%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM519+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 01:40:50 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 5 unt; 4 def)
% Number of atoms : 73 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 26 ~; 23 |; 20 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 4 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f51,hypothesis,
( ( doDivides0(xr,xm)
& ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) )
| ( doDivides0(xr,xn)
& ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
~ ( doDivides0(xr,xn)
| ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
~ ( doDivides0(xr,xm)
| ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f243,definition,
( sP2_prd
<=> ( doDivides0(xr,xn)
& ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f244,plain,
( ( doDivides0(xr,xm)
& ? [W0] :
( xm = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) )
| sP2_prd ),
inference(formula_renaming,[status(thm)],[f51,f243]) ).
fof(f245,plain,
( ( doDivides0(xr,xm)
& xm = sdtasdt0(xr,sK12_skl)
& aNaturalNumber0(sK12_skl) )
| sP2_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(W0,sK12_skl)],[f244]) ).
fof(f248,plain,
( doDivides0(xr,xm)
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f249,plain,
( ~ doDivides0(xr,xn)
& ! [W0] :
( xn != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f251,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f252,plain,
( ~ doDivides0(xr,xm)
& ! [W0] :
( xm != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f254,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f280,plain,
( ( ~ doDivides0(xr,xn)
| ! [W0] :
( xn != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) )
| sP2_prd )
& ( ( doDivides0(xr,xn)
& ? [W0] :
( xn = sdtasdt0(xr,W0)
& aNaturalNumber0(W0) ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f243]) ).
fof(f281,plain,
( ( ~ doDivides0(xr,xn)
| ! [W0] :
( xn != sdtasdt0(xr,W0)
| ~ aNaturalNumber0(W0) )
| sP2_prd )
& ( ( doDivides0(xr,xn)
& xn = sdtasdt0(xr,sK16_skl)
& aNaturalNumber0(sK16_skl) )
| ~ sP2_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(W0,sK16_skl)],[f280]) ).
fof(f284,plain,
( doDivides0(xr,xn)
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f286,definition,
( sQ0_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f297,definition,
( sQ3_spl
<=> doDivides0(xr,xm) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ3_spl
| doDivides0(xr,xm) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f248,f286,f297]) ).
fof(f309,definition,
( sQ6_spl
<=> doDivides0(xr,xn) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ6_spl
| doDivides0(xr,xn) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f284,f286,f309]) ).
fof(f582,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f251]) ).
fof(f583,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f584,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f254]) ).
fof(f585,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
$false,
inference(sat_refutation,[status(thm)],[f300,f312,f583,f585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM519+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:36:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.064963 seconds
% 0.12/0.44 % CPU time: 0.203094 seconds
% 0.12/0.44 % Total memory used: 108.060 MB
% 0.12/0.44 % Net memory used: 107.824 MB
%------------------------------------------------------------------------------