TSTP Solution File: NUM550+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM550+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:27:39 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 16 unt; 1 def)
% Number of atoms : 118 ( 76 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 60 ~; 40 |; 18 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ) ).
fof(m__2270,hypothesis,
( aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ).
fof(m__,conjecture,
~ ( ~ ? [W0] : aElementOf0(W0,xQ)
& xQ = slcrc0 ) ).
fof(subgoal_0,plain,
( ~ ? [W0] : aElementOf0(W0,xQ)
=> xQ != slcrc0 ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ~ ? [W0] : aElementOf0(W0,xQ)
=> xQ != slcrc0 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& aSet0(xQ)
& aSubsetOf0(xQ,xS)
& ! [W0] :
( ~ aElementOf0(W0,xQ)
| aElementOf0(W0,xS) ) ),
inference(canonicalize,[],[m__2270]) ).
fof(normalize_0_1,plain,
sbrdtbr0(xQ) = xk,
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aSet0(W0)
| ( W0 != slcrc0
<=> sbrdtbr0(W0) != sz00 ) ),
inference(canonicalize,[],[mCardEmpty]) ).
fof(normalize_0_3,plain,
! [W0] :
( ~ aSet0(W0)
| ( W0 != slcrc0
<=> sbrdtbr0(W0) != sz00 ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ( W0 != slcrc0
| ~ aSet0(W0)
| sbrdtbr0(W0) = sz00 )
& ( sbrdtbr0(W0) != sz00
| ~ aSet0(W0)
| W0 = slcrc0 ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( W0 != slcrc0
| ~ aSet0(W0)
| sbrdtbr0(W0) = sz00 ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(canonicalize,[],[mDefEmp]) ).
fof(normalize_0_7,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0,W1] :
( ( W0 != slcrc0
| ~ aElementOf0(W1,W0) )
& ( W0 != slcrc0
| aSet0(W0) )
& ( ~ aSet0(W0)
| W0 = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(W0),W0) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( W0 != slcrc0
| aSet0(W0) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( xQ = slcrc0
& ! [W0] : ~ aElementOf0(W0,xQ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
xQ = slcrc0,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( xk != sz00
& aSet0(xS)
& aSet0(xT) ),
inference(canonicalize,[],[m__2202_02]) ).
fof(normalize_0_13,plain,
xk != sz00,
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
sbrdtbr0(xQ) = xk,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( W0 != slcrc0
| ~ aSet0(W0)
| sbrdtbr0(W0) = sz00 ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( slcrc0 != slcrc0
| ~ aSet0(slcrc0)
| sbrdtbr0(slcrc0) = sz00 ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(slcrc0))]]) ).
cnf(refute_0_3,plain,
slcrc0 = slcrc0,
introduced(tautology,[refl,[$fot(slcrc0)]]) ).
cnf(refute_0_4,plain,
( ~ aSet0(slcrc0)
| sbrdtbr0(slcrc0) = sz00 ),
inference(resolve,[$cnf( $equal(slcrc0,slcrc0) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( W0 != slcrc0
| aSet0(W0) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( slcrc0 != slcrc0
| aSet0(slcrc0) ),
inference(subst,[],[refute_0_5:[bind(W0,$fot(slcrc0))]]) ).
cnf(refute_0_7,plain,
aSet0(slcrc0),
inference(resolve,[$cnf( $equal(slcrc0,slcrc0) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
sbrdtbr0(slcrc0) = sz00,
inference(resolve,[$cnf( aSet0(slcrc0) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
xQ = slcrc0,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
sbrdtbr0(xQ) = sbrdtbr0(xQ),
introduced(tautology,[refl,[$fot(sbrdtbr0(xQ))]]) ).
cnf(refute_0_11,plain,
( sbrdtbr0(xQ) != sbrdtbr0(xQ)
| xQ != slcrc0
| sbrdtbr0(xQ) = sbrdtbr0(slcrc0) ),
introduced(tautology,[equality,[$cnf( $equal(sbrdtbr0(xQ),sbrdtbr0(xQ)) ),[1,0],$fot(slcrc0)]]) ).
cnf(refute_0_12,plain,
( xQ != slcrc0
| sbrdtbr0(xQ) = sbrdtbr0(slcrc0) ),
inference(resolve,[$cnf( $equal(sbrdtbr0(xQ),sbrdtbr0(xQ)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
sbrdtbr0(xQ) = sbrdtbr0(slcrc0),
inference(resolve,[$cnf( $equal(xQ,slcrc0) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( sbrdtbr0(slcrc0) != sz00
| sbrdtbr0(xQ) != sbrdtbr0(slcrc0)
| sbrdtbr0(xQ) = sz00 ),
inference(subst,[],[refute_0_18:[bind(X,$fot(sbrdtbr0(xQ))),bind(Y,$fot(sbrdtbr0(slcrc0))),bind(Z,$fot(sz00))]]) ).
cnf(refute_0_20,plain,
( sbrdtbr0(slcrc0) != sz00
| sbrdtbr0(xQ) = sz00 ),
inference(resolve,[$cnf( $equal(sbrdtbr0(xQ),sbrdtbr0(slcrc0)) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
sbrdtbr0(xQ) = sz00,
inference(resolve,[$cnf( $equal(sbrdtbr0(slcrc0),sz00) )],[refute_0_8,refute_0_20]) ).
cnf(refute_0_22,plain,
( sbrdtbr0(xQ) != sz00
| sbrdtbr0(xQ) != xk
| sz00 = xk ),
introduced(tautology,[equality,[$cnf( $equal(sbrdtbr0(xQ),xk) ),[0],$fot(sz00)]]) ).
cnf(refute_0_23,plain,
( sbrdtbr0(xQ) != xk
| sz00 = xk ),
inference(resolve,[$cnf( $equal(sbrdtbr0(xQ),sz00) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
sz00 = xk,
inference(resolve,[$cnf( $equal(sbrdtbr0(xQ),xk) )],[refute_0_0,refute_0_23]) ).
cnf(refute_0_25,plain,
xk != sz00,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_26,plain,
( sz00 != xk
| xk = sz00 ),
inference(subst,[],[refute_0_16:[bind(X,$fot(sz00)),bind(Y,$fot(xk))]]) ).
cnf(refute_0_27,plain,
sz00 != xk,
inference(resolve,[$cnf( $equal(xk,sz00) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( $equal(sz00,xk) )],[refute_0_24,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM550+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 : n021.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 17:02:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45
% 0.19/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.45
%------------------------------------------------------------------------------