TSTP Solution File: ANA112^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA112^1 : 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 : Mon May 20 18:41:51 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 45 ( 13 unt; 21 typ; 0 def)
% Number of atoms : 590 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 24 avg)
% Number of connectives : 48 ( 27 ~; 14 |; 3 &; 0 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 80 ( 79 >; 1 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-6 aty)
% Number of variables : 102 ( 15 ^ 66 !; 10 ?; 102 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
'type/nums/num': $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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_4,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_8,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_9,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_10,type,
sK0: 'type/nums/num' ).
thf(func_def_11,type,
sK1: 'type/nums/num' ).
thf(func_def_12,type,
sK2: 'type/nums/num' ).
thf(func_def_13,type,
sK3: 'type/nums/num' ).
thf(func_def_14,type,
sK4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real' ).
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(f71,plain,
$false,
inference(trivial_inequality_removal,[],[f70]) ).
thf(f70,plain,
vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3))),sK4) != vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4),
inference(equality_resolution,[],[f69]) ).
thf(f69,plain,
! [X0: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4)) != vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,X0)) )
| ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3))),sK4) != vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),X0) ) ),
inference(subsumption_resolution,[],[f66,f19]) ).
thf(f19,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( $true = vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1)) ),
inference(cnf_transformation,[],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( $true = vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1)) ),
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: 'type/nums/num',X2: 'type/nums/num'] : vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(f66,plain,
! [X0: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( ( $true != vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1)) )
| ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4)) != vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,X0)) )
| ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3))),sK4) != vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),X0) ) ),
inference(equality_resolution,[],[f63]) ).
thf(f63,plain,
! [X0: $tType,X2: X0 > 'type/nums/num' > 'type/realax/real',X1: X0 > $o] :
( ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4)) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X1),vAPP(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),X2)) )
| ( $true != vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) )
| ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4)) != vAPP(sTfun('type/nums/num',sTfun(X0,'type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun(X0,'type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X1)),vAPP(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun(X0,'type/realax/real')),cCOMB,X2)) ) ),
inference(subsumption_resolution,[],[f61,f19]) ).
thf(f61,plain,
! [X0: $tType,X2: X0 > 'type/nums/num' > 'type/realax/real',X1: X0 > $o] :
( ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4)) != vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X1),vAPP(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),X2)) )
| ( $true != vAPP(sTfun('type/nums/num',$o),$o,'const/sets/FINITE'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3)) )
| ( $true != vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) )
| ( vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4)) != vAPP(sTfun('type/nums/num',sTfun(X0,'type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun(X0,'type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X1)),vAPP(sTfun(X0,sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun(X0,'type/realax/real')),cCOMB,X2)) ) ),
inference(constrained_superposition,[],[f18,f20]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4)),X2)) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3)),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X1,sTfun(X0,'type/realax/real')),cCOMB,X2))) )
| ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4)),X2)) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3)),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X1,sTfun(X0,'type/realax/real')),cCOMB,X2))) )
| ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true ) ),
inference(flattening,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4)),X2)) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3)),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X1,sTfun(X0,'type/realax/real')),cCOMB,X2))) )
| ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) != $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) = $true ) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real'),vAPP(sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X0,'type/realax/real')),bCOMB,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4)),X2)) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real'),vAPP(sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),sTfun(sTfun(X1,sTfun(X0,'type/realax/real')),sTfun(X1,'type/realax/real')),bCOMB,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3)),vAPP(sTfun(X0,sTfun(X1,'type/realax/real')),sTfun(X1,sTfun(X0,'type/realax/real')),cCOMB,X2))) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),
^ [X5: X0] : vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(X0,sTfun(X1,'type/realax/real'),X2,X5))) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),
^ [X6: X1] :
vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),
^ [X7: X0] : vAPP(X1,'type/realax/real',vAPP(X0,sTfun(X1,'type/realax/real'),X2,X7),X6))) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: $tType,X2: X0 > X1 > 'type/realax/real',X3: X0 > $o,X4: X1 > $o] :
( ( vAPP(sTfun(X1,$o),$o,'const/sets/FINITE'(X1),X4)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X3) )
=> ( vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),
^ [X5: X0] : vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),vAPP(X0,sTfun(X1,'type/realax/real'),X2,X5))) = vAPP(sTfun(X1,'type/realax/real'),'type/realax/real',vAPP(sTfun(X1,$o),sTfun(sTfun(X1,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X1),X4),
^ [X5: X1] :
vAPP(sTfun(X0,'type/realax/real'),'type/realax/real',vAPP(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real'),'const/iterate/sum'(X0),X3),
^ [X6: X0] : vAPP(X1,'type/realax/real',vAPP(X0,sTfun(X1,'type/realax/real'),X2,X6),X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SWAP_') ).
thf(f18,plain,
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4)) != vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4))),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4)) != vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X2),X3))),X4)) != vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,X4))) )
=> ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK0),sK1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK2),sK3))),sK4)) != vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',sK2),sK3)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',sK0),sK1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,sK4))) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
? [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X2),X3))),X4)) != vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,X4))) ),
inference(ennf_transformation,[],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X1)),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X2),X3))),X4)) = vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real'),vAPP(sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),sTfun(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num','type/realax/real')),bCOMB,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1))),vAPP(sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),sTfun('type/nums/num',sTfun('type/nums/num','type/realax/real')),cCOMB,X4))) ),
inference(fool_elimination,[],[f7]) ).
thf(f7,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X1)),
^ [X5: 'type/nums/num'] : vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X2),X3)),vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X4,X5))) = vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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)),
^ [X6: 'type/nums/num'] :
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X1)),
^ [X7: 'type/nums/num'] : vAPP('type/nums/num','type/realax/real',vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X4,X7),X6))) ),
inference(rectify,[],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num',X5: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X2)),
^ [X6: 'type/nums/num'] : vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X5,X6))) = vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',X3),X4)),
^ [X6: 'type/nums/num'] :
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X2)),
^ [X7: 'type/nums/num'] : vAPP('type/nums/num','type/realax/real',vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X5,X7),X6))) ),
inference(negated_conjecture,[],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num',X4: 'type/nums/num',X5: 'type/nums/num' > 'type/nums/num' > 'type/realax/real'] :
( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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),X2)),
^ [X6: 'type/nums/num'] : vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X5,X6))) = vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('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/..',X3),X4)),
^ [X6: 'type/nums/num'] :
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),'const/iterate/sum'('type/nums/num'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),X2)),
^ [X7: 'type/nums/num'] : vAPP('type/nums/num','type/realax/real',vAPP('type/nums/num',sTfun('type/nums/num','type/realax/real'),X5,X7),X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_SWAP_NUMSEG_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA112^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 07:45:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (22871)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (22874)WARNING: value z3 for option sas not known
% 0.14/0.37 % (22873)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (22872)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (22875)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (22874)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)
% 0.14/0.37 % (22876)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)
% 0.14/0.37 % (22877)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)
% 0.14/0.37 % (22878)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)
% 0.14/0.37 % Exception at run slice level% Exception at run slice level% Exception at run slice level
% 0.14/0.37
% 0.14/0.37 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
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.37 % (22878)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.37 % (22874)First to succeed.
% 0.14/0.37 % (22878)Also succeeded, but the first one will report.
% 0.14/0.38 % (22874)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22871"
% 0.14/0.38 % (22874)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (22874)------------------------------
% 0.14/0.38 % (22874)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (22874)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (22874)Memory used [KB]: 874
% 0.14/0.38 % (22874)Time elapsed: 0.011 s
% 0.14/0.38 % (22874)Instructions burned: 16 (million)
% 0.14/0.38 % (22871)Success in time 0.013 s
%------------------------------------------------------------------------------