TSTP Solution File: NUM547+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 : 300s
% DateTime : Wed May 31 12:29:38 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 6 unt; 1 def)
% Number of atoms : 251 ( 46 equ)
% Maximal formula atoms : 43 ( 8 avg)
% Number of connectives : 320 ( 98 ~; 79 |; 123 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 73 (; 57 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
? [W0] :
( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ? [W0] :
( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f77,plain,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f78,plain,
! [W0] :
( ( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(NNF_transformation,[status(esa)],[f77]) ).
fof(f79,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(miniscoping,[status(esa)],[f78]) ).
fof(f80,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| aElementOf0(sk0_0(W0),W0) ) ),
inference(skolemization,[status(esa)],[f79]) ).
fof(f83,plain,
! [X0] :
( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f269,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xT) ) )
& ~ aSubsetOf0(W0,xT) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
inference(pre_NNF_transformation,[status(esa)],[f63]) ).
fof(f270,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xT) ) )
& ~ aSubsetOf0(W0,xT) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
inference(miniscoping,[status(esa)],[f269]) ).
fof(f271,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ( aElementOf0(sk0_11(W0),W0)
& ~ aElementOf0(sk0_11(W0),xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ( aElementOf0(sk0_12(W0),W0)
& ~ aElementOf0(sk0_12(W0),xT) ) )
& ~ aSubsetOf0(W0,xT) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ! [W0] :
( ( ( ~ aSet0(W0)
| ( aElementOf0(sk0_13(W0),W0)
& ~ aElementOf0(sk0_13(W0),xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk
| aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aElementOf0(sk0_14,slbdtsldtrb0(xS,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
inference(skolemization,[status(esa)],[f270]) ).
fof(f272,plain,
aSet0(slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(esa)],[f271]) ).
fof(f298,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnf_transformation,[status(esa)],[f271]) ).
fof(f300,plain,
! [W0] :
( ( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk )
& ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
inference(pre_NNF_transformation,[status(esa)],[f66]) ).
fof(f301,plain,
( ! [W0] :
( ( ( ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ~ aElementOf0(W1,xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk )
& ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
inference(miniscoping,[status(esa)],[f300]) ).
fof(f302,plain,
( ! [W0] :
( ( ( ~ aSet0(W0)
| ( aElementOf0(sk0_15(W0),W0)
& ~ aElementOf0(sk0_15(W0),xS) ) )
& ~ aSubsetOf0(W0,xS) )
| sbrdtbr0(W0) != xk )
& ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
inference(skolemization,[status(esa)],[f301]) ).
fof(f306,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(esa)],[f302]) ).
fof(f376,plain,
( spl0_7
<=> slbdtsldtrb0(xS,xk) = slcrc0 ),
introduced(split_symbol_definition) ).
fof(f377,plain,
( slbdtsldtrb0(xS,xk) = slcrc0
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,plain,
( spl0_8
<=> aSet0(slbdtsldtrb0(xS,xk)) ),
introduced(split_symbol_definition) ).
fof(f381,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| spl0_8 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( slbdtsldtrb0(xS,xk) = slcrc0
| ~ aSet0(slbdtsldtrb0(xS,xk)) ),
inference(resolution,[status(thm)],[f83,f306]) ).
fof(f383,plain,
( spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f382,f376,f379]) ).
fof(f386,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f272]) ).
fof(f387,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f390,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f298]) ).
fof(f391,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
$false,
inference(sat_refutation,[status(thm)],[f383,f387,f391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM547+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n009.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 : 300
% 0.12/0.34 % DateTime : Tue May 30 09:53:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58 % Elapsed time: 0.017835 seconds
% 0.24/0.58 % CPU time: 0.041667 seconds
% 0.24/0.58 % Memory used: 15.648 MB
%------------------------------------------------------------------------------