TSTP Solution File: NUM532+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM532+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:27:29 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 11 unt; 1 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 79 ( 35 ~; 33 |; 6 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ) ).
fof(m__467,hypothesis,
aSet0(xA) ).
fof(m__,conjecture,
aSubsetOf0(xA,xA) ).
fof(subgoal_0,plain,
aSubsetOf0(xA,xA),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ aSubsetOf0(xA,xA),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
aSet0(xA),
inference(canonicalize,[],[m__467]) ).
fof(normalize_0_1,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
<=> ( ~ aSet0(W1)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) ) ) ) ),
inference(canonicalize,[],[mDefSub]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aSubsetOf0(W1,W0)
<=> ( ~ aSet0(W1)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) ) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W0,W1,W2] :
( ( ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aSet0(W1) )
& ( ~ aElementOf0(W2,W1)
| ~ aSet0(W0)
| ~ aSubsetOf0(W1,W0)
| aElementOf0(W2,W0) )
& ( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
~ aSubsetOf0(xA,xA),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
! [W0,W1] :
( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
aSet0(xA),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ aSet0(W0)
| ~ aSet0(W1)
| aElementOf0(skolemFOFtoCNF_W2(W0,W1),W1)
| aSubsetOf0(W1,W0) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ aSet0(xA)
| aElementOf0(skolemFOFtoCNF_W2(xA,xA),xA)
| aSubsetOf0(xA,xA) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xA)),bind(W1,$fot(xA))]]) ).
cnf(refute_0_3,plain,
( aElementOf0(skolemFOFtoCNF_W2(xA,xA),xA)
| aSubsetOf0(xA,xA) ),
inference(resolve,[$cnf( aSet0(xA) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ aSubsetOf0(xA,xA),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
aElementOf0(skolemFOFtoCNF_W2(xA,xA),xA),
inference(resolve,[$cnf( aSubsetOf0(xA,xA) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(W0,W1),W0)
| ~ aSet0(W0)
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ aElementOf0(skolemFOFtoCNF_W2(xA,xA),xA)
| ~ aSet0(xA)
| aSubsetOf0(xA,xA) ),
inference(subst,[],[refute_0_6:[bind(W0,$fot(xA)),bind(W1,$fot(xA))]]) ).
cnf(refute_0_8,plain,
( ~ aSet0(xA)
| aSubsetOf0(xA,xA) ),
inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W2(xA,xA),xA) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
aSubsetOf0(xA,xA),
inference(resolve,[$cnf( aSet0(xA) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( aSubsetOf0(xA,xA) )],[refute_0_9,refute_0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM532+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 08:17:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------