TSTP Solution File: NUM605+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 : Tue Apr 30 20:35:18 EDT 2024
% Result : Theorem 3.83s 0.91s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 17 unt; 2 def)
% Number of atoms : 164 ( 56 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 189 ( 73 ~; 70 |; 33 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 52 ( 47 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(f57,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,hypothesis,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,conjecture,
xQ != slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f112,plain,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f113,plain,
! [W0] :
( ( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(NNF_transformation,[status(esa)],[f112]) ).
fof(f114,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| ? [W1] : aElementOf0(W1,W0) ) ),
inference(miniscoping,[status(esa)],[f113]) ).
fof(f115,plain,
( ! [W0] :
( W0 != slcrc0
| ( aSet0(W0)
& ! [W1] : ~ aElementOf0(W1,W0) ) )
& ! [W0] :
( W0 = slcrc0
| ~ aSet0(W0)
| aElementOf0(sk0_0(W0),W0) ) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0] :
( X0 != slcrc0
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f222,plain,
! [W0] :
( ~ aSet0(W0)
| ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f223,plain,
! [W0] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) != sz00
| W0 = slcrc0 )
& ( sbrdtbr0(W0) = sz00
| W0 != slcrc0 ) ) ),
inference(NNF_transformation,[status(esa)],[f222]) ).
fof(f225,plain,
! [X0] :
( ~ aSet0(X0)
| sbrdtbr0(X0) = sz00
| X0 != slcrc0 ),
inference(cnf_transformation,[status(esa)],[f223]) ).
fof(f283,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f57]) ).
fof(f284,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ! [W2] :
( ( W2 != slbdtsldtrb0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ( ~ aElementOf0(W3,W2)
| ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) )
& ( aElementOf0(W3,W2)
| ~ aSubsetOf0(W3,W0)
| sbrdtbr0(W3) != W1 ) ) ) )
& ( W2 = slbdtsldtrb0(W0,W1)
| ~ aSet0(W2)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
| ~ aSubsetOf0(W3,W0)
| sbrdtbr0(W3) != W1 )
& ( aElementOf0(W3,W2)
| ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f283]) ).
fof(f285,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ( ! [W2] :
( W2 != slbdtsldtrb0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ~ aElementOf0(W3,W2)
| ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) )
& ! [W3] :
( aElementOf0(W3,W2)
| ~ aSubsetOf0(W3,W0)
| sbrdtbr0(W3) != W1 ) ) )
& ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
| ~ aSet0(W2)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
| ~ aSubsetOf0(W3,W0)
| sbrdtbr0(W3) != W1 )
& ( aElementOf0(W3,W2)
| ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f284]) ).
fof(f286,plain,
! [W0,W1] :
( ~ aSet0(W0)
| ~ aElementOf0(W1,szNzAzT0)
| ( ! [W2] :
( W2 != slbdtsldtrb0(W0,W1)
| ( aSet0(W2)
& ! [W3] :
( ~ aElementOf0(W3,W2)
| ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) )
& ! [W3] :
( aElementOf0(W3,W2)
| ~ aSubsetOf0(W3,W0)
| sbrdtbr0(W3) != W1 ) ) )
& ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
| ~ aSet0(W2)
| ( ( ~ aElementOf0(sk0_10(W2,W1,W0),W2)
| ~ aSubsetOf0(sk0_10(W2,W1,W0),W0)
| sbrdtbr0(sk0_10(W2,W1,W0)) != W1 )
& ( aElementOf0(sk0_10(W2,W1,W0),W2)
| ( aSubsetOf0(sk0_10(W2,W1,W0),W0)
& sbrdtbr0(sk0_10(W2,W1,W0)) = W1 ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f285]) ).
fof(f289,plain,
! [X0,X1,X2,X3] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X3,X2)
| sbrdtbr0(X3) = X1 ),
inference(cnf_transformation,[status(esa)],[f286]) ).
fof(f360,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f372,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f422,plain,
aSet0(xO),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f432,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f433,plain,
xQ = slcrc0,
inference(cnf_transformation,[status(esa)],[f101]) ).
fof(f440,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(esa)],[f116]) ).
fof(f452,plain,
( ~ aSet0(slcrc0)
| sbrdtbr0(slcrc0) = sz00 ),
inference(destructive_equality_resolution,[status(esa)],[f225]) ).
fof(f465,plain,
! [X0,X1,X2] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X2) = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f289]) ).
fof(f482,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xO,xK)),
inference(forward_demodulation,[status(thm)],[f433,f432]) ).
fof(f523,plain,
( spl0_8
<=> aSet0(xO) ),
introduced(split_symbol_definition) ).
fof(f525,plain,
( ~ aSet0(xO)
| spl0_8 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f559,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f422]) ).
fof(f560,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f768,plain,
sbrdtbr0(slcrc0) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f452,f440]) ).
fof(f823,plain,
( spl0_55
<=> aElementOf0(xK,szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f825,plain,
( ~ aElementOf0(xK,szNzAzT0)
| spl0_55 ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f831,plain,
( $false
| spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f360]) ).
fof(f832,plain,
spl0_55,
inference(contradiction_clause,[status(thm)],[f831]) ).
fof(f4707,plain,
( spl0_523
<=> sbrdtbr0(slcrc0) = xK ),
introduced(split_symbol_definition) ).
fof(f4708,plain,
( sbrdtbr0(slcrc0) = xK
| ~ spl0_523 ),
inference(component_clause,[status(thm)],[f4707]) ).
fof(f4813,plain,
( ~ aSet0(xO)
| ~ aElementOf0(xK,szNzAzT0)
| sbrdtbr0(slcrc0) = xK ),
inference(resolution,[status(thm)],[f465,f482]) ).
fof(f4814,plain,
( ~ spl0_8
| ~ spl0_55
| spl0_523 ),
inference(split_clause,[status(thm)],[f4813,f523,f823,f4707]) ).
fof(f4822,plain,
( sz00 = xK
| ~ spl0_523 ),
inference(forward_demodulation,[status(thm)],[f768,f4708]) ).
fof(f4823,plain,
( $false
| ~ spl0_523 ),
inference(forward_subsumption_resolution,[status(thm)],[f4822,f372]) ).
fof(f4824,plain,
~ spl0_523,
inference(contradiction_clause,[status(thm)],[f4823]) ).
fof(f4825,plain,
$false,
inference(sat_refutation,[status(thm)],[f560,f832,f4814,f4824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:42:01 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 3.83/0.91 % Refutation found
% 3.83/0.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.83/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.35/0.93 % Elapsed time: 0.576391 seconds
% 4.35/0.93 % CPU time: 4.403643 seconds
% 4.35/0.93 % Total memory used: 107.605 MB
% 4.35/0.93 % Net memory used: 105.762 MB
%------------------------------------------------------------------------------