%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM590+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:06 PM UTC 2026
% Result : Theorem 0.22s 5.73s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 7 unt; 2 def)
% Number of atoms : 102 ( 14 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 32 ~; 25 |; 40 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( aElementOf0(W0,xY)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(xY)
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,conjecture,
( aSubsetOf0(xY,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xY)
=> aElementOf0(W0,szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
~ ( aSubsetOf0(xY,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xY)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
fof(f409,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& ! [W1] :
( aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W1,sdtlpdtrp0(xN,W0)) )
& aSet0(sdtlpdtrp0(xN,W0)) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f411,plain,
! [X0,X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f409]) ).
fof(f499,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f500,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( aElementOf0(W0,xY)
<=> ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) ) )
& aSet0(xY)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f501,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,xY) )
& ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,xY) ) )
& aSet0(xY)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(NNF_transformation,[status(thm)],[f500]) ).
fof(f502,plain,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& ! [W0] :
( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
| ~ aElement0(W0)
| aElementOf0(W0,xY) )
& ! [W0] :
( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(W0,sdtlpdtrp0(xN,xi))
& aElement0(W0) )
| ~ aElementOf0(W0,xY) )
& aSet0(xY)
& ! [W0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
| ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(miniscoping,[status(thm)],[f501]) ).
fof(f507,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,xY) ),
inference(cnf_transformation,[status(thm)],[f502]) ).
fof(f512,plain,
( ~ aSubsetOf0(xY,szNzAzT0)
& ? [W0] :
( ~ aElementOf0(W0,szNzAzT0)
& aElementOf0(W0,xY) ) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f513,plain,
( ~ aSubsetOf0(xY,szNzAzT0)
& ~ aElementOf0(sK27_skl,szNzAzT0)
& aElementOf0(sK27_skl,xY) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl]),skolemize(W0,sK27_skl)],[f512]) ).
fof(f514,plain,
aElementOf0(sK27_skl,xY),
inference(cnf_transformation,[status(thm)],[f513]) ).
fof(f515,plain,
~ aElementOf0(sK27_skl,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f513]) ).
fof(f800,plain,
! [X0] :
( ~ aElementOf0(sK27_skl,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f411,f515]) ).
fof(f856,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(sK27_skl,xY) ),
inference(resolution,[status(thm)],[f507,f800]) ).
fof(f857,definition,
( sQ12_spl
<=> aElementOf0(sK27_skl,xY) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f859,plain,
( sQ12_spl
| ~ aElementOf0(sK27_skl,xY) ),
inference(component_clause,[status(thm)],[f857]) ).
fof(f860,definition,
( sQ13_spl
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f862,plain,
( sQ13_spl
| ~ aElementOf0(xi,szNzAzT0) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f856,f857,f860]) ).
fof(f864,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f859,f514]) ).
fof(f865,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f864]) ).
fof(f995,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f862]) ).
fof(f996,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f995]) ).
fof(f997,plain,
$false,
inference(sat_refutation,[status(thm)],[f863,f865,f996]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM590+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.65 % Computer : n010.cluster.edu
% 0.18/5.65 % Model : x86_64 x86_64
% 0.18/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.65 % Memory : 8046.5625MB
% 0.18/5.65 % OS : Linux 6.8.0-71-generic
% 0.18/5.66 % CPULimit : 300
% 0.18/5.66 % WCLimit : 300
% 0.18/5.66 % DateTime : Mon Sep 21 02:43:01 UTC 2026
% 0.18/5.66 % CPUTime :
% 0.22/5.70 % Drodi V4.1.1
% 0.22/5.73 % Refutation found
% 0.22/5.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.76 % Elapsed time: 0.092992 seconds
% 0.22/5.76 % CPU time: 0.260739 seconds
% 0.22/5.76 % Total memory used: 76.869 MB
% 0.22/5.76 % Net memory used: 76.622 MB
%------------------------------------------------------------------------------