TSTP Solution File: ANA091^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ANA091^1 : 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 : n028.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 18:40:27 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 76 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 576 ( 170 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 753 ( 86 ~; 76 |; 48 &; 508 @)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-3 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 157 ( 5 ^ 123 !; 25 ?; 157 :)
% ( 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_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_18,type,
sK5: 'type/realax/real' ).
thf(func_def_20,type,
sK7:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
ph8:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK9: 'type/realax/real' ).
thf(f136,plain,
$false,
inference(avatar_sat_refutation,[],[f110,f131,f135]) ).
thf(f135,plain,
( spl6_5
| ~ spl6_6 ),
inference(avatar_split_clause,[],[f134,f108,f105]) ).
thf(f105,plain,
( spl6_5
<=> ! [X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
thf(f108,plain,
( spl6_6
<=> ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
thf(f134,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) )
| ~ spl6_6 ),
inference(subsumption_resolution,[],[f133,f52]) ).
thf(f52,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f49,plain,
( ( $true = $false )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
inference(superposition,[],[f44,f36]) ).
thf(f36,plain,
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
& ( $true
= ( 'const/realax/real_le' @ sK5 @ sK4 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) )
& ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK3 @ X4 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f16,f25]) ).
thf(f25,plain,
( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) ) )
=> ( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
& ( $true
= ( 'const/realax/real_le' @ sK5 @ sK4 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) )
& ! [X4: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sK3 @ X4 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
!= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
= $true )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
!= $true ) )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) ),
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 )
& ! [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ X4 )
= $true ) )
& ( ( 'const/realax/real_le' @ X3 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X2 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X2 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X3 @ X2 )
& ! [X4: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X4 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_') ).
thf(f44,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f43,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $false )
| ( ( ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
@ X2 )
= $false ) ),
inference(pi_clausification,[],[f41]) ).
thf(f41,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= $false )
| ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f40,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) )
| ( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= $false ) ),
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,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
= ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] :
? [X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(f133,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f132,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( $true != $true ) )
| ~ spl6_6 ),
inference(superposition,[],[f27,f109]) ).
thf(f109,plain,
( ! [X0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f27,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o] :
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) )
| ( ! [X3: 'type/realax/real'] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) )
!= $true ) )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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' @ X1 @ X2 )
!= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o,X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 )
= $true )
& ( ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) )
!= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f21,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 ) )
| ( ! [X3: 'type/realax/real'] :
( ? [X4: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X3 @ X4 ) ) )
| ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
= $true ) )
& ! [X5: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,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 ) )
| ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( $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(flattening,[],[f19]) ).
thf(f19,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X4: 'type/realax/real'] :
( ? [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
& ( $true
!= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
| ( $true
= ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
& ! [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
!= $true ) ) )
| ! [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,[],[f12]) ).
thf(f12,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 ) ) )
=> ( ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
= $true )
=> ( $true
= ( 'const/realax/real_le' @ X4 @ X5 ) ) )
=> ( $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 ) ) ) ) ),
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'] :
( ( '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,[],[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'] :
( ( '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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(f131,plain,
~ spl6_5,
inference(avatar_contradiction_clause,[],[f130]) ).
thf(f130,plain,
( $false
| ~ spl6_5 ),
inference(subsumption_resolution,[],[f127,f37]) ).
thf(f37,plain,
( $true
= ( 'const/realax/real_le' @ sK5 @ sK4 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f127,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK5 @ sK4 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK5 @ sK4 ) )
| ( $true != $true )
| ~ spl6_5 ),
inference(superposition,[],[f120,f36]) ).
thf(f120,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
| ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
| ~ spl6_5 ),
inference(superposition,[],[f90,f106]) ).
thf(f106,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f105]) ).
thf(f90,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
| ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f89,plain,
! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ sK4 )
!= $true )
| ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) ),
inference(superposition,[],[f38,f33]) ).
thf(f33,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,[],[f18]) ).
thf(f18,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(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' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f14,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,[],[f13]) ).
thf(f13,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/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f38,plain,
( $true
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f110,plain,
( spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f103,f108,f105]) ).
thf(f103,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true ) ),
inference(subsumption_resolution,[],[f102,f52]) ).
thf(f102,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f100,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
| ( $true != $true )
| ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
= $true ) ),
inference(superposition,[],[f35,f30]) ).
thf(f30,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f35,plain,
! [X4: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) )
| ( $true
= ( 'const/realax/real_le' @ sK3 @ X4 ) ) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA091^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 07:46:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 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
% 0.15/0.37 % (4163)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (4157)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (4161)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)
% 0.15/0.38 % (4158)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)
% 0.15/0.38 % (4160)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (4159)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)
% 0.15/0.38 % (4162)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)
% 0.15/0.38 % (4164)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)
% 0.15/0.38 % (4160)Instruction limit reached!
% 0.15/0.38 % (4160)------------------------------
% 0.15/0.38 % (4160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (4160)Termination reason: Unknown
% 0.15/0.38 % (4161)Instruction limit reached!
% 0.15/0.38 % (4161)------------------------------
% 0.15/0.38 % (4161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (4161)Termination reason: Unknown
% 0.15/0.38 % (4161)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (4161)Memory used [KB]: 895
% 0.15/0.38 % (4161)Time elapsed: 0.004 s
% 0.15/0.38 % (4161)Instructions burned: 3 (million)
% 0.15/0.38 % (4161)------------------------------
% 0.15/0.38 % (4161)------------------------------
% 0.15/0.38 % (4160)Termination phase: Unused predicate definition removal
% 0.15/0.38
% 0.15/0.38 % (4160)Memory used [KB]: 895
% 0.15/0.38 % (4160)Time elapsed: 0.004 s
% 0.15/0.38 % (4160)Instructions burned: 2 (million)
% 0.15/0.38 % (4160)------------------------------
% 0.15/0.38 % (4160)------------------------------
% 0.15/0.38 % (4164)Instruction limit reached!
% 0.15/0.38 % (4164)------------------------------
% 0.15/0.38 % (4164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (4164)Termination reason: Unknown
% 0.15/0.38 % (4164)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (4164)Memory used [KB]: 895
% 0.15/0.38 % (4164)Time elapsed: 0.005 s
% 0.15/0.38 % (4164)Instructions burned: 3 (million)
% 0.15/0.38 % (4164)------------------------------
% 0.15/0.38 % (4164)------------------------------
% 0.15/0.38 % (4157)First to succeed.
% 0.15/0.38 % (4158)Instruction limit reached!
% 0.15/0.38 % (4158)------------------------------
% 0.15/0.38 % (4158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (4158)Termination reason: Unknown
% 0.15/0.38 % (4158)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (4158)Memory used [KB]: 5500
% 0.15/0.38 % (4158)Time elapsed: 0.007 s
% 0.15/0.38 % (4158)Instructions burned: 5 (million)
% 0.15/0.38 % (4158)------------------------------
% 0.15/0.38 % (4158)------------------------------
% 0.15/0.38 % (4163)Instruction limit reached!
% 0.15/0.38 % (4163)------------------------------
% 0.15/0.38 % (4163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (4163)Termination reason: Unknown
% 0.15/0.39 % (4163)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (4163)Memory used [KB]: 5628
% 0.15/0.39 % (4163)Time elapsed: 0.017 s
% 0.15/0.39 % (4163)Instructions burned: 18 (million)
% 0.15/0.39 % (4163)------------------------------
% 0.15/0.39 % (4163)------------------------------
% 0.15/0.39 % (4157)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (4157)------------------------------
% 0.15/0.39 % (4157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (4157)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (4157)Memory used [KB]: 5628
% 0.15/0.39 % (4157)Time elapsed: 0.017 s
% 0.15/0.39 % (4157)Instructions burned: 16 (million)
% 0.15/0.39 % (4157)------------------------------
% 0.15/0.39 % (4157)------------------------------
% 0.15/0.39 % (4156)Success in time 0.03 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------