TSTP Solution File: ANA076^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA076^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.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 18:40:23 EDT 2024
% Result : Theorem 0.20s 0.40s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 116 ( 5 unt; 14 typ; 0 def)
% Number of atoms : 981 ( 269 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 1220 ( 153 ~; 178 |; 52 &; 796 @)
% ( 8 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 14 con; 0-3 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 5 ^ 161 !; 22 ?; 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/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_13,type,
sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_14,type,
sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_15,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_16,type,
sK3: 'type/realax/real' ).
thf(func_def_17,type,
sK4: 'type/realax/real' ).
thf(func_def_19,type,
sK6:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_20,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK8: 'type/realax/real' ).
thf(f342,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f121,f162,f172,f199,f210,f218,f261,f292,f315,f341]) ).
thf(f341,plain,
( spl5_14
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f337,f313,f197]) ).
thf(f197,plain,
( spl5_14
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
thf(f313,plain,
( spl5_18
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
thf(f337,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) ) )
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f336,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( $true != $true ) )
| ~ spl5_18 ),
inference(superposition,[],[f37,f314]) ).
thf(f314,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) )
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f37,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ X3 @ sK4 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( $true
= ( 'const/realax/real_le' @ sK3 @ X3 ) )
& ( $true
= ( 'const/realax/real_le' @ X3 @ sK4 ) ) ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK2 ) )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != 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'] :
( ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( ( $true
= ( 'const/realax/real_le' @ sK3 @ X3 ) )
& ( $true
= ( 'const/realax/real_le' @ X3 @ sK4 ) ) ) )
& ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK2 ) )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f18,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' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
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/sup' @ X0 ) @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( ( 'const/realax/real_le' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,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' @ X1 @ X3 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
& ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,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' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ 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' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ 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' @ X1 @ X3 )
& ( 'const/realax/real_le' @ X3 @ X2 ) ) ) )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
& ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_BOUNDS_') ).
thf(f315,plain,
( spl5_18
| spl5_8 ),
inference(avatar_split_clause,[],[f311,f119,f313]) ).
thf(f119,plain,
( spl5_8
<=> ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
thf(f311,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) ),
inference(subsumption_resolution,[],[f310,f35]) ).
thf(f35,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(cnf_transformation,[],[f26]) ).
thf(f310,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f308,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) ) ),
inference(superposition,[],[f37,f32]) ).
thf(f32,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/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 ) )
& ( $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,X1: 'type/realax/real'] :
( ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
& ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f21,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ! [X4: 'type/realax/real'] :
? [X5: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) )
| ? [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
& ( ( 'const/realax/real_le' @ X5 @ X4 )
!= $true ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) )
| ! [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ 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'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) )
=> ( ( 'const/realax/real_le' @ X5 @ X4 )
= $true ) )
=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) )
& ! [X3: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,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' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X5 @ X4 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ),
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' @ X2 @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_') ).
thf(f292,plain,
( spl5_2
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f291,plain,
( $false
| spl5_2
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f280,f35]) ).
thf(f280,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| spl5_2
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f279,plain,
( ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| spl5_2
| ~ spl5_7 ),
inference(superposition,[],[f273,f48]) ).
thf(f48,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f47]) ).
thf(f47,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
= $true )
| ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f46]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $true )
| ( ( ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
@ ( sK6 @ X0 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[],[f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) )
| ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f39]) ).
thf(f39,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $false
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) )
| ( $true
= ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f34]) ).
thf(f34,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
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/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f273,plain,
( ! [X0: 'type/realax/real'] :
( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| spl5_2
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f270,f38]) ).
thf(f38,plain,
! [X3: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ X3 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f270,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ X0 )
!= $true ) )
| spl5_2
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f268,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ X0 )
!= $true )
| ( $true != $true ) )
| spl5_2
| ~ spl5_7 ),
inference(superposition,[],[f265,f117]) ).
thf(f117,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f116,plain,
( spl5_7
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
thf(f265,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ sK3 @ X0 )
!= $true ) )
| spl5_2 ),
inference(trivial_inequality_removal,[],[f263]) ).
thf(f263,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) ) )
| ( ( 'const/realax/real_le' @ sK3 @ X0 )
!= $true ) )
| spl5_2 ),
inference(superposition,[],[f56,f27]) ).
thf(f27,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: '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(cnf_transformation,[],[f20]) ).
thf(f20,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,[],[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,[],[f12]) ).
thf(f12,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,[],[f11]) ).
thf(f11,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/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f56,plain,
( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK2 ) )
!= $true )
| spl5_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f54,plain,
( spl5_2
<=> ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
thf(f261,plain,
( spl5_1
| ~ spl5_10
| ~ spl5_14 ),
inference(avatar_split_clause,[],[f258,f197,f160,f50]) ).
thf(f50,plain,
( spl5_1
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
thf(f160,plain,
( spl5_10
<=> ! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ sK2 ) @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
thf(f258,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ~ spl5_10
| ~ spl5_14 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f257,plain,
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ~ spl5_10
| ~ spl5_14 ),
inference(duplicate_literal_removal,[],[f256]) ).
thf(f256,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ( $true != $true )
| ~ spl5_10
| ~ spl5_14 ),
inference(superposition,[],[f161,f198]) ).
thf(f198,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true ) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f161,plain,
( ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ sK2 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f218,plain,
( spl5_7
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f217,f119,f116]) ).
thf(f217,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f170,f35]) ).
thf(f170,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f166,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK2 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl5_8 ),
inference(superposition,[],[f29,f120]) ).
thf(f120,plain,
( ! [X0: 'type/realax/real'] :
( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f29,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f210,plain,
( ~ spl5_8
| ~ spl5_13 ),
inference(avatar_contradiction_clause,[],[f209]) ).
thf(f209,plain,
( $false
| ~ spl5_8
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f207,plain,
( ( $true != $true )
| ~ spl5_8
| ~ spl5_13 ),
inference(superposition,[],[f195,f120]) ).
thf(f195,plain,
( ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK1 @ X1 @ sK2 ) @ X1 )
!= $true )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f194,plain,
( spl5_13
<=> ! [X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ ( sK1 @ X1 @ sK2 ) @ X1 )
!= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
thf(f199,plain,
( spl5_13
| spl5_14 ),
inference(avatar_split_clause,[],[f192,f197,f194]) ).
thf(f192,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK1 @ X1 @ sK2 ) @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true ) ),
inference(subsumption_resolution,[],[f191,f35]) ).
thf(f191,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ ( sK1 @ X1 @ sK2 ) @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f189,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK1 @ X1 @ sK2 ) @ X1 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ sK4 ) )
| ( $true != $true ) ),
inference(superposition,[],[f37,f33]) ).
thf(f33,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f172,plain,
( spl5_10
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f171,f119,f160]) ).
thf(f171,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ X0 )
!= $true ) )
| ~ spl5_8 ),
inference(subsumption_resolution,[],[f168,f35]) ).
thf(f168,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f165,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ ( sK0 @ X0 @ sK2 ) @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true != $true ) )
| ~ spl5_8 ),
inference(superposition,[],[f31,f120]) ).
thf(f31,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( sK1 @ X4 @ X0 ) @ X4 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f162,plain,
( spl5_8
| spl5_10 ),
inference(avatar_split_clause,[],[f158,f160,f119]) ).
thf(f158,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ sK2 ) @ X1 ) ) ),
inference(subsumption_resolution,[],[f157,f35]) ).
thf(f157,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ sK2 ) @ X1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f153,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ sK2 ) @ X1 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ X1 ) ) ),
inference(superposition,[],[f37,f30]) ).
thf(f30,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/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ ( sK0 @ X1 @ X0 ) @ X1 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f121,plain,
( spl5_7
| spl5_8 ),
inference(avatar_split_clause,[],[f114,f119,f116]) ).
thf(f114,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK2 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) ) ),
inference(subsumption_resolution,[],[f113,f35]) ).
thf(f113,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f111,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( sK1 @ X0 @ sK2 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
inference(superposition,[],[f37,f28]) ).
thf(f28,plain,
! [X3: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f57,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f36,f54,f50]) ).
thf(f36,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/sup' @ sK2 ) @ sK4 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/sup' @ sK2 ) )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ANA076^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 07:59:37 EDT 2024
% 0.20/0.34 % CPUTime :
% 0.20/0.34 This is a TH1_THM_EQU_NAR problem
% 0.20/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.36 % (13254)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)
% 0.20/0.36 % (13259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.36 % (13253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.36 % (13257)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)
% 0.20/0.37 % (13254)Instruction limit reached!
% 0.20/0.37 % (13254)------------------------------
% 0.20/0.37 % (13254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (13254)Termination reason: Unknown
% 0.20/0.37 % (13254)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (13254)Memory used [KB]: 5500
% 0.20/0.37 % (13254)Time elapsed: 0.005 s
% 0.20/0.37 % (13254)Instructions burned: 5 (million)
% 0.20/0.37 % (13254)------------------------------
% 0.20/0.37 % (13254)------------------------------
% 0.20/0.37 % (13257)Instruction limit reached!
% 0.20/0.37 % (13257)------------------------------
% 0.20/0.37 % (13257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (13257)Termination reason: Unknown
% 0.20/0.37 % (13257)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (13257)Memory used [KB]: 895
% 0.20/0.37 % (13257)Time elapsed: 0.003 s
% 0.20/0.37 % (13257)Instructions burned: 3 (million)
% 0.20/0.37 % (13257)------------------------------
% 0.20/0.37 % (13257)------------------------------
% 0.20/0.37 % (13260)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)
% 0.20/0.37 % (13260)Instruction limit reached!
% 0.20/0.37 % (13260)------------------------------
% 0.20/0.37 % (13260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (13260)Termination reason: Unknown
% 0.20/0.37 % (13260)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (13260)Memory used [KB]: 5500
% 0.20/0.37 % (13260)Time elapsed: 0.003 s
% 0.20/0.37 % (13260)Instructions burned: 3 (million)
% 0.20/0.37 % (13260)------------------------------
% 0.20/0.37 % (13260)------------------------------
% 0.20/0.37 % (13255)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)
% 0.20/0.37 % (13256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (13258)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)
% 0.20/0.38 % (13259)Instruction limit reached!
% 0.20/0.38 % (13259)------------------------------
% 0.20/0.38 % (13259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13259)Termination reason: Unknown
% 0.20/0.38 % (13259)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (13259)Memory used [KB]: 5628
% 0.20/0.38 % (13259)Time elapsed: 0.015 s
% 0.20/0.38 % (13259)Instructions burned: 19 (million)
% 0.20/0.38 % (13259)------------------------------
% 0.20/0.38 % (13259)------------------------------
% 0.20/0.38 % (13256)Instruction limit reached!
% 0.20/0.38 % (13256)------------------------------
% 0.20/0.38 % (13256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (13256)Termination reason: Unknown
% 0.20/0.38 % (13256)Termination phase: Preprocessing 3
% 0.20/0.38
% 0.20/0.38 % (13256)Memory used [KB]: 895
% 0.20/0.38 % (13256)Time elapsed: 0.003 s
% 0.20/0.38 % (13256)Instructions burned: 2 (million)
% 0.20/0.38 % (13256)------------------------------
% 0.20/0.38 % (13256)------------------------------
% 0.20/0.38 % (13261)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)
% 0.20/0.38 % (13262)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)
% 0.20/0.39 % (13255)Instruction limit reached!
% 0.20/0.39 % (13255)------------------------------
% 0.20/0.39 % (13255)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (13255)Termination reason: Unknown
% 0.20/0.39 % (13255)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (13255)Memory used [KB]: 5756
% 0.20/0.39 % (13255)Time elapsed: 0.017 s
% 0.20/0.39 % (13255)Instructions burned: 28 (million)
% 0.20/0.39 % (13255)------------------------------
% 0.20/0.39 % (13255)------------------------------
% 0.20/0.39 % (13264)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 theBenchmark for (2999ds/1041Mi)
% 0.20/0.39 % (13265)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.39 % (13262)Instruction limit reached!
% 0.20/0.39 % (13262)------------------------------
% 0.20/0.39 % (13262)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (13262)Termination reason: Unknown
% 0.20/0.39 % (13262)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (13262)Memory used [KB]: 5628
% 0.20/0.39 % (13262)Time elapsed: 0.010 s
% 0.20/0.39 % (13262)Instructions burned: 15 (million)
% 0.20/0.39 % (13262)------------------------------
% 0.20/0.39 % (13262)------------------------------
% 0.20/0.39 % (13253)First to succeed.
% 0.20/0.40 % (13263)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)
% 0.20/0.40 % (13265)Instruction limit reached!
% 0.20/0.40 % (13265)------------------------------
% 0.20/0.40 % (13265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (13258)Also succeeded, but the first one will report.
% 0.20/0.40 % (13265)Termination reason: Unknown
% 0.20/0.40 % (13265)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (13265)Memory used [KB]: 1023
% 0.20/0.40 % (13265)Time elapsed: 0.007 s
% 0.20/0.40 % (13265)Instructions burned: 8 (million)
% 0.20/0.40 % (13265)------------------------------
% 0.20/0.40 % (13265)------------------------------
% 0.20/0.40 % (13253)Refutation found. Thanks to Tanya!
% 0.20/0.40 % SZS status Theorem for theBenchmark
% 0.20/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40 % (13253)------------------------------
% 0.20/0.40 % (13253)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (13253)Termination reason: Refutation
% 0.20/0.40
% 0.20/0.40 % (13253)Memory used [KB]: 5884
% 0.20/0.40 % (13253)Time elapsed: 0.033 s
% 0.20/0.40 % (13253)Instructions burned: 51 (million)
% 0.20/0.40 % (13253)------------------------------
% 0.20/0.40 % (13253)------------------------------
% 0.20/0.40 % (13252)Success in time 0.045 s
% 0.20/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------