TSTP Solution File: NUM547+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 151 ( 38 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 176 ( 67 ~; 64 |; 34 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 50 (; 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,conjecture,
? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ ? [W0] : 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(f248,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(f249,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)],[f248]) ).
fof(f250,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)],[f249]) ).
fof(f251,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)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| X2 != slbdtsldtrb0(X0,X1)
| aSet0(X2) ),
inference(cnf_transformation,[status(esa)],[f251]) ).
fof(f265,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f266,plain,
aSet0(xS),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f270,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f272,plain,
! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
inference(pre_NNF_transformation,[status(esa)],[f66]) ).
fof(f273,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(esa)],[f272]) ).
fof(f303,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0)
| aSet0(slbdtsldtrb0(X0,X1)) ),
inference(destructive_equality_resolution,[status(esa)],[f252]) ).
fof(f325,plain,
( spl0_3
<=> aSet0(xS) ),
introduced(split_symbol_definition) ).
fof(f327,plain,
( ~ aSet0(xS)
| spl0_3 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f333,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f266]) ).
fof(f334,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f368,plain,
( spl0_11
<=> slbdtsldtrb0(xS,xk) = slcrc0 ),
introduced(split_symbol_definition) ).
fof(f369,plain,
( slbdtsldtrb0(xS,xk) = slcrc0
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( spl0_12
<=> aSet0(slbdtsldtrb0(xS,xk)) ),
introduced(split_symbol_definition) ).
fof(f373,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| spl0_12 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( slbdtsldtrb0(xS,xk) = slcrc0
| ~ aSet0(slbdtsldtrb0(xS,xk)) ),
inference(resolution,[status(thm)],[f83,f273]) ).
fof(f375,plain,
( spl0_11
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f374,f368,f371]) ).
fof(f382,plain,
( spl0_13
<=> aElementOf0(xk,szNzAzT0) ),
introduced(split_symbol_definition) ).
fof(f384,plain,
( ~ aElementOf0(xk,szNzAzT0)
| spl0_13 ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0)
| spl0_12 ),
inference(resolution,[status(thm)],[f373,f303]) ).
fof(f386,plain,
( ~ spl0_3
| ~ spl0_13
| spl0_12 ),
inference(split_clause,[status(thm)],[f385,f325,f382,f371]) ).
fof(f387,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f265]) ).
fof(f388,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f270]) ).
fof(f390,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f391,plain,
$false,
inference(sat_refutation,[status(thm)],[f334,f375,f386,f388,f390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM547+1 : 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 : n003.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 10:01:53 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
% 0.12/0.38 % Elapsed time: 0.028439 seconds
% 0.12/0.38 % CPU time: 0.045412 seconds
% 0.12/0.38 % Memory used: 15.408 MB
%------------------------------------------------------------------------------