TSTP Solution File: ANA084^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA084^1 : TPTP v8.1.2. 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 : Sun May 5 04:31:06 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 73 ( 2 unt; 13 typ; 0 def)
% Number of atoms : 570 ( 161 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 692 ( 108 ~; 92 |; 51 &; 419 @)
% ( 5 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 82 ( 0 ^ 54 !; 24 ?; 82 :)
% ( 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/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/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_10,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_11,type,
sK1: 'type/realax/real' ).
thf(func_def_12,type,
sK2: 'type/realax/real' ).
thf(func_def_14,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: 'type/realax/real' ).
thf(f88,plain,
$false,
inference(avatar_sat_refutation,[],[f40,f44,f49,f77,f83,f87]) ).
thf(f87,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f86]) ).
thf(f86,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f85,f35]) ).
thf(f35,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f33,plain,
( spl3_1
<=> ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
thf(f85,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f84,f31]) ).
thf(f31,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f23,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ sK1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true ) )
& ( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
& ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f22,f21]) ).
thf(f21,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ X1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= $true ) )
& ( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X3 @ X1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) )
=> ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ sK1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true ) )
& ( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
= $true )
& ( ( 'const/realax/real_lt' @ X3 @ sK1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f22,plain,
( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK0 )
= $true )
& ( ( 'const/realax/real_lt' @ X3 @ sK1 )
= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
& ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f20,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ X1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= $true ) )
& ( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X3 @ X1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ X1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= $true ) )
& ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X2 @ X1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f18,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ X1 )
!= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= $true ) )
& ( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X2 @ X1 )
= $true ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f17,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
<~> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X2 @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f16]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
<~> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X2 @ X1 )
= $true ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
<=> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_lt' @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Nlabb3S6Eu/Vampire---4.8_15404','thm/sets/REAL_INF_LT_FINITE_') ).
thf(f84,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f80,f30]) ).
thf(f30,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f23]) ).
thf(f80,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| ~ spl3_3 ),
inference(superposition,[],[f43,f26]) ).
thf(f26,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
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/inf' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $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/inf' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ '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 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ '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 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Nlabb3S6Eu/Vampire---4.8_15404','thm/sets/INF_FINITE_') ).
thf(f43,plain,
( ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ sK1 )
!= $true ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f42,plain,
( spl3_3
<=> ! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ sK1 )
!= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
thf(f83,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f82]) ).
thf(f82,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(subsumption_resolution,[],[f81,f48]) ).
thf(f48,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f46,plain,
( spl3_4
<=> ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
thf(f81,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
( ( $true != $true )
| ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f43,f39]) ).
thf(f39,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f37,plain,
( spl3_2
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
thf(f77,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[],[f76,f33,f42]) ).
thf(f76,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true ) )
| spl3_1 ),
inference(subsumption_resolution,[],[f75,f30]) ).
thf(f75,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
| spl3_1 ),
inference(subsumption_resolution,[],[f74,f31]) ).
thf(f74,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f73,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true ) )
| spl3_1 ),
inference(superposition,[],[f72,f25]) ).
thf(f25,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $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(cnf_transformation,[],[f13]) ).
thf(f72,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f71,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ X0 )
!= $true )
| ( $true != $true ) )
| spl3_1 ),
inference(superposition,[],[f34,f24]) ).
thf(f24,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $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_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_lt' @ 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' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_lt' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $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_le' @ X0 @ X1 )
& ( 'const/realax/real_lt' @ 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_le' @ X0 @ X1 )
& ( 'const/realax/real_lt' @ X1 @ X2 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Nlabb3S6Eu/Vampire---4.8_15404','thm/realarith/REAL_LET_TRANS_') ).
thf(f34,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| spl3_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f49,plain,
( spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f27,f33,f46]) ).
thf(f27,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f44,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f29,f42,f33]) ).
thf(f29,plain,
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 )
!= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $true )
| ( ( 'const/realax/real_lt' @ X2 @ sK1 )
!= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f40,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f28,f37,f33]) ).
thf(f28,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA084^1 : TPTP v8.1.2. Released v7.0.0.
% 0.06/0.14 % 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 : n025.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 : Fri May 3 15:29:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH1_THM_EQU_NAR problem
% 0.14/0.35 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/tmp/tmp.Nlabb3S6Eu/Vampire---4.8_15404
% 0.14/0.37 % (15514)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 Vampire---4 for (2999ds/4Mi)
% 0.14/0.37 % (15518)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.14/0.37 % (15517)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.37 % (15516)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.37 % (15515)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 Vampire---4 for (2999ds/27Mi)
% 0.14/0.37 % (15519)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.37 % (15516)Instruction limit reached!
% 0.14/0.37 % (15516)------------------------------
% 0.14/0.37 % (15516)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15516)Termination reason: Unknown
% 0.14/0.37 % (15516)Termination phase: Preprocessing 3
% 0.14/0.37
% 0.14/0.37 % (15516)Memory used [KB]: 895
% 0.14/0.37 % (15516)Time elapsed: 0.003 s
% 0.14/0.37 % (15516)Instructions burned: 2 (million)
% 0.14/0.37 % (15516)------------------------------
% 0.14/0.37 % (15516)------------------------------
% 0.14/0.37 % (15517)Instruction limit reached!
% 0.14/0.37 % (15517)------------------------------
% 0.14/0.37 % (15517)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15517)Termination reason: Unknown
% 0.14/0.37 % (15517)Termination phase: Preprocessing 2
% 0.14/0.37
% 0.14/0.37 % (15517)Memory used [KB]: 895
% 0.14/0.37 % (15517)Time elapsed: 0.003 s
% 0.14/0.37 % (15517)Instructions burned: 2 (million)
% 0.14/0.37 % (15517)------------------------------
% 0.14/0.37 % (15517)------------------------------
% 0.14/0.37 % (15513)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.14/0.37 % (15514)Instruction limit reached!
% 0.14/0.37 % (15514)------------------------------
% 0.14/0.37 % (15514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15514)Termination reason: Unknown
% 0.14/0.37 % (15514)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (15514)Memory used [KB]: 5500
% 0.14/0.37 % (15514)Time elapsed: 0.005 s
% 0.14/0.37 % (15514)Instructions burned: 4 (million)
% 0.14/0.37 % (15514)------------------------------
% 0.14/0.37 % (15514)------------------------------
% 0.14/0.37 % (15518)First to succeed.
% 0.14/0.37 % (15520)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.14/0.37 % (15520)Instruction limit reached!
% 0.14/0.37 % (15520)------------------------------
% 0.14/0.37 % (15520)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15520)Termination reason: Unknown
% 0.14/0.37 % (15520)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (15520)Memory used [KB]: 5500
% 0.14/0.37 % (15520)Time elapsed: 0.004 s
% 0.14/0.37 % (15520)Instructions burned: 3 (million)
% 0.14/0.37 % (15519)Also succeeded, but the first one will report.
% 0.14/0.37 % (15520)------------------------------
% 0.14/0.37 % (15520)------------------------------
% 0.14/0.37 % (15518)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for Vampire---4
% 0.14/0.37 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.37 % (15518)------------------------------
% 0.21/0.37 % (15518)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (15518)Termination reason: Refutation
% 0.21/0.37
% 0.21/0.37 % (15518)Memory used [KB]: 5628
% 0.21/0.37 % (15518)Time elapsed: 0.006 s
% 0.21/0.37 % (15518)Instructions burned: 5 (million)
% 0.21/0.37 % (15518)------------------------------
% 0.21/0.37 % (15518)------------------------------
% 0.21/0.37 % (15512)Success in time 0.012 s
% 0.21/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------