%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM587+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.10s 5.58s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 11 unt; 3 def)
% Number of atoms : 80 ( 3 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 87 ( 36 ~; 30 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 25 ( 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,hypothesis,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,hypothesis,
( aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
& xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f91]) ).
fof(f117,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f118,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f119]) ).
fof(f122,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f349,plain,
aSet0(xT),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f356,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f392,plain,
xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f393,plain,
aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f394,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f454,plain,
aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(forward_demodulation,[status(thm)],[f392,f393]) ).
fof(f480,definition,
( sQ4_spl
<=> aSet0(xT) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ4_spl
| ~ aSet0(xT) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f491,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f349]) ).
fof(f492,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f641,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f122,f394]) ).
fof(f644,definition,
! [X0] :
( sQ35_spl
<=> ( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xT) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f645,plain,
! [X0] :
( ~ sQ35_spl
| ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xT) ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f647,plain,
( sQ35_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f641,f480,f644]) ).
fof(f654,plain,
( ~ sQ35_spl
| ~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(resolution,[status(thm)],[f645,f356]) ).
fof(f661,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f654,f454]) ).
fof(f662,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f663,plain,
$false,
inference(sat_refutation,[status(thm)],[f492,f647,f662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM587+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.52 % Computer : n004.cluster.edu
% 0.10/5.52 % Model : x86_64 x86_64
% 0.10/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.52 % Memory : 8046.5625MB
% 0.10/5.52 % OS : Linux 6.8.0-71-generic
% 0.10/5.52 % CPULimit : 300
% 0.10/5.52 % WCLimit : 300
% 0.10/5.52 % DateTime : Mon Sep 21 02:42:25 UTC 2026
% 0.10/5.52 % CPUTime :
% 0.10/5.54 % Drodi V4.1.1
% 0.10/5.58 % Refutation found
% 0.10/5.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.62 % Elapsed time: 0.078847 seconds
% 0.14/5.62 % CPU time: 0.334523 seconds
% 0.14/5.62 % Total memory used: 113.851 MB
% 0.14/5.62 % Net memory used: 113.411 MB
%------------------------------------------------------------------------------