TSTP Solution File: NUN048^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN048^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Tue May 21 02:17:46 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 66 ( 12 unt; 21 typ; 0 def)
% Number of atoms : 582 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 12 avg)
% Number of connectives : 89 ( 25 ~; 29 |; 20 &; 0 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 51 ( 50 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 5 con; 0-6 aty)
% Number of variables : 104 ( 0 ^ 87 !; 9 ?; 104 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_2,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_3,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_4,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_5,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_6,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_7,type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_13,type,
sK1: 'type/nums/num' ).
thf(func_def_14,type,
sK2: 'type/nums/num' ).
thf(func_def_15,type,
sK3: 'type/nums/num' > 'type/nums/num' > ( 'type/nums/num' > 'type/nums/num' ) > 'type/nums/num' ).
thf(func_def_16,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_17,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f878,plain,
$false,
inference(trivial_inequality_removal,[],[f877]) ).
thf(f877,plain,
$true = $false,
inference(forward_demodulation,[],[f822,f430]) ).
thf(f430,plain,
$false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,sK2),sK1),sK0)),sK2),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f401,plain,
( ( $true = $false )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,sK2),sK1),sK0)),sK2) ) ),
inference(superposition,[],[f362,f160]) ).
thf(f160,plain,
! [X0: 'type/nums/num'] :
( ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),sK2) )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),X0) ) ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f119,plain,
! [X0: 'type/nums/num'] :
( ( $true = $false )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),sK2) )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),X0) ) ),
inference(superposition,[],[f106,f80]) ).
thf(f80,plain,
$false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
( ( $true = $false )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2) ) ),
inference(superposition,[],[f36,f26]) ).
thf(f26,plain,
$true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',sK2),sK1),
inference(cnf_transformation,[],[f23]) ).
thf(f23,plain,
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK1),sK2)),sK0) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',sK2),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f22]) ).
thf(f22,plain,
( ? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1) = $true ) )
=> ( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK1),sK2)),sK0) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',sK2),sK1) ) ) ),
introduced(choice_axiom,[]) ).
thf(f17,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1) = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1) = $true )
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1)
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1)
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X2),X1)
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_TRIV_NUMSEG_') ).
thf(f36,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = $false )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1) = $false ) ),
inference(not_proxy_clausification,[],[f35]) ).
thf(f35,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = $false )
| ( $true = vAPP($o,$o,vNOT,vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = vAPP($o,$o,vNOT,vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1)) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = vAPP($o,$o,vNOT,vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1)) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ~ vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1) = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ~ vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<',X0),X1) = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/NOT_LT_') ).
thf(f106,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $false )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) = $false ) ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f105,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true != $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $false )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) = $false ) ),
inference(superposition,[],[f100,f8]) ).
thf(f8,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f100,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true != vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X2),X0) )
| ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X2),X1) )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) = $false ) ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f99,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true != $true )
| ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X2),X1) )
| ( $true != vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X2),X0) )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) = $false ) ),
inference(superposition,[],[f30,f8]) ).
thf(f30,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) != $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) != $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) != $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) != $true ) ),
inference(flattening,[],[f18]) ).
thf(f18,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) != $true )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) != $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $true )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) = $true ) )
=> ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) = $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2)
& vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) )
=> vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2)
& vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) )
=> vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LE_TRANS_') ).
thf(f362,plain,
$true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,sK2),sK1),sK0)),
inference(unit_resulting_resolution,[],[f27,f31]) ).
thf(f31,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)) )
| ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) )
| ( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP('type/nums/num','type/nums/num',X0,vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)),X2) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f21,f24]) ).
thf(f24,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ? [X3: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num',X0,X3) != vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2) = $true )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) = $true ) )
=> ( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP('type/nums/num','type/nums/num',X0,vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)),X2) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f21,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) )
| ? [X3: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num',X0,X3) != vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2) = $true )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) = $true ) ) ),
inference(flattening,[],[f20]) ).
thf(f20,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) )
| ? [X3: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num',X0,X3) != vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2) = $true )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) = $true ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ! [X3: 'type/nums/num'] :
( ( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2) = $true )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) = $true ) )
=> ( vAPP('type/nums/num','type/nums/num',X0,X3) = vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') ) )
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ! [X3: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2)
& vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) )
=> ( vAPP('type/nums/num','type/nums/num',X0,X3) = vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') ) )
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ! [X3: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),X2)
& vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X3) )
=> ( vAPP('type/nums/num','type/nums/num',X0,X3) = vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') ) )
=> ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_NUMSEG_') ).
thf(f27,plain,
vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') != vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK1),sK2)),sK0),
inference(cnf_transformation,[],[f23]) ).
thf(f822,plain,
$true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,sK2),sK1),sK0)),sK2),
inference(unit_resulting_resolution,[],[f27,f32]) ).
thf(f32,plain,
! [X2: 'type/nums/num',X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num'] :
( ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num')),sK3,X2),X1),X0)),X2) )
| ( vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/nums/num'),'type/nums/num'),'const/iterate/nsum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X1),X2)),X0) ) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN048^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 15:14:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (6629)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (6632)WARNING: value z3 for option sas not known
% 0.21/0.37 % (6633)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (6631)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (6630)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (6636)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37 % (6634)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37 % (6635)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (6632)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (6636)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.37 % Exception at run slice level% Exception at run slice level% Exception at run slice level
% 0.21/0.37
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.37
% 0.21/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.39 % (6637)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.39 % (6638)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.39 % (6639)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.39 % (6637)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % (6638)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.39 % Exception at run slice level
% 0.21/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (6640)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.21/0.43 % (6638)First to succeed.
% 0.21/0.43 % (6638)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6629"
% 0.21/0.43 % (6638)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43 % (6638)------------------------------
% 0.21/0.43 % (6638)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43 % (6638)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (6638)Memory used [KB]: 898
% 0.21/0.43 % (6638)Time elapsed: 0.042 s
% 0.21/0.43 % (6638)Instructions burned: 93 (million)
% 0.21/0.43 % (6629)Success in time 0.065 s
%------------------------------------------------------------------------------