TSTP Solution File: NUM514+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM514+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 12:27:20 EDT 2022
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 83 ( 47 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 29 ~; 15 |; 33 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 4 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2504,hypothesis,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(sdtsldt0(xn,xr),W0) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ).
fof(m__2613,hypothesis,
( aNaturalNumber0(sdtsldt0(xk,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ).
fof(m__,conjecture,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ) ).
fof(subgoal_0,plain,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
=> doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ~ ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ) )
=> doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ! [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( sdtsldt0(xn,xr) != xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [W0] :
( sdtpldt0(sdtsldt0(xn,xr),W0) = xn
& aNaturalNumber0(W0) ) ),
inference(canonicalize,[],[m__2504]) ).
fof(normalize_0_2,plain,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ! [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2,normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm)
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(canonicalize,[],[m__2613]) ).
fof(normalize_0_8,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm)
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(simplify,[],[normalize_0_7,normalize_0_2,normalize_0_3]) ).
fof(normalize_0_9,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm)
| sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(sdtasdt0(xp,sdtsldt0(xk,xr)))),bind(Y,$fot(sdtasdt0(sdtsldt0(xn,xr),xm)))]]) ).
cnf(refute_0_6,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(resolve,[$cnf( $equal(sdtasdt0(xp,sdtsldt0(xk,xr)),sdtasdt0(sdtsldt0(xn,xr),xm)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr))
| sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(xp,W0)
| sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,W0)) ),[0],$fot(sdtasdt0(xp,sdtsldt0(xk,xr)))]]) ).
cnf(refute_0_8,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(xp,W0)
| sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,sdtsldt0(xk,xr))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(xp,W0)
| ~ aNaturalNumber0(W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,W0)) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(xp,sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xk,xr)) ),
inference(subst,[],[refute_0_9:[bind(W0,$fot(sdtsldt0(xk,xr)))]]) ).
cnf(refute_0_11,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(xp,sdtsldt0(xk,xr)),
introduced(tautology,[refl,[$fot(sdtasdt0(xp,sdtsldt0(xk,xr)))]]) ).
cnf(refute_0_12,plain,
~ aNaturalNumber0(sdtsldt0(xk,xr)),
inference(resolve,[$cnf( $equal(sdtasdt0(xp,sdtsldt0(xk,xr)),sdtasdt0(xp,sdtsldt0(xk,xr))) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( aNaturalNumber0(sdtsldt0(xk,xr)) )],[refute_0_13,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM514+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 13:19:06 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.46
%------------------------------------------------------------------------------