TSTP Solution File: NUM584+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM584+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 12:27:58 EDT 2022
% Result : Theorem 0.39s 0.56s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 151 ( 23 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 173 ( 46 ~; 29 |; 70 &)
% ( 13 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3989_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ).
fof(m__4007,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ).
fof(m__4024,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) )
& aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ).
fof(m__,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ) ).
fof(subgoal_0,plain,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ~ ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) )
=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xQ)
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ~ ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(W0,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) )
=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
| ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( sbrdtbr0(xQ) = xk
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(xQ)
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ! [W0] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ! [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
inference(canonicalize,[],[m__3989_02]) ).
fof(normalize_0_2,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ) ),
inference(canonicalize,[],[m__4007]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ) ),
inference(simplify,[],[normalize_0_3,normalize_0_2,normalize_0_5]) ).
fof(normalize_0_7,plain,
aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(W0,xS) )
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ) ),
inference(canonicalize,[],[m__4024]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ~ aElement0(W0)
| ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& ~ aElementOf0(W0,xQ) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(W0,xS) ) ),
inference(simplify,[],[normalize_0_9,normalize_0_2,normalize_0_7,normalize_0_5,normalize_0_11]) ).
fof(normalize_0_13,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_15,plain,
! [W0] :
( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(W0,xS) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_2,normalize_0_7,normalize_0_8,normalize_0_13,normalize_0_15,normalize_0_5,normalize_0_11]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM584+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 5 03:30:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.56
% 0.39/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.39/0.57
%------------------------------------------------------------------------------