TSTP Solution File: ANA088^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA088^1 : 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 : n005.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 04:31:07 EDT 2024
% Result : Theorem 0.15s 0.35s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 115 ( 3 unt; 14 typ; 0 def)
% Number of atoms : 982 ( 269 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1228 ( 157 ~; 180 |; 55 &; 797 @)
% ( 9 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 13 con; 0-3 aty)
% Number of variables : 192 ( 0 ^ 162 !; 26 ?; 192 :)
% ( 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/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_12,type,
sK4: 'type/realax/real' ).
thf(func_def_13,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK8: 'type/realax/real' ).
thf(f236,plain,
$false,
inference(avatar_sat_refutation,[],[f53,f94,f99,f107,f113,f141,f178,f193,f201,f203,f235]) ).
thf(f235,plain,
( spl6_11
| ~ spl6_12 ),
inference(avatar_split_clause,[],[f234,f111,f105]) ).
thf(f105,plain,
( spl6_11
<=> ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
thf(f111,plain,
( spl6_12
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
thf(f234,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f232,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_12 ),
inference(superposition,[],[f39,f112]) ).
thf(f112,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f39,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
& ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( ( 'const/realax/real_le' @ X3 @ sK4 )
= $true )
& ( ( 'const/realax/real_le' @ sK3 @ X3 )
= $true ) ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f25]) ).
thf(f25,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
& ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( ( 'const/realax/real_le' @ X3 @ sK4 )
= $true )
& ( ( 'const/realax/real_le' @ sK3 @ X3 )
= $true ) ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f17]) ).
thf(f17,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ 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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/REAL_INF_BOUNDS_') ).
thf(f203,plain,
( spl6_9
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f202,f89,f97]) ).
thf(f97,plain,
( spl6_9
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
thf(f89,plain,
( spl6_7
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
thf(f202,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_7 ),
inference(subsumption_resolution,[],[f199,f41]) ).
thf(f41,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(cnf_transformation,[],[f26]) ).
thf(f199,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f197,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
!= $true )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_7 ),
inference(superposition,[],[f34,f90]) ).
thf(f90,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f34,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,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 ) )
& ! [X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23,f22]) ).
thf(f22,plain,
! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f21,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 ) )
& ! [X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) ) )
=> ( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 ) )
=> ( ( 'const/realax/real_le' @ X3 @ X4 )
= $true ) )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ X4 ) )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/INF_') ).
thf(f201,plain,
( spl6_8
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f200,f89,f92]) ).
thf(f92,plain,
( spl6_8
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
thf(f200,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
| ~ spl6_7 ),
inference(subsumption_resolution,[],[f198,f41]) ).
thf(f198,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f196,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) )
| ~ spl6_7 ),
inference(superposition,[],[f36,f90]) ).
thf(f36,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' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f193,plain,
( spl6_2
| ~ spl6_9
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f190,f105,f97,f50]) ).
thf(f50,plain,
( spl6_2
<=> ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
thf(f190,plain,
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f189,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(duplicate_literal_removal,[],[f188]) ).
thf(f188,plain,
( ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl6_9
| ~ spl6_11 ),
inference(superposition,[],[f98,f106]) ).
thf(f106,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f105]) ).
thf(f98,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f178,plain,
( spl6_1
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f177]) ).
thf(f177,plain,
( $false
| spl6_1
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f175,f41]) ).
thf(f175,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f171,plain,
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| spl6_1
| ~ spl6_8 ),
inference(superposition,[],[f162,f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f29]) ).
thf(f29,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( $true
= ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X3: X0] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) )
& ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
<=> ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true ) ),
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/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f162,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| spl6_1
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f160,f40]) ).
thf(f40,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( 'const/realax/real_le' @ X3 @ sK4 )
= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f160,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK4 ) ) )
| spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f152,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ sK4 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true != $true ) )
| spl6_1
| ~ spl6_8 ),
inference(superposition,[],[f76,f93]) ).
thf(f93,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f76,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK4 ) ) )
| spl6_1 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK4 ) )
| ( $true != $true ) )
| spl6_1 ),
inference(superposition,[],[f48,f37]) ).
thf(f37,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,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 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f19]) ).
thf(f19,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' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( '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' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/realax/REAL_LE_TRANS_') ).
thf(f48,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
| spl6_1 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f46,plain,
( spl6_1
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
thf(f141,plain,
( ~ spl6_7
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f140]) ).
thf(f140,plain,
( $false
| ~ spl6_7
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f138,plain,
( ( $true != $true )
| ~ spl6_7
| ~ spl6_10 ),
inference(superposition,[],[f103,f90]) ).
thf(f103,plain,
( ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f102,plain,
( spl6_10
<=> ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
thf(f113,plain,
( spl6_7
| spl6_12 ),
inference(avatar_split_clause,[],[f109,f111,f89]) ).
thf(f109,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ),
inference(subsumption_resolution,[],[f82,f41]) ).
thf(f82,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(superposition,[],[f39,f31]) ).
thf(f31,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f107,plain,
( spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f100,f105,f102]) ).
thf(f100,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) ) ),
inference(subsumption_resolution,[],[f84,f41]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f77,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
inference(superposition,[],[f39,f32]) ).
thf(f32,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f99,plain,
( spl6_9
| spl6_7 ),
inference(avatar_split_clause,[],[f95,f89,f97]) ).
thf(f95,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ),
inference(subsumption_resolution,[],[f85,f41]) ).
thf(f85,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f80,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) ) ),
inference(superposition,[],[f39,f33]) ).
thf(f33,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f94,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f87,f92,f89]) ).
thf(f87,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) ) ),
inference(subsumption_resolution,[],[f86,f41]) ).
thf(f86,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
= $true ) ),
inference(superposition,[],[f39,f35]) ).
thf(f35,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f53,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f38,f50,f46]) ).
thf(f38,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ANA088^1 : TPTP v8.1.2. Released v7.0.0.
% 0.05/0.11 % 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
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 15:30:53 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 This is a TH1_THM_EQU_NAR problem
% 0.15/0.31 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.qV3j58wWel/Vampire---4.8_3631
% 0.15/0.33 % (3742)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.33 % (3741)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)
% 0.15/0.33 % (3744)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)
% 0.15/0.33 % (3739)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)
% 0.15/0.33 % (3743)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)
% 0.15/0.33 % (3742)Instruction limit reached!
% 0.15/0.33 % (3742)------------------------------
% 0.15/0.33 % (3742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (3742)Termination reason: Unknown
% 0.15/0.33 % (3742)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (3745)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.33 % (3742)Memory used [KB]: 5500
% 0.15/0.33 % (3743)Instruction limit reached!
% 0.15/0.33 % (3743)------------------------------
% 0.15/0.33 % (3743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (3743)Termination reason: Unknown
% 0.15/0.33 % (3742)Time elapsed: 0.003 s
% 0.15/0.33 % (3743)Termination phase: shuffling
% 0.15/0.33 % (3742)Instructions burned: 3 (million)
% 0.15/0.33
% 0.15/0.33 % (3742)------------------------------
% 0.15/0.33 % (3742)------------------------------
% 0.15/0.33 % (3743)Memory used [KB]: 895
% 0.15/0.33 % (3743)Time elapsed: 0.002 s
% 0.15/0.33 % (3743)Instructions burned: 2 (million)
% 0.15/0.33 % (3743)------------------------------
% 0.15/0.33 % (3743)------------------------------
% 0.15/0.33 % (3746)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)
% 0.15/0.34 % (3746)Instruction limit reached!
% 0.15/0.34 % (3746)------------------------------
% 0.15/0.34 % (3746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (3746)Termination reason: Unknown
% 0.15/0.34 % (3746)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (3746)Memory used [KB]: 5500
% 0.15/0.34 % (3746)Time elapsed: 0.004 s
% 0.15/0.34 % (3746)Instructions burned: 3 (million)
% 0.15/0.34 % (3746)------------------------------
% 0.15/0.34 % (3746)------------------------------
% 0.15/0.34 % (3740)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)
% 0.15/0.34 % (3740)Instruction limit reached!
% 0.15/0.34 % (3740)------------------------------
% 0.15/0.34 % (3740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (3740)Termination reason: Unknown
% 0.15/0.34 % (3740)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (3740)Memory used [KB]: 5500
% 0.15/0.34 % (3740)Time elapsed: 0.003 s
% 0.15/0.34 % (3740)Instructions burned: 4 (million)
% 0.15/0.34 % (3740)------------------------------
% 0.15/0.34 % (3740)------------------------------
% 0.15/0.34 % (3745)Instruction limit reached!
% 0.15/0.34 % (3745)------------------------------
% 0.15/0.34 % (3745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (3745)Termination reason: Unknown
% 0.15/0.34 % (3745)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (3745)Memory used [KB]: 5628
% 0.15/0.34 % (3745)Time elapsed: 0.012 s
% 0.15/0.34 % (3745)Instructions burned: 18 (million)
% 0.15/0.34 % (3745)------------------------------
% 0.15/0.34 % (3745)------------------------------
% 0.15/0.34 % (3747)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.34 % (3741)Instruction limit reached!
% 0.15/0.34 % (3741)------------------------------
% 0.15/0.34 % (3741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (3741)Termination reason: Unknown
% 0.15/0.34 % (3741)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (3741)Memory used [KB]: 5756
% 0.15/0.34 % (3741)Time elapsed: 0.016 s
% 0.15/0.34 % (3741)Instructions burned: 27 (million)
% 0.15/0.34 % (3741)------------------------------
% 0.15/0.34 % (3741)------------------------------
% 0.15/0.35 % (3744)First to succeed.
% 0.15/0.35 % (3748)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.15/0.35 % (3744)Refutation found. Thanks to Tanya!
% 0.15/0.35 % SZS status Theorem for Vampire---4
% 0.15/0.35 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.35 % (3744)------------------------------
% 0.15/0.35 % (3744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (3744)Termination reason: Refutation
% 0.15/0.35
% 0.15/0.35 % (3744)Memory used [KB]: 5628
% 0.15/0.35 % (3744)Time elapsed: 0.022 s
% 0.15/0.35 % (3744)Instructions burned: 33 (million)
% 0.15/0.35 % (3744)------------------------------
% 0.15/0.35 % (3744)------------------------------
% 0.15/0.35 % (3738)Success in time 0.033 s
% 0.15/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------