%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM548+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 : n014.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 01:40:57 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 11 unt; 3 def)
% Number of atoms : 61 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 18 ~; 17 |; 9 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
~ isFinite0(xQ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f184,plain,
! [W0] :
( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f185,plain,
! [W0] :
( ( ( ~ isFinite0(W0)
| aElementOf0(sbrdtbr0(W0),szNzAzT0) )
& ( isFinite0(W0)
| ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f184]) ).
fof(f186,plain,
! [X0] :
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f266,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f301,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f302,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f305,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f307,plain,
~ isFinite0(xQ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f345,plain,
( isFinite0(xQ)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f305,f186]) ).
fof(f346,definition,
( sQ0_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ0_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ1_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ1_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,definition,
( sQ2_spl
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ2_spl
| isFinite0(xQ) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f345,f346,f349,f352]) ).
fof(f356,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f307]) ).
fof(f357,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f302]) ).
fof(f359,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f476,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f266]) ).
fof(f477,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f476]) ).
fof(f478,plain,
$false,
inference(sat_refutation,[status(thm)],[f355,f357,f359,f477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM548+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:39:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.052497 seconds
% 0.14/0.43 % CPU time: 0.148541 seconds
% 0.14/0.43 % Total memory used: 80.873 MB
% 0.14/0.43 % Net memory used: 80.784 MB
%------------------------------------------------------------------------------