%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM557+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 01:40:59 PM UTC 2026
% Result : Theorem 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 5 unt; 2 def)
% Number of atoms : 49 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 46 ( 16 ~; 13 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 4 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f72,hypothesis,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f342,plain,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f72]) ).
fof(f344,plain,
aSubsetOf0(xP,xS),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f345,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f346,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xP) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f347,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ~ aElementOf0(sK15_skl,xS)
& aElementOf0(sK15_skl,xP) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W0,sK15_skl)],[f346]) ).
fof(f350,plain,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f361,definition,
( sQ1_spl
<=> sbrdtbr0(xP) = xk ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ1_spl
| sbrdtbr0(xP) != xk ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f369,definition,
( sQ3_spl
<=> aSubsetOf0(xP,xS) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( sQ3_spl
| ~ aSubsetOf0(xP,xS) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f350,f369,f361]) ).
fof(f414,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f363]) ).
fof(f415,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f416,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f344]) ).
fof(f417,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f418,plain,
$false,
inference(sat_refutation,[status(thm)],[f372,f415,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM557+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 02:39:55 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.07/0.39 % Refutation found
% 0.07/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.067090 seconds
% 0.12/0.42 % CPU time: 0.166565 seconds
% 0.12/0.42 % Total memory used: 108.711 MB
% 0.12/0.42 % Net memory used: 108.571 MB
%------------------------------------------------------------------------------