TSTP Solution File: NUN051^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN051^1 : 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 : n020.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 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 48 ( 11 unt; 21 typ; 0 def)
% Number of atoms : 413 ( 40 equ; 0 cnn)
% Maximal formula atoms : 4 ( 15 avg)
% Number of connectives : 30 ( 11 ~; 7 |; 4 &; 0 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 49 ( 48 >; 1 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 5 con; 0-6 aty)
% Number of variables : 67 ( 4 ^ 47 !; 6 ?; 67 :)
% ( 10 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_2,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_3,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_5,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_7,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_11,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
sK0: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_14,type,
sK1: 'type/nums/num' ).
thf(func_def_15,type,
sK2: 'type/nums/num' ).
thf(func_def_16,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f153,plain,
$false,
inference(trivial_inequality_removal,[],[f151]) ).
thf(f151,plain,
$true = $false,
inference(superposition,[],[f17,f130]) ).
thf(f130,plain,
$false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2),
inference(unit_resulting_resolution,[],[f18,f72]) ).
thf(f72,plain,
! [X2: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X2),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X1))) = 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',$o)),'const/iterate/..',X1),X0)),X2) )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = $false ) ),
inference(superposition,[],[f58,f55]) ).
thf(f55,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X1),X0)),X0) = X1 )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f54,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true != $true )
| ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X1),X0)),X0) = X1 )
| ( $false = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X0),X1) ) ),
inference(superposition,[],[f20,f7]) ).
thf(f7,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f20,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) != $true )
| ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1)),X1) = X0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1)),X1) = X0 )
| ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) != $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0) = $true )
=> ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1)),X1) = X0 ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0)
=> ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1)),X1) = X0 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X0)
=> ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X0),X1)),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/SUB_ADD_') ).
thf(f58,plain,
! [X2: 'type/nums/num' > 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X1)),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X2),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X0))) = 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',$o)),'const/iterate/..',X0),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X1),X0))),X2) ),
inference(superposition,[],[f21,f19]) ).
thf(f19,plain,
! [X0: 'type/nums/num'] : ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X0) = X0 ),
inference(cnf_transformation,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num'] : ( vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/ADD_CLAUSES_0') ).
thf(f21,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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/..',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X2),X0)),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X0))),X1) = 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',$o)),'const/iterate/..',X2),X3)),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X1),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X0))) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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/..',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X2),X0)),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X0))),X1) = 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',$o)),'const/iterate/..',X2),X3)),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X1),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X0))) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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/..',vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X2),X0)),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X0))),X1) = 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',$o)),'const/iterate/..',X2),X3)),
^ [X4: 'type/nums/num'] : vAPP('type/nums/num','type/nums/num',X1,vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X4),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_OFFSET_') ).
thf(f18,plain,
vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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) != 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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',sK2),sK1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,sK0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),sK1))),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
( ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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) != 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/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',sK2),sK1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,sK0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),sK1))) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15]) ).
thf(f15,plain,
( ? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X1))) )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $true ) )
=> ( ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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) != 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/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',sK2),sK1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,sK0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),sK1))) )
& ( $true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X1))) )
& ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2) = $true )
=> ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num','type/nums/num'),sTfun(sTfun('type/nums/num','type/nums/num'),sTfun('type/nums/num','type/nums/num')),bCOMB,X0),vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),sTfun('type/nums/num',sTfun('type/nums/num','type/nums/num')),cCOMB,'const/arith/+'),X1))) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2)
=> ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),
^ [X3: 'type/nums/num'] : vAPP('type/nums/num','type/nums/num',X0,vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X1))) ) ),
inference(rectify,[],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2)
=> ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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',$o)),'const/iterate/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),
^ [X3: 'type/nums/num'] : vAPP('type/nums/num','type/nums/num',X0,vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X1))) ) ),
inference(negated_conjecture,[],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X1),X2)
=> ( vAPP(sTfun('type/nums/num','type/nums/num'),'type/nums/num',vAPP(sTfun('type/nums/num',$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(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/..',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/-',X2),X1))),
^ [X3: 'type/nums/num'] : vAPP('type/nums/num','type/nums/num',X0,vAPP('type/nums/num','type/nums/num',vAPP('type/nums/num',sTfun('type/nums/num','type/nums/num'),'const/arith/+',X3),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_OFFSET_0_') ).
thf(f17,plain,
$true = vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',sK1),sK2),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN051^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 15:07:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (11880)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (11883)WARNING: value z3 for option sas not known
% 0.13/0.37 % (11882)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (11884)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (11881)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (11885)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)
% 0.13/0.37 % (11886)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)
% 0.13/0.37 % (11883)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)
% 0.13/0.37 % (11887)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)
% 0.13/0.37 % (11887)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level% Exception at run slice level
% 0.13/0.37
% 0.13/0.37 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (11888)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.39 % (11889)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)
% 0.20/0.39 % (11890)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)
% 0.20/0.39 % (11888)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 % (11889)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (11887)First to succeed.
% 0.20/0.39 % (11887)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11880"
% 0.20/0.39 % (11887)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (11887)------------------------------
% 0.20/0.39 % (11887)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39 % (11887)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (11887)Memory used [KB]: 937
% 0.20/0.39 % (11887)Time elapsed: 0.022 s
% 0.20/0.39 % (11887)Instructions burned: 45 (million)
% 0.20/0.39 % (11880)Success in time 0.025 s
%------------------------------------------------------------------------------