TSTP Solution File: NUM604+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM604+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:28:09 EDT 2022
% Result : Theorem 0.57s 0.76s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 73 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 24 ~; 21 |; 18 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ).
fof(m__5034,hypothesis,
( aElementOf0(xi,szNzAzT0)
& sdtlpdtrp0(xe,xi) = xx ) ).
fof(m__5045,hypothesis,
( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ) ).
fof(m__,conjecture,
aElementOf0(xx,xS) ).
fof(subgoal_0,plain,
aElementOf0(xx,xS),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ aElementOf0(xx,xS),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ) ),
inference(canonicalize,[],[m__5045]) ).
fof(normalize_0_1,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
inference(canonicalize,[],[m__5034]) ).
fof(normalize_0_4,plain,
aElementOf0(xi,szNzAzT0),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe)
& ! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
inference(canonicalize,[],[m__4660]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
& ! [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0,W1] :
( ( ~ aElementOf0(W0,szNzAzT0)
| sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) )
& ( ~ aElementOf0(W0,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
| sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_11,plain,
~ aElementOf0(xx,xS),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| aElementOf0(W0,xS) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,xi))
| aElementOf0(xx,xS) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(xx))]]) ).
cnf(refute_0_2,plain,
aElementOf0(xi,szNzAzT0),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ aElementOf0(W0,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)) ),
inference(subst,[],[refute_0_3:[bind(W0,$fot(xi))]]) ).
cnf(refute_0_5,plain,
aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)),
inference(resolve,[$cnf( aElementOf0(xi,szNzAzT0) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( sdtlpdtrp0(xe,xi) != xx
| ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)) ),[0],$fot(xx)]]) ).
cnf(refute_0_8,plain,
( ~ aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi))
| aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,xi),xx) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
aElementOf0(xx,xS),
inference(resolve,[$cnf( aElementOf0(xx,sdtlpdtrp0(xN,xi)) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
~ aElementOf0(xx,xS),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( aElementOf0(xx,xS) )],[refute_0_10,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM604+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 19:26:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.76
% 0.57/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.57/0.76
%------------------------------------------------------------------------------