TSTP Solution File: NUM549+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM549+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 12:29:39 EDT 2023
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 7 unt; 1 def)
% Number of atoms : 119 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 51 ~; 48 |; 15 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 32 (; 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,conjecture,
? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f75,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f79,plain,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f80,plain,
! [W0] :
( ( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(NNF_transformation,[status(esa)],[f79]) ).
fof(f81,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(miniscoping,[status(esa)],[f80]) ).
fof(f82,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| aElementOf0(sk0_0(W0),W0) ) ),
inference(skolemization,[status(esa)],[f81]) ).
fof(f83,plain,
! [X0] :
( X0 != slcrc0
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f85,plain,
! [X0] :
( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f189,plain,
! [W0] :
( ~ aSet0(W0)
| ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f190,plain,
! [W0] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) != sz00
| W0 = slcrc0 )
& ( sbrdtbr0(W0) = sz00
| W0 != slcrc0 ) ) ),
inference(NNF_transformation,[status(esa)],[f189]) ).
fof(f192,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) = sz00
| X0 != slcrc0 ),
inference(cnf_transformation,[status(esa)],[f190]) ).
fof(f270,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f275,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f277,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f278,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(pre_NNF_transformation,[status(esa)],[f68]) ).
fof(f279,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[status(esa)],[f278]) ).
fof(f286,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(esa)],[f83]) ).
fof(f298,plain,
( ~ aSet0(slcrc0)
| sbrdtbr0(slcrc0) = sz00 ),
inference(destructive_equality_resolution,[status(esa)],[f192]) ).
fof(f340,plain,
( spl0_6
<=> xQ = slcrc0 ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( xQ = slcrc0
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( spl0_7
<=> aSet0(xQ) ),
introduced(split_symbol_definition) ).
fof(f345,plain,
( ~ aSet0(xQ)
| spl0_7 ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( spl0_8
<=> aElement0(sk0_0(xQ)) ),
introduced(split_symbol_definition) ).
fof(f348,plain,
( ~ aElement0(sk0_0(xQ))
| spl0_8 ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,plain,
( xQ = slcrc0
| ~ aSet0(xQ)
| ~ aElement0(sk0_0(xQ)) ),
inference(resolution,[status(thm)],[f85,f279]) ).
fof(f350,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f349,f340,f343,f346]) ).
fof(f351,plain,
! [X0] :
( X0 = slcrc0
| ~ aSet0(X0)
| ~ aSet0(X0)
| aElement0(sk0_0(X0)) ),
inference(resolution,[status(thm)],[f85,f76]) ).
fof(f352,plain,
! [X0] :
( X0 = slcrc0
| ~ aSet0(X0)
| aElement0(sk0_0(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f351]) ).
fof(f415,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f275]) ).
fof(f416,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f419,plain,
( xQ = slcrc0
| ~ aSet0(xQ)
| spl0_8 ),
inference(resolution,[status(thm)],[f348,f352]) ).
fof(f420,plain,
( spl0_6
| ~ spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f419,f340,f343,f346]) ).
fof(f422,plain,
( sbrdtbr0(slcrc0) = xk
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f341,f277]) ).
fof(f499,plain,
( ~ aSet0(slcrc0)
| xk = sz00
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f422,f298]) ).
fof(f500,plain,
( xk = sz00
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f286]) ).
fof(f509,plain,
( sz00 != sz00
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f500,f270]) ).
fof(f510,plain,
( $false
| ~ spl0_6 ),
inference(trivial_equality_resolution,[status(esa)],[f509]) ).
fof(f511,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
$false,
inference(sat_refutation,[status(thm)],[f350,f416,f420,f511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM549+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue May 30 09:57:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.59 % Elapsed time: 0.019299 seconds
% 0.27/0.59 % CPU time: 0.052081 seconds
% 0.27/0.59 % Memory used: 15.507 MB
%------------------------------------------------------------------------------