TSTP Solution File: NUM551+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM551+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 2.06s 2.24s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 9 unt; 1 def)
% Number of atoms : 76 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 36 ~; 28 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ) ).
fof(m__2313,hypothesis,
xQ != slcrc0 ).
fof(m__,conjecture,
? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ) ).
fof(subgoal_0,plain,
? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( sbrdtbr0(xQ) = xk
& aSet0(xQ)
& isFinite0(xQ) ),
inference(canonicalize,[],[m__2291]) ).
fof(normalize_0_1,plain,
aSet0(xQ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(canonicalize,[],[mDefEmp]) ).
fof(normalize_0_3,plain,
! [W0] :
( W0 != slcrc0
<=> ( ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aSet0(W0)
| W0 = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(W0),W0) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
xQ != slcrc0,
inference(canonicalize,[],[m__2313]) ).
fof(normalize_0_7,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(canonicalize,[],[mEOfElem]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0,W1] :
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(specialize,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
aSet0(xQ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aSet0(W0)
| W0 = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(W0),W0) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ aSet0(xQ)
| xQ = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(xQ),xQ) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xQ))]]) ).
cnf(refute_0_3,plain,
( xQ = slcrc0
| aElementOf0(skolemFOFtoCNF_W1(xQ),xQ) ),
inference(resolve,[$cnf( aSet0(xQ) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
xQ != slcrc0,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
aElementOf0(skolemFOFtoCNF_W1(xQ),xQ),
inference(resolve,[$cnf( $equal(xQ,slcrc0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ aElementOf0(W1,W0)
| ~ aSet0(W0)
| aElement0(W1) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ aElementOf0(skolemFOFtoCNF_W1(xQ),xQ)
| ~ aSet0(xQ)
| aElement0(skolemFOFtoCNF_W1(xQ)) ),
inference(subst,[],[refute_0_6:[bind(W0,$fot(xQ)),bind(W1,$fot(skolemFOFtoCNF_W1(xQ)))]]) ).
cnf(refute_0_8,plain,
( ~ aSet0(xQ)
| aElement0(skolemFOFtoCNF_W1(xQ)) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1(xQ),xQ) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
aElement0(skolemFOFtoCNF_W1(xQ)),
inference(resolve,[$cnf( aSet0(xQ) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ aElement0(skolemFOFtoCNF_W1(xQ))
| ~ aElementOf0(skolemFOFtoCNF_W1(xQ),xQ) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(skolemFOFtoCNF_W1(xQ)))]]) ).
cnf(refute_0_12,plain,
~ aElement0(skolemFOFtoCNF_W1(xQ)),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1(xQ),xQ) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W1(xQ)) )],[refute_0_9,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM551+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 08:56:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.06/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.06/2.24
% 2.06/2.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.06/2.24
%------------------------------------------------------------------------------