TSTP Solution File: ANA092^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA092^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.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 04:31:08 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 32
% Syntax : Number of formulae : 122 ( 1 unt; 14 typ; 0 def)
% Number of atoms : 1139 ( 308 equ; 0 cnn)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 1410 ( 191 ~; 215 |; 60 &; 892 @)
% ( 12 <=>; 38 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 16 con; 0-3 aty)
% Number of variables : 208 ( 0 ^ 163 !; 42 ?; 208 :)
% ( 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' ).
thf(func_def_9,type,
sK1: 'type/realax/real' > $o ).
thf(func_def_10,type,
sK2: 'type/realax/real' ).
thf(func_def_11,type,
sK3: 'type/realax/real' ).
thf(func_def_12,type,
sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_13,type,
sK5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK8: 'type/realax/real' ).
thf(f245,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f55,f59,f98,f111,f116,f134,f147,f182,f196,f202,f242,f244]) ).
thf(f244,plain,
( spl6_13
| ~ spl6_9 ),
inference(avatar_split_clause,[],[f243,f93,f109]) ).
thf(f109,plain,
( spl6_13
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
thf(f93,plain,
( spl6_9
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
thf(f243,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_9 ),
inference(subsumption_resolution,[],[f200,f31]) ).
thf(f31,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
( ( ( $true
!= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
& ( $true
!= ( 'const/realax/real_le' @ sK0 @ sK2 ) ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK0 @ X3 )
= $true ) ) )
& ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24,f23,f22]) ).
thf(f22,plain,
( ? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X3 ) ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X1 ) )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ( ( $true
!= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
& ( $true
!= ( 'const/realax/real_le' @ sK0 @ X2 ) ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK0 @ X3 )
= $true ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
( ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
& ( $true
!= ( 'const/realax/real_le' @ sK0 @ X2 ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
& ( $true
!= ( 'const/realax/real_le' @ sK0 @ sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f24,plain,
( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X5 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f21,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X3 ) ) ) )
& ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X1 ) )
| ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ? [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
& ( $true
!= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X3 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[],[f19]) ).
thf(f19,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ? [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
& ( $true
!= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X3 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f18,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) )
<~> ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X3 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[],[f17]) ).
thf(f17,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) )
<~> ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) ) )
& ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X3 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ? [X2: 'type/realax/real'] :
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X3 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ X1 ) ) )
<=> ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X1 ) )
=> ( $true
= ( 'const/realax/real_le' @ X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
~ ! [X1: 'type/realax/real',X2: 'type/realax/real' > $o] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
= $true )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ( ! [X6: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X6 @ X2 ) )
=> ( $true
= ( 'const/realax/real_le' @ X1 @ X6 ) ) )
<=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X1: 'type/realax/real',X2: 'type/realax/real' > $o] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X6: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X6 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X6 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: 'type/realax/real',X2: 'type/realax/real' > $o,X3: X0] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: 'type/realax/real',X2: 'type/realax/real' > $o,X3: X0] :
( ( ? [X4: 'type/realax/real'] :
! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X2 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X2 ) ) )
=> ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X2 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Z5izGk0v2p/Vampire---4.8_25246','thm/sets/REAL_LE_INF_EQ_') ).
thf(f200,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f197,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_9 ),
inference(superposition,[],[f38,f94]) ).
thf(f94,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f38,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ) )
| ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f26,f28,f27]) ).
thf(f27,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/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f26,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/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ) )
| ! [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 ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X4 @ X5 )
!= $true ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ) )
| ! [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 ) ) ),
inference(ennf_transformation,[],[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 )
= $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 )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( ( 'const/realax/real_le' @ X4 @ X5 )
= $true ) )
=> ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,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,[],[f2]) ).
thf(f2,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/tmp/tmp.Z5izGk0v2p/Vampire---4.8_25246','thm/sets/INF_') ).
thf(f242,plain,
( spl6_1
| ~ spl6_13
| ~ spl6_16 ),
inference(avatar_contradiction_clause,[],[f241]) ).
thf(f241,plain,
( $false
| spl6_1
| ~ spl6_13
| ~ spl6_16 ),
inference(subsumption_resolution,[],[f239,f45]) ).
thf(f45,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| spl6_1 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f43,plain,
( spl6_1
<=> ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
thf(f239,plain,
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ~ spl6_13
| ~ spl6_16 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f238,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ~ spl6_13
| ~ spl6_16 ),
inference(duplicate_literal_removal,[],[f237]) ).
thf(f237,plain,
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ~ spl6_13
| ~ spl6_16 ),
inference(superposition,[],[f110,f133]) ).
thf(f133,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f132,plain,
( spl6_16
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
thf(f110,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f202,plain,
( spl6_10
| ~ spl6_9 ),
inference(avatar_split_clause,[],[f201,f93,f96]) ).
thf(f96,plain,
( spl6_10
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
thf(f201,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true ) )
| ~ spl6_9 ),
inference(subsumption_resolution,[],[f199,f31]) ).
thf(f199,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f198]) ).
thf(f198,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 )
!= $true ) )
| ~ spl6_9 ),
inference(superposition,[],[f36,f94]) ).
thf(f36,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f196,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f195]) ).
thf(f195,plain,
( $false
| ~ spl6_1
| spl6_2
| ~ spl6_3
| ~ spl6_10 ),
inference(subsumption_resolution,[],[f193,f54]) ).
thf(f54,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f52,plain,
( spl6_3
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
thf(f193,plain,
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
| ~ spl6_1
| spl6_2
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f191,plain,
( ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
| ~ spl6_1
| spl6_2
| ~ spl6_10 ),
inference(superposition,[],[f190,f97]) ).
thf(f97,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 ) ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f190,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ~ spl6_1
| spl6_2 ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f188,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ( $true != $true )
| ~ spl6_1
| spl6_2 ),
inference(superposition,[],[f184,f44]) ).
thf(f44,plain,
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f184,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK0 @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) ) )
| spl6_2 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f183,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK0 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK2 ) ) )
| spl6_2 ),
inference(superposition,[],[f49,f30]) ).
thf(f30,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,[],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f13]) ).
thf(f13,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.Z5izGk0v2p/Vampire---4.8_25246','thm/realax/REAL_LE_TRANS_') ).
thf(f49,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK0 @ sK2 ) )
| spl6_2 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f47,plain,
( spl6_2
<=> ( $true
= ( 'const/realax/real_le' @ sK0 @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
thf(f182,plain,
( spl6_16
| ~ spl6_4
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f180,f114,f57,f132]) ).
thf(f57,plain,
( spl6_4
<=> ! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK0 @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
thf(f114,plain,
( spl6_14
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
thf(f180,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_4
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f178,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true != $true ) )
| ~ spl6_4
| ~ spl6_14 ),
inference(superposition,[],[f58,f115]) ).
thf(f115,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f58,plain,
( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK0 @ X3 )
= $true ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f147,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f146]) ).
thf(f146,plain,
( $false
| ~ spl6_9
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f143,plain,
( ( $true != $true )
| ~ spl6_9
| ~ spl6_12 ),
inference(superposition,[],[f105,f94]) ).
thf(f105,plain,
( ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f104,plain,
( spl6_12
<=> ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
thf(f134,plain,
( spl6_12
| spl6_16
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f130,f57,f132,f104]) ).
thf(f130,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_4 ),
inference(subsumption_resolution,[],[f123,f31]) ).
thf(f123,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f120]) ).
thf(f120,plain,
( ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) )
| ~ spl6_4 ),
inference(superposition,[],[f58,f40]) ).
thf(f40,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f116,plain,
( spl6_14
| spl6_9 ),
inference(avatar_split_clause,[],[f112,f93,f114]) ).
thf(f112,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true ) ),
inference(subsumption_resolution,[],[f87,f31]) ).
thf(f87,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f85,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) ) ),
inference(superposition,[],[f32,f41]) ).
thf(f41,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f32,plain,
! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ sK1 )
!= $true )
| ( ( 'const/realax/real_le' @ sK3 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f111,plain,
( spl6_9
| spl6_13 ),
inference(avatar_split_clause,[],[f107,f109,f93]) ).
thf(f107,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true ) ),
inference(subsumption_resolution,[],[f88,f31]) ).
thf(f88,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(superposition,[],[f32,f39]) ).
thf(f39,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f98,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[],[f91,f96,f93]) ).
thf(f91,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 ) ) ),
inference(subsumption_resolution,[],[f90,f31]) ).
thf(f90,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK5 @ X0 @ sK1 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) ) ),
inference(superposition,[],[f32,f37]) ).
thf(f37,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f59,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f33,f57,f43]) ).
thf(f33,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK0 @ X3 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f55,plain,
( ~ spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f35,f52,f43]) ).
thf(f35,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f50,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f34,f47,f43]) ).
thf(f34,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA092^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.14 % 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
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 15:32:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH1_THM_EQU_NAR problem
% 0.15/0.36 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/tmp/tmp.Z5izGk0v2p/Vampire---4.8_25246
% 0.15/0.38 % (25354)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)
% 0.15/0.38 % (25356)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)
% 0.15/0.38 % (25355)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)
% 0.15/0.38 % (25358)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)
% 0.15/0.38 % (25359)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)
% 0.15/0.38 % (25357)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (25360)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38 % (25361)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)
% 0.15/0.38 % (25358)Instruction limit reached!
% 0.15/0.38 % (25358)------------------------------
% 0.15/0.38 % (25358)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25358)Termination reason: Unknown
% 0.15/0.38 % (25358)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (25358)Memory used [KB]: 895
% 0.15/0.38 % (25358)Time elapsed: 0.003 s
% 0.15/0.38 % (25358)Instructions burned: 2 (million)
% 0.15/0.38 % (25358)------------------------------
% 0.15/0.38 % (25358)------------------------------
% 0.15/0.38 % (25357)Instruction limit reached!
% 0.15/0.38 % (25357)------------------------------
% 0.15/0.38 % (25357)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25357)Termination reason: Unknown
% 0.15/0.38 % (25357)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (25357)Memory used [KB]: 1023
% 0.15/0.38 % (25357)Time elapsed: 0.003 s
% 0.15/0.38 % (25357)Instructions burned: 3 (million)
% 0.15/0.38 % (25357)------------------------------
% 0.15/0.38 % (25357)------------------------------
% 0.15/0.38 % (25361)Instruction limit reached!
% 0.15/0.38 % (25361)------------------------------
% 0.15/0.38 % (25361)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25361)Termination reason: Unknown
% 0.15/0.38 % (25361)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (25361)Memory used [KB]: 5500
% 0.15/0.38 % (25361)Time elapsed: 0.004 s
% 0.15/0.38 % (25361)Instructions burned: 3 (million)
% 0.15/0.38 % (25361)------------------------------
% 0.15/0.38 % (25361)------------------------------
% 0.15/0.38 % (25355)Instruction limit reached!
% 0.15/0.38 % (25355)------------------------------
% 0.15/0.38 % (25355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25355)Termination reason: Unknown
% 0.15/0.38 % (25355)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (25355)Memory used [KB]: 5500
% 0.15/0.38 % (25355)Time elapsed: 0.005 s
% 0.15/0.38 % (25355)Instructions burned: 4 (million)
% 0.15/0.38 % (25355)------------------------------
% 0.15/0.38 % (25355)------------------------------
% 0.15/0.39 % (25360)Instruction limit reached!
% 0.15/0.39 % (25360)------------------------------
% 0.15/0.39 % (25360)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (25360)Termination reason: Unknown
% 0.15/0.39 % (25360)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (25360)Memory used [KB]: 5628
% 0.15/0.39 % (25360)Time elapsed: 0.015 s
% 0.15/0.39 % (25360)Instructions burned: 18 (million)
% 0.15/0.39 % (25360)------------------------------
% 0.15/0.39 % (25360)------------------------------
% 0.15/0.39 % (25362)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)
% 0.15/0.40 % (25364)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.40 % (25363)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)
% 0.15/0.40 % (25365)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.15/0.40 % (25356)Instruction limit reached!
% 0.15/0.40 % (25356)------------------------------
% 0.15/0.40 % (25356)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (25356)Termination reason: Unknown
% 0.15/0.40 % (25356)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (25356)Memory used [KB]: 5628
% 0.15/0.40 % (25356)Time elapsed: 0.021 s
% 0.15/0.40 % (25356)Instructions burned: 27 (million)
% 0.15/0.40 % (25356)------------------------------
% 0.15/0.40 % (25356)------------------------------
% 0.15/0.40 % (25364)Instruction limit reached!
% 0.15/0.40 % (25364)------------------------------
% 0.15/0.40 % (25364)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (25364)Termination reason: Unknown
% 0.15/0.40 % (25364)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (25364)Memory used [KB]: 5500
% 0.15/0.40 % (25364)Time elapsed: 0.004 s
% 0.15/0.40 % (25364)Instructions burned: 3 (million)
% 0.15/0.40 % (25364)------------------------------
% 0.15/0.40 % (25364)------------------------------
% 0.15/0.40 % (25359)First to succeed.
% 0.15/0.41 % (25359)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for Vampire---4
% 0.15/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.41 % (25359)------------------------------
% 0.15/0.41 % (25359)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (25359)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (25359)Memory used [KB]: 5756
% 0.15/0.41 % (25359)Time elapsed: 0.028 s
% 0.15/0.41 % (25359)Instructions burned: 31 (million)
% 0.15/0.41 % (25359)------------------------------
% 0.15/0.41 % (25359)------------------------------
% 0.15/0.41 % (25353)Success in time 0.027 s
% 0.15/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------