TSTP Solution File: ANA110^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA110^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 : Sun May 5 04:32:26 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 50 ( 18 unt; 26 typ; 0 def)
% Number of atoms : 506 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 21 avg)
% Number of connectives : 19 ( 9 ~; 2 |; 4 &; 0 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 72 ( 71 >; 1 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 4 con; 0-6 aty)
% Number of variables : 58 ( 0 ^ 42 !; 4 ?; 58 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $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/realax/real_of_num': 'type/nums/num' > 'type/realax/real' ).
thf(func_def_3,type,
'const/realax/real_add': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_4,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_7,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_8,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_9,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_10,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_11,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_12,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_13,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_19,type,
sK1: 'type/nums/num' ).
thf(func_def_20,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_21,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_22,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(f66,plain,
$false,
inference(unit_resulting_resolution,[],[f18,f63]) ).
thf(f63,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] : ( vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X0)),vAPP('type/nums/num','type/realax/real',X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) = 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),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) ),
inference(forward_demodulation,[],[f62,f20]) ).
thf(f20,plain,
! [X0: $tType] : ( 'const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add') ),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: $tType] : ( 'const/iterate/sum'(X0) = vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,'type/realax/real'),'type/realax/real')),'const/iterate/iterate'(X0,'type/realax/real'),'const/realax/real_add') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f62,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real')),'const/iterate/iterate'('type/nums/num','type/realax/real'),'const/realax/real_add'),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','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X0)),vAPP('type/nums/num','type/realax/real',X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ),
inference(forward_demodulation,[],[f57,f19]) ).
thf(f19,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add') = vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),
inference(cnf_transformation,[],[f2]) ).
thf(f2,axiom,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add') = vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_REAL_ADD_') ).
thf(f57,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num','type/realax/real'),'type/realax/real')),'const/iterate/iterate'('type/nums/num','type/realax/real'),'const/realax/real_add'),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X0),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X0)),vAPP('type/nums/num','type/realax/real',X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'type/realax/real','const/iterate/neutral'('type/realax/real'),'const/realax/real_add')) ),
inference(unit_resulting_resolution,[],[f23,f21]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > X0 > X0,X1: 'type/nums/num' > X0,X5: 'type/nums/num'] :
( ( vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X2) != $true )
| ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X5),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X5)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X2)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),X2,vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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)),X1)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4)))),vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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)),X1)) )
& ! [X5: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X5),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X5)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X2)) ) )
| ( vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X2) != $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( ( vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X2) = $true )
=> ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),X2,vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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)),X1)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4)))),vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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)),X1)) )
& ! [X5: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X5),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X5)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X2)) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X2)
=> ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),X2,vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),X1)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4)))),vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),X1)) )
& ! [X5: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X5),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = X5),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X2)) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: 'type/nums/num' > X0,X2: X0 > X0 > X0] :
( vAPP(sTfun(X0,sTfun(X0,X0)),$o,'const/iterate/monoidal'(X0),X2)
=> ( ! [X3: 'type/nums/num',X4: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),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),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),'const/arith/<=',X3),vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),X2,vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),X1)),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/SUC',X4)))),vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),X4)),X1)) )
& ! [X3: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num',X0),X0,vAPP(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(sTfun('type/nums/num',$o),sTfun(sTfun('type/nums/num',X0),X0)),'const/iterate/iterate'('type/nums/num',X0),X2),vAPP('type/nums/num',sTfun('type/nums/num',$o),vAPP('type/nums/num',sTfun('type/nums/num',sTfun('type/nums/num',$o)),'const/iterate/..',X3),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP($o,sTfun(X0,sTfun(X0,X0)),'const/class/COND'(X0),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = X3),vAPP('type/nums/num',X0,X1,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP(sTfun(X0,sTfun(X0,X0)),X0,'const/iterate/neutral'(X0),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_NUMSEG_') ).
thf(f23,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add') = $true,
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add'),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),$o,'const/iterate/monoidal'('type/realax/real'),'const/realax/real_add'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f18,plain,
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',sK1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),sK0) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),sK1)),vAPP('type/nums/num','type/realax/real',sK0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',sK1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),sK0) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),sK1)),vAPP('type/nums/num','type/realax/real',sK0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f16]) ).
thf(f16,plain,
( ? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',X1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X0) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X1)),vAPP('type/nums/num','type/realax/real',X0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) )
=> ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',sK1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),sK0) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),sK1)),vAPP('type/nums/num','type/realax/real',sK0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',X1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X0) != vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X1)),vAPP('type/nums/num','type/realax/real',X0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ),
inference(ennf_transformation,[],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',X1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X0) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num',$o,vAPP('type/nums/num',sTfun('type/nums/num',$o),vEQ('type/nums/num'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0')),X1)),vAPP('type/nums/num','type/realax/real',X0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ),
inference(fool_elimination,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',X1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X0) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = X1),vAPP('type/nums/num','type/realax/real',X0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] : ( vAPP(sTfun('type/nums/num','type/realax/real'),'type/realax/real',vAPP(sTfun('type/nums/num',$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/..',X1),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),X0) = vAPP('type/realax/real','type/realax/real',vAPP('type/realax/real',sTfun('type/realax/real','type/realax/real'),vAPP($o,sTfun('type/realax/real',sTfun('type/realax/real','type/realax/real')),'const/class/COND'('type/realax/real'),vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0') = X1),vAPP('type/nums/num','type/realax/real',X0,vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))),vAPP('type/nums/num','type/realax/real','const/realax/real_of_num',vAPP('type/nums/num','type/nums/num','const/nums/NUMERAL','const/nums/_0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_CLAUSES_NUMSEG_0') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ANA110^1 : TPTP v8.1.2. Released v7.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 15:32:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (22997)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (23000)WARNING: value z3 for option sas not known
% 0.14/0.38 % (22998)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (22999)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (23001)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (23000)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)
% 0.14/0.38 % (23002)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)
% 0.14/0.38 % (23003)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)
% 0.14/0.38 % (23004)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)
% 0.14/0.38 % Exception at run slice level% Exception at run slice level
% 0.14/0.38
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38 % (23004)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % (23004)First to succeed.
% 0.14/0.39 % (23004)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22997"
% 0.14/0.39 % (23004)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (23004)------------------------------
% 0.14/0.39 % (23004)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (23004)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (23004)Memory used [KB]: 793
% 0.14/0.39 % (23004)Time elapsed: 0.008 s
% 0.14/0.39 % (23004)Instructions burned: 12 (million)
% 0.14/0.39 % (22997)Success in time 0.024 s
%------------------------------------------------------------------------------