%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM482+1 : 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 01:40:41 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 9 unt; 5 def)
% Number of atoms : 111 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 116 ( 46 ~; 43 |; 16 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 28 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
( isPrime0(xk)
=> ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ( isPrime0(xk)
=> ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f47,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f51,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f64,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f65,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f124,plain,
! [W0,W1] :
( ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f125,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(NNF_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sK1_skl(W1,W0))
& aNaturalNumber0(sK1_skl(W1,W0)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f125]) ).
fof(f129,plain,
! [X0,X1,X2] :
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f156,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f164,plain,
( ! [W0] :
( ~ isPrime0(W0)
| ~ doDivides0(W0,xk)
| ~ aNaturalNumber0(W0) )
& isPrime0(xk) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f165,plain,
isPrime0(xk),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f173,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f129]) ).
fof(f179,plain,
( ~ isPrime0(xk)
| ~ doDivides0(xk,xk) ),
inference(resolution,[status(thm)],[f156,f166]) ).
fof(f180,definition,
( sQ0_spl
<=> doDivides0(xk,xk) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f183,definition,
( sQ1_spl
<=> isPrime0(xk) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ1_spl
| ~ isPrime0(xk) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f179,f180,f183]) ).
fof(f212,definition,
( sQ7_spl
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ7_spl
| ~ aNaturalNumber0(sz10) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f231,definition,
( sQ11_spl
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ11_spl
| ~ aNaturalNumber0(xk) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f173,f52]) ).
fof(f361,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f156]) ).
fof(f362,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f376,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f47]) ).
fof(f377,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f385,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[f65,f156]) ).
fof(f429,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0(xk,xk)
| ~ aNaturalNumber0(xk) ),
inference(paramodulation,[status(thm)],[f385,f239]) ).
fof(f430,plain,
( ~ sQ7_spl
| sQ0_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f429,f231,f180,f212]) ).
fof(f431,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f165]) ).
fof(f432,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f433,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f362,f377,f430,f432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM482+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:33:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.045952 seconds
% 0.14/0.41 % CPU time: 0.147366 seconds
% 0.14/0.41 % Total memory used: 65.250 MB
% 0.14/0.41 % Net memory used: 65.121 MB
%------------------------------------------------------------------------------