TSTP Solution File: ANA068^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA068^1 : 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 : n003.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 18:41:44 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of formulae : 61 ( 25 unt; 21 typ; 0 def)
% Number of atoms : 346 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 48 ( 25 ~; 17 |; 3 &; 0 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 75 ( 74 >; 1 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 2 con; 0-6 aty)
% Number of variables : 76 ( 2 ^ 52 !; 2 ?; 76 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/INFINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_6,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_13,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_14,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_15,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f126,plain,
$false,
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
$true = $false,
inference(superposition,[],[f82,f84]) ).
thf(f84,plain,
! [X0: 'type/realax/real'] : ( $false = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o),vAPP(sTfun(sTfun('type/realax/real',$o),$o),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o)),bCOMB,vSIGMA('type/realax/real')),vAPP(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o)),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o))),cCOMB,vAPP(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),vAPP(sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o)))),bCOMB,sCOMB),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o)))),cCOMB,vAPP(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),vAPP(sTfun(sTfun($o,sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o))))),bCOMB,bCOMB),'const/sets/SETSPEC'('type/realax/real'))),vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0)))),iCOMB)))) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f83,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $false = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o),vAPP(sTfun(sTfun('type/realax/real',$o),$o),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o)),bCOMB,vSIGMA('type/realax/real')),vAPP(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o)),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o))),cCOMB,vAPP(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),vAPP(sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o)))),bCOMB,sCOMB),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o)))),cCOMB,vAPP(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),vAPP(sTfun(sTfun($o,sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o))))),bCOMB,bCOMB),'const/sets/SETSPEC'('type/realax/real'))),vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0)))),iCOMB)))) ) ),
inference(superposition,[],[f24,f8]) ).
thf(f8,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f24,plain,
! [X0: 'type/realax/real'] : ( $true != vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o),vAPP(sTfun(sTfun('type/realax/real',$o),$o),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o)),bCOMB,vSIGMA('type/realax/real')),vAPP(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o)),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o))),cCOMB,vAPP(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),vAPP(sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o)))),bCOMB,sCOMB),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o)))),cCOMB,vAPP(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),vAPP(sTfun(sTfun($o,sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o))))),bCOMB,bCOMB),'const/sets/SETSPEC'('type/realax/real'))),vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0)))),iCOMB)))) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
! [X0: 'type/realax/real'] : ( $true != vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o),vAPP(sTfun(sTfun('type/realax/real',$o),$o),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o)),bCOMB,vSIGMA('type/realax/real')),vAPP(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o)),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o))),cCOMB,vAPP(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),vAPP(sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o)))),bCOMB,sCOMB),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o)))),cCOMB,vAPP(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),vAPP(sTfun(sTfun($o,sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o))))),bCOMB,bCOMB),'const/sets/SETSPEC'('type/realax/real'))),vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0)))),iCOMB)))) ),
inference(flattening,[],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real'] : ( $true != vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),vAPP(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o),vAPP(sTfun(sTfun('type/realax/real',$o),$o),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun('type/realax/real',$o)),bCOMB,vSIGMA('type/realax/real')),vAPP(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o)),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',sTfun('type/realax/real',$o))),cCOMB,vAPP(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),vAPP(sTfun(sTfun('type/realax/real',sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o))),sTfun(sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real','type/realax/real'),sTfun('type/realax/real',$o)))),bCOMB,sCOMB),vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o))),vAPP(sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',sTfun('type/realax/real',$o)))),cCOMB,vAPP(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),vAPP(sTfun(sTfun($o,sTfun('type/realax/real',$o)),sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o)))),sTfun(sTfun('type/realax/real',sTfun($o,sTfun('type/realax/real',$o))),sTfun('type/realax/real',sTfun(sTfun('type/realax/real',$o),sTfun('type/realax/real',sTfun('type/realax/real',$o))))),bCOMB,bCOMB),'const/sets/SETSPEC'('type/realax/real'))),vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0)))),iCOMB)))) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
! [X0: 'type/realax/real'] :
~ vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),
vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),
^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : vAPP('type/realax/real',$o,vAPP($o,sTfun('type/realax/real',$o),vAPP('type/realax/real',sTfun($o,sTfun('type/realax/real',$o)),'const/sets/SETSPEC'('type/realax/real'),X1),vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0),X2)),X2))),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real'] :
~ vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),
vAPP(sTfun('type/realax/real',$o),sTfun('type/realax/real',$o),'const/sets/GSPEC'('type/realax/real'),
^ [X1: 'type/realax/real'] :
? [X2: 'type/realax/real'] : vAPP('type/realax/real',$o,vAPP($o,sTfun('type/realax/real',$o),vAPP('type/realax/real',sTfun($o,sTfun('type/realax/real',$o)),'const/sets/SETSPEC'('type/realax/real'),X1),vAPP('type/realax/real',$o,vAPP('type/realax/real',sTfun('type/realax/real',$o),'const/realax/real_le',X0),X2)),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
thf(f82,plain,
! [X0: 'type/realax/real' > $o] : ( $true = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),X0) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f79,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),X0) )
| ( 'const/sets/UNIV'('type/realax/real') != 'const/sets/UNIV'('type/realax/real') ) ),
inference(constrained_superposition,[],[f78,f74]) ).
thf(f74,plain,
$true = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f67,plain,
( ( $true = $false )
| ( $true = vAPP(sTfun('type/realax/real',$o),$o,'const/sets/FINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) ) ),
inference(superposition,[],[f31,f61]) ).
thf(f61,plain,
vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) = $false,
inference(trivial_inequality_removal,[],[f60]) ).
thf(f60,plain,
( ( $true != $true )
| ( vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) = $false ) ),
inference(superposition,[],[f23,f8]) ).
thf(f23,plain,
vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) != $true,
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) != $true,
inference(flattening,[],[f10]) ).
thf(f10,plain,
vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')) != $true,
inference(fool_elimination,[],[f9]) ).
thf(f9,plain,
~ vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
vAPP(sTfun('type/realax/real',$o),$o,'const/sets/INFINITE'('type/realax/real'),'const/sets/UNIV'('type/realax/real')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).
thf(f31,plain,
! [X0: $tType,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(not_proxy_clausification,[],[f28]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = $true )
| ( $false = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
! [X0: $tType,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1)) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = ~ vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,'const/sets/INFINITE'(X0),X1) = ~ vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).
thf(f78,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),'const/sets/UNIV'(X0)) )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f75,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( $true != vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),'const/sets/UNIV'(X0)) ) ),
inference(superposition,[],[f27,f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),'const/sets/UNIV'(X0)) = $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o] : ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),'const/sets/UNIV'(X0)) = $true ),
inference(fool_elimination,[],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),'const/sets/UNIV'(X0)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),'const/sets/UNIV'(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).
thf(f27,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(flattening,[],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true )
| ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) != $true )
| ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) != $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2) = $true )
& ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) = $true ) )
=> ( vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) = $true ) ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),'const/sets/SUBSET'(X0),X1),X2)
& vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X2) )
=> vAPP(sTfun(X0,$o),$o,'const/sets/FINITE'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : ANA068^1 : TPTP v8.2.0. Released v7.0.0.
% 0.02/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n003.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 07:59:53 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % (26417)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (26422)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)
% 0.16/0.32 % (26423)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)
% 0.16/0.32 % (26420)WARNING: value z3 for option sas not known
% 0.16/0.32 % (26424)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)
% 0.16/0.32 % (26424)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.32 % (26418)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32 % (26420)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)
% 0.16/0.32 % (26419)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.32 % Exception at run slice level
% 0.16/0.32 User error: % (26421)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.32 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.32 % Exception at run slice level
% 0.16/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.32 % Exception at run slice level
% 0.16/0.32 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.32 % (26423)First to succeed.
% 0.16/0.32 % (26423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26417"
% 0.16/0.33 % (26422)Also succeeded, but the first one will report.
% 0.16/0.33 % (26423)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33 % (26423)------------------------------
% 0.16/0.33 % (26423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.33 % (26423)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (26423)Memory used [KB]: 880
% 0.16/0.33 % (26423)Time elapsed: 0.006 s
% 0.16/0.33 % (26423)Instructions burned: 14 (million)
% 0.16/0.33 % (26417)Success in time 0.017 s
%------------------------------------------------------------------------------