK0 ) ) ) )
| ~ spl2_13 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ X0 @ sK3 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_lt' @ X0 @ ( 'const/sets/sup' @ sK0 ) ) ) )
| ~ spl2_13 ),
inference(superposition,[],[f23,f124]) ).
thf(f124,plain,
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f122,plain,
( spl2_13
<=> ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
thf(f23,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_lt' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_LTE_TRANS_') ).
thf(f125,plain,
( spl2_13
| spl2_10
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f120,f45,f85,f122]) ).
thf(f85,plain,
( spl2_10
<=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
thf(f45,plain,
( spl2_3
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f120,plain,
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f119,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl2_3 ),
inference(forward_demodulation,[],[f118,f22]) ).
thf(f22,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
& ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) ) )
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_lt' @ X1 @ Y0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
& ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) ) )
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_lt' @ X1 @ Y0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f16]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_lt' @ X1 @ Y0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_lt' @ X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_lt' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LT_SUP_FINITE_') ).
thf(f118,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f117,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_3 ),
inference(superposition,[],[f24,f47]) ).
thf(f47,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( '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 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( '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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( '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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_FINITE_') ).
thf(f106,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f105,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f42,f52]) ).
thf(f42,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f40,plain,
( spl2_2
<=> ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f103,plain,
( spl2_11
| spl2_10 ),
inference(avatar_split_clause,[],[f102,f85,f89]) ).
thf(f102,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f101,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f25,f22]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f98,plain,
~ spl2_10,
inference(avatar_contradiction_clause,[],[f97]) ).
thf(f97,plain,
( $false
| ~ spl2_10 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f96,plain,
( ( sK0 != sK0 )
| ~ spl2_10 ),
inference(superposition,[],[f20,f87]) ).
thf(f87,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f20,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f19]) ).
thf(f56,plain,
( spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f30,f54,f50]) ).
thf(f30,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK1 @ X1 )
= $false )
| ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
! [X1: 'type/realax/real'] :
( ( $false
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(pi_clausification,[],[f27]) ).
thf(f27,plain,
( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) ) )
!= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f48,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f34,f40,f45]) ).
thf(f34,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[],[f32]) ).
thf(f32,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ sK3 ) ) ) ),
inference(beta_eta_normalization,[],[f31]) ).
thf(f31,plain,
( ( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) ) ),
inference(sigma_clausification,[],[f26]) ).
thf(f26,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_lt' @ sK1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f43,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f33,f40,f36]) ).
thf(f33,plain,
( ( $true
= ( 'const/realax/real_lt' @ sK1 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ sK1 @ sK3 ) ) ),
inference(binary_proxy_clausification,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ANA071^1 : TPTP v8.2.0. Released v7.0.0.
% 0.10/0.13 % 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
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 07:54:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH1_THM_EQU_NAR problem
% 0.13/0.34 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
% 0.13/0.36 % (21702)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)
% 0.13/0.36 % (21707)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)
% 0.13/0.36 % (21705)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)
% 0.13/0.36 % (21707)Instruction limit reached!
% 0.13/0.36 % (21707)------------------------------
% 0.13/0.36 % (21707)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (21707)Termination reason: Unknown
% 0.13/0.36 % (21707)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (21707)Memory used [KB]: 5500
% 0.13/0.36 % (21707)Time elapsed: 0.004 s
% 0.13/0.36 % (21707)Instructions burned: 4 (million)
% 0.13/0.36 % (21707)------------------------------
% 0.13/0.36 % (21707)------------------------------
% 0.13/0.36 % (21700)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.36 % (21702)First to succeed.
% 0.13/0.37 % (21702)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (21702)------------------------------
% 0.13/0.37 % (21702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (21702)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (21702)Memory used [KB]: 5628
% 0.13/0.37 % (21702)Time elapsed: 0.007 s
% 0.13/0.37 % (21702)Instructions burned: 9 (million)
% 0.13/0.37 % (21702)------------------------------
% 0.13/0.37 % (21702)------------------------------
% 0.13/0.37 % (21699)Success in time 0.019 s
% 0.13/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------