TSTP Solution File: ANA088^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA088^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:40:26 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 117 ( 3 unt; 14 typ; 0 def)
% Number of atoms : 991 ( 270 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1238 ( 160 ~; 184 |; 55 &; 800 @)
% ( 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:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
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(f213,plain,
$false,
inference(avatar_sat_refutation,[],[f53,f95,f100,f105,f113,f141,f170,f179,f204,f210,f212]) ).
thf(f212,plain,
( spl6_9
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f211,f93,f98]) ).
thf(f98,plain,
( spl6_9
<=> ! [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_9])]) ).
thf(f93,plain,
( spl6_8
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
thf(f211,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f207,f36]) ).
thf(f36,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK3 ) )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( $true
= ( 'const/realax/real_le' @ X3 @ sK3 ) )
& ( $true
= ( 'const/realax/real_le' @ sK2 @ X3 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f16,f25]) ).
thf(f25,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 ) )
& ! [X3: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) ) )
=> ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK3 ) )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( $true
= ( 'const/realax/real_le' @ X3 @ sK3 ) )
& ( $true
= ( 'const/realax/real_le' @ sK2 @ X3 ) ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( '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 ) )
& ! [X3: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,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/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,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,[],[f9]) ).
thf(f9,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 )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) ) )
=> ( ( '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'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) ) )
=> ( ( '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'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( ( 'const/realax/real_le' @ X3 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X3 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_INF_BOUNDS_') ).
thf(f207,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f205,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_8 ),
inference(superposition,[],[f38,f94]) ).
thf(f94,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f38,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f30,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/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f29,f28]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
( ? [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f29,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 ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f27,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'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X2 @ X3 ) ) )
| ( $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,[],[f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
| ( $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,[],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
& ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
| ( $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,[],[f12]) ).
thf(f12,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 ) )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) )
& ! [X3: 'type/realax/real'] :
( ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
=> ( $true
= ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,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'] :
( ! [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] :
( ( ? [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'] :
( ! [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/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(f210,plain,
( spl6_10
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f209,f93,f103]) ).
thf(f103,plain,
( spl6_10
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
thf(f209,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) ) )
| ~ spl6_8 ),
inference(subsumption_resolution,[],[f208,f36]) ).
thf(f208,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f206]) ).
thf(f206,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) ) )
| ~ spl6_8 ),
inference(superposition,[],[f42,f94]) ).
thf(f42,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) )
| ( ( '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 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f204,plain,
( spl6_2
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f203]) ).
thf(f203,plain,
( $false
| spl6_2
| ~ spl6_10 ),
inference(subsumption_resolution,[],[f201,f36]) ).
thf(f201,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| spl6_2
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f195,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| spl6_2
| ~ spl6_10 ),
inference(superposition,[],[f190,f32]) ).
thf(f32,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
=> ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X1 ) @ X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X3: X0] :
( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
& ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
| ! [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
<=> ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
= ( ? [X2: X0] : ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f190,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) )
| spl6_2
| ~ spl6_10 ),
inference(subsumption_resolution,[],[f188,f34]) ).
thf(f34,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK3 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f188,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK3 ) ) )
| spl6_2
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f184,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK1 ) ) )
| spl6_2
| ~ spl6_10 ),
inference(superposition,[],[f182,f104]) ).
thf(f104,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f182,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK3 ) ) )
| spl6_2 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f181,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK3 ) )
| ( $true != $true ) )
| spl6_2 ),
inference(superposition,[],[f52,f43]) ).
thf(f43,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,[],[f18]) ).
thf(f18,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,[],[f17]) ).
thf(f17,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,[],[f8]) ).
thf(f8,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,[],[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/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f52,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK3 ) )
| spl6_2 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f50,plain,
( spl6_2
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
thf(f179,plain,
( spl6_1
| ~ spl6_9
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f178]) ).
thf(f178,plain,
( $false
| spl6_1
| ~ spl6_9
| ~ spl6_12 ),
inference(subsumption_resolution,[],[f177,f48]) ).
thf(f48,plain,
( ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
!= $true )
| spl6_1 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f46,plain,
( spl6_1
<=> ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
thf(f177,plain,
( ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_9
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f176,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_9
| ~ spl6_12 ),
inference(duplicate_literal_removal,[],[f175]) ).
thf(f175,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
= $true )
| ~ spl6_9
| ~ spl6_12 ),
inference(superposition,[],[f99,f112]) ).
thf(f112,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f111,plain,
( spl6_12
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
thf(f99,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_9 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f170,plain,
( spl6_12
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f169,f90,f111]) ).
thf(f90,plain,
( spl6_7
<=> ! [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 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
thf(f169,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f167,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) ) )
| ~ spl6_7 ),
inference(superposition,[],[f33,f91]) ).
thf(f91,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_7 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f33,plain,
! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ X3 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f141,plain,
( ~ spl6_8
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f140]) ).
thf(f140,plain,
( $false
| ~ spl6_8
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f138,plain,
( ( $true != $true )
| ~ spl6_8
| ~ spl6_11 ),
inference(superposition,[],[f109,f94]) ).
thf(f109,plain,
( ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f108,plain,
( spl6_11
<=> ! [X1: 'type/realax/real'] :
( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
thf(f113,plain,
( spl6_11
| spl6_12 ),
inference(avatar_split_clause,[],[f106,f111,f108]) ).
thf(f106,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) ) ),
inference(subsumption_resolution,[],[f82,f36]) ).
thf(f82,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f80,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK4 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK5 @ X1 @ sK1 ) ) ) ),
inference(superposition,[],[f33,f40]) ).
thf(f40,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X4 @ ( sK5 @ X4 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f105,plain,
( spl6_8
| spl6_10 ),
inference(avatar_split_clause,[],[f101,f103,f93]) ).
thf(f101,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) ) ),
inference(subsumption_resolution,[],[f83,f36]) ).
thf(f83,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f77,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ X1 ) )
| ( $true != $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK1 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(superposition,[],[f33,f41]) ).
thf(f41,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f100,plain,
( spl6_9
| spl6_8 ),
inference(avatar_split_clause,[],[f96,f93,f98]) ).
thf(f96,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) ) ),
inference(subsumption_resolution,[],[f84,f36]) ).
thf(f84,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f78,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK4 @ X1 @ sK1 ) ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(superposition,[],[f33,f37]) ).
thf(f37,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ ( sK4 @ X2 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f95,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f88,f93,f90]) ).
thf(f88,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) ) ),
inference(subsumption_resolution,[],[f85,f36]) ).
thf(f85,plain,
! [X0: 'type/realax/real',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 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( sK5 @ X0 @ sK1 ) ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X1 @ sK1 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK1 ) ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(superposition,[],[f33,f39]) ).
thf(f39,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f53,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f35,f50,f46]) ).
thf(f35,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK3 ) )
| ( ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/inf' @ sK1 ) )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA088^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 20 07:51:53 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.34 This is a TH1_THM_EQU_NAR problem
% 0.15/0.35 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/benchmark/theBenchmark.p
% 0.15/0.36 % (1505)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.36 % (1506)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.36 % (1499)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.36 % (1500)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.36 % (1503)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.36 % (1501)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.36 % (1502)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.36 % (1504)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.36 % (1502)Instruction limit reached!
% 0.15/0.36 % (1502)------------------------------
% 0.15/0.36 % (1502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (1502)Termination reason: Unknown
% 0.15/0.36 % (1503)Instruction limit reached!
% 0.15/0.36 % (1503)------------------------------
% 0.15/0.36 % (1503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (1503)Termination reason: Unknown
% 0.15/0.36 % (1503)Termination phase: Property scanning
% 0.15/0.36
% 0.15/0.36 % (1503)Memory used [KB]: 895
% 0.15/0.36 % (1503)Time elapsed: 0.003 s
% 0.15/0.36 % (1503)Instructions burned: 2 (million)
% 0.15/0.36 % (1503)------------------------------
% 0.15/0.36 % (1503)------------------------------
% 0.15/0.36 % (1502)Termination phase: Preprocessing 3
% 0.15/0.36
% 0.15/0.36 % (1502)Memory used [KB]: 895
% 0.15/0.36 % (1502)Time elapsed: 0.003 s
% 0.15/0.36 % (1502)Instructions burned: 2 (million)
% 0.15/0.36 % (1502)------------------------------
% 0.15/0.36 % (1502)------------------------------
% 0.15/0.36 % (1506)Instruction limit reached!
% 0.15/0.36 % (1506)------------------------------
% 0.15/0.36 % (1506)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (1506)Termination reason: Unknown
% 0.15/0.37 % (1506)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (1506)Memory used [KB]: 5500
% 0.15/0.37 % (1506)Time elapsed: 0.004 s
% 0.15/0.37 % (1506)Instructions burned: 4 (million)
% 0.15/0.37 % (1506)------------------------------
% 0.15/0.37 % (1506)------------------------------
% 0.15/0.37 % (1500)Instruction limit reached!
% 0.15/0.37 % (1500)------------------------------
% 0.15/0.37 % (1500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (1500)Termination reason: Unknown
% 0.15/0.37 % (1500)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (1500)Memory used [KB]: 5500
% 0.15/0.37 % (1500)Time elapsed: 0.005 s
% 0.15/0.37 % (1500)Instructions burned: 5 (million)
% 0.15/0.37 % (1500)------------------------------
% 0.15/0.37 % (1500)------------------------------
% 0.15/0.37 % (1505)Instruction limit reached!
% 0.15/0.37 % (1505)------------------------------
% 0.15/0.37 % (1505)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (1505)Termination reason: Unknown
% 0.15/0.37 % (1505)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (1505)Memory used [KB]: 5628
% 0.15/0.37 % (1505)Time elapsed: 0.012 s
% 0.15/0.37 % (1505)Instructions burned: 18 (million)
% 0.15/0.37 % (1505)------------------------------
% 0.15/0.37 % (1505)------------------------------
% 0.15/0.38 % (1501)Instruction limit reached!
% 0.15/0.38 % (1501)------------------------------
% 0.15/0.38 % (1501)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (1501)Termination reason: Unknown
% 0.15/0.38 % (1501)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (1501)Memory used [KB]: 5756
% 0.15/0.38 % (1501)Time elapsed: 0.022 s
% 0.15/0.38 % (1501)Instructions burned: 28 (million)
% 0.15/0.38 % (1501)------------------------------
% 0.15/0.38 % (1501)------------------------------
% 0.15/0.38 % (1509)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.38 % (1507)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 theBenchmark for (2999ds/37Mi)
% 0.15/0.39 % (1511)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.39 % (1509)Instruction limit reached!
% 0.15/0.39 % (1509)------------------------------
% 0.15/0.39 % (1509)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1509)Termination reason: Unknown
% 0.15/0.39 % (1509)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (1509)Memory used [KB]: 5500
% 0.15/0.39 % (1509)Time elapsed: 0.004 s
% 0.15/0.39 % (1509)Instructions burned: 3 (million)
% 0.15/0.39 % (1509)------------------------------
% 0.15/0.39 % (1509)------------------------------
% 0.15/0.39 % (1508)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 theBenchmark for (2999ds/15Mi)
% 0.15/0.39 % (1504)First to succeed.
% 0.21/0.39 % (1511)Instruction limit reached!
% 0.21/0.39 % (1511)------------------------------
% 0.21/0.39 % (1511)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (1511)Termination reason: Unknown
% 0.21/0.39 % (1511)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (1511)Memory used [KB]: 1023
% 0.21/0.39 % (1511)Time elapsed: 0.006 s
% 0.21/0.39 % (1511)Instructions burned: 8 (million)
% 0.21/0.39 % (1511)------------------------------
% 0.21/0.39 % (1511)------------------------------
% 0.21/0.39 % (1504)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (1504)------------------------------
% 0.21/0.39 % (1504)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (1504)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (1504)Memory used [KB]: 5628
% 0.21/0.39 % (1504)Time elapsed: 0.030 s
% 0.21/0.39 % (1504)Instructions burned: 28 (million)
% 0.21/0.39 % (1504)------------------------------
% 0.21/0.39 % (1504)------------------------------
% 0.21/0.39 % (1498)Success in time 0.048 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------