TSTP Solution File: SEV514^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV514^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% 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 Jun 24 16:04:12 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 317 ( 88 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 625 ( 48 ~; 35 |; 20 &; 505 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 0 ^ 72 !; 11 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'type/nums/num': $tType ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_7,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_8,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_9,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_13,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > X0 ) ).
thf(func_def_14,type,
sK1: 'type/nums/num' ).
thf(func_def_15,type,
sK2: 'type/nums/num' ).
thf(func_def_16,type,
sK3: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_18,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f39,plain,
$false,
inference(subsumption_resolution,[],[f38,f34]) ).
thf(f34,plain,
( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
= $true ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f32,plain,
( ( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f24,f31]) ).
thf(f31,plain,
( ( 'const/sets/IN' @ 'type/nums/num' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/..' @ sK1 @ sK2 ) )
= $true ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f30,plain,
( ( ( 'const/sets/IN' @ 'type/nums/num' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ ( 'const/iterate/..' @ sK1 @ sK2 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f27,f21]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= $true )
| ( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ ( sK0 @ X0 @ X2 @ X1 ) ) )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ? [X3: X0] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ X3 ) )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
=> ( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ ( sK0 @ X0 @ X2 @ X1 ) ) )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= $true )
| ? [X3: X0] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ X3 ) )
!= $true )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ! [X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ X3 ) )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o] :
( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_') ).
thf(f27,plain,
( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true )
& ! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( sK3 @ X3 ) )
= $true )
| ( $true
!= ( 'const/arith/<=' @ sK1 @ X3 ) )
| ( ( 'const/arith/<=' @ X3 @ sK2 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f19]) ).
thf(f19,plain,
( ? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) )
!= $true )
& ! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) )
= $true )
| ( ( 'const/arith/<=' @ X0 @ X3 )
!= $true )
| ( ( 'const/arith/<=' @ X3 @ X1 )
!= $true ) ) )
=> ( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true )
& ! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( sK3 @ X3 ) )
= $true )
| ( $true
!= ( 'const/arith/<=' @ sK1 @ X3 ) )
| ( ( 'const/arith/<=' @ X3 @ sK2 )
!= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) )
!= $true )
& ! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) )
= $true )
| ( ( 'const/arith/<=' @ X0 @ X3 )
!= $true )
| ( ( 'const/arith/<=' @ X3 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f12]) ).
thf(f12,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) )
!= $true )
& ! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) )
= $true )
| ( ( 'const/arith/<=' @ X3 @ X1 )
!= $true )
| ( ( 'const/arith/<=' @ X0 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ! [X3: 'type/nums/num'] :
( ( ( ( 'const/arith/<=' @ X3 @ X1 )
= $true )
& ( ( 'const/arith/<=' @ X0 @ X3 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) )
= $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ! [X3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X3 @ X1 )
& ( 'const/arith/<=' @ X0 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ! [X3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X3 @ X1 )
& ( 'const/arith/<=' @ X0 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) ) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real'] :
( ! [X3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X3 @ X1 )
& ( 'const/arith/<=' @ X0 @ X3 ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X2 @ X3 ) ) )
=> ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_NUMSEG_') ).
thf(f24,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
!= $true )
| ( ( 'const/arith/<=' @ X0 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( ( ( 'const/arith/<=' @ X2 @ X1 )
= $true )
& ( ( 'const/arith/<=' @ X0 @ X2 )
= $true ) )
| ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
!= $true ) )
& ( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true )
| ( ( 'const/arith/<=' @ X2 @ X1 )
!= $true )
| ( ( 'const/arith/<=' @ X0 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f17]) ).
thf(f17,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( ( ( 'const/arith/<=' @ X2 @ X1 )
= $true )
& ( ( 'const/arith/<=' @ X0 @ X2 )
= $true ) )
| ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
!= $true ) )
& ( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true )
| ( ( 'const/arith/<=' @ X2 @ X1 )
!= $true )
| ( ( 'const/arith/<=' @ X0 @ X2 )
!= $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( ( 'const/arith/<=' @ X2 @ X1 )
= $true )
& ( ( 'const/arith/<=' @ X0 @ X2 )
= $true ) )
<=> ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X2 )
& ( ( 'const/arith/<=' @ X2 @ X1 )
= ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X0 @ X2 )
& ( ( 'const/arith/<=' @ X2 @ X1 )
= ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/IN_NUMSEG_') ).
thf(f38,plain,
( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true ),
inference(subsumption_resolution,[],[f37,f35]) ).
thf(f35,plain,
( ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| ( ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ sK2 )
= $true ) ),
inference(superposition,[],[f25,f31]) ).
thf(f25,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
!= $true )
| ( ( 'const/arith/<=' @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f37,plain,
( ( ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ sK2 )
!= $true )
| ( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f36,plain,
( ( ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) @ sK2 )
!= $true )
| ( $true != $true )
| ( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK3 ) )
!= $true ) ),
inference(superposition,[],[f27,f29]) ).
thf(f29,plain,
! [X0: 'type/nums/num' > $o] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ X0 @ sK3 ) ) )
| ( $true
!= ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ X0 @ sK3 ) @ sK2 ) )
| ( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ X0 @ sK3 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f28,plain,
! [X0: 'type/nums/num' > $o] :
( ( ( 'const/arith/<=' @ sK1 @ ( sK0 @ 'type/nums/num' @ X0 @ sK3 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ X0 @ sK3 ) ) )
| ( $true != $true )
| ( $true
!= ( 'const/arith/<=' @ ( sK0 @ 'type/nums/num' @ X0 @ sK3 ) @ sK2 ) ) ),
inference(superposition,[],[f22,f26]) ).
thf(f26,plain,
! [X3: 'type/nums/num'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( sK3 @ X3 ) )
= $true )
| ( ( 'const/arith/<=' @ X3 @ sK2 )
!= $true )
| ( $true
!= ( 'const/arith/<=' @ sK1 @ X3 ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( X1 @ ( sK0 @ X0 @ X2 @ X1 ) ) )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/realax/real_of_num' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV514^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:32:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH1_THM_EQU_NAR problem
% 0.20/0.35 Running higher-order theorem proving
% 0.20/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.37 % (12693)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (12692)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 % (12690)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (12694)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 % (12695)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)
% 0.20/0.37 % (12696)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (12691)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)
% 0.20/0.37 % (12693)Instruction limit reached!
% 0.20/0.37 % (12693)------------------------------
% 0.20/0.37 % (12693)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (12693)Termination reason: Unknown
% 0.20/0.37 % (12694)Instruction limit reached!
% 0.20/0.37 % (12694)------------------------------
% 0.20/0.37 % (12694)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (12694)Termination reason: Unknown
% 0.20/0.37 % (12694)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (12694)Memory used [KB]: 1023
% 0.20/0.37 % (12694)Time elapsed: 0.004 s
% 0.20/0.37 % (12694)Instructions burned: 2 (million)
% 0.20/0.37 % (12694)------------------------------
% 0.20/0.37 % (12694)------------------------------
% 0.20/0.37 % (12693)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (12693)Memory used [KB]: 5500
% 0.20/0.37 % (12693)Time elapsed: 0.004 s
% 0.20/0.37 % (12693)Instructions burned: 2 (million)
% 0.20/0.37 % (12693)------------------------------
% 0.20/0.37 % (12693)------------------------------
% 0.20/0.37 % (12691)Instruction limit reached!
% 0.20/0.37 % (12691)------------------------------
% 0.20/0.37 % (12691)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (12691)Termination reason: Unknown
% 0.20/0.37 % (12691)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (12691)Memory used [KB]: 5500
% 0.20/0.37 % (12691)Time elapsed: 0.005 s
% 0.20/0.37 % (12691)Instructions burned: 4 (million)
% 0.20/0.37 % (12691)------------------------------
% 0.20/0.37 % (12691)------------------------------
% 0.20/0.37 % (12695)First to succeed.
% 0.20/0.38 % (12695)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (12695)------------------------------
% 0.20/0.38 % (12695)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (12695)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (12695)Memory used [KB]: 5500
% 0.20/0.38 % (12695)Time elapsed: 0.008 s
% 0.20/0.38 % (12695)Instructions burned: 5 (million)
% 0.20/0.38 % (12695)------------------------------
% 0.20/0.38 % (12695)------------------------------
% 0.20/0.38 % (12689)Success in time 0.021 s
%------------------------------------------------------------------------------