%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:40:39 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 15 unt; 7 def)
% Number of atoms : 108 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 39 |; 10 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f52,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f74,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f75,plain,
! [X0,X1,X2] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f141,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f143,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f152,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f162,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f165,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f166,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f171,definition,
( sQ0_spl
<=> aNaturalNumber0(xp) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ0_spl
| ~ aNaturalNumber0(xp) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ1_spl
<=> aNaturalNumber0(xr) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ1_spl
| ~ aNaturalNumber0(xr) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f185,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f162]) ).
fof(f186,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f189,definition,
( sQ4_spl
<=> aNaturalNumber0(xl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ4_spl
| ~ aNaturalNumber0(xl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f200,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f141]) ).
fof(f201,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f204,definition,
( sQ7_spl
<=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ7_spl
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ8_spl
<=> aNaturalNumber0(sdtasdt0(xl,xr)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ8_spl
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f218,plain,
( sQ8_spl
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f209,f53]) ).
fof(f219,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f218,f189,f174,f207]) ).
fof(f220,plain,
( sQ7_spl
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[f206,f53]) ).
fof(f221,plain,
( sQ7_spl
| ~ sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f220,f189,f171,f204]) ).
fof(f222,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f173]) ).
fof(f223,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f251,plain,
( sdtasdt0(xl,xr) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(resolution,[status(thm)],[f75,f165]) ).
fof(f262,definition,
( sQ16_spl
<=> aNaturalNumber0(xn) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ16_spl
| ~ aNaturalNumber0(xn) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,definition,
( sQ17_spl
<=> sdtasdt0(xl,xr) = xn ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ17_spl
| sdtasdt0(xl,xr) = xn ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( sQ17_spl
| ~ sQ16_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f251,f204,f207,f262,f265]) ).
fof(f295,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f143]) ).
fof(f296,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f299,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f166]) ).
fof(f300,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f301,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f201,f219,f221,f223,f268,f296,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.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 02:33:21 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.37 % 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
% 0.12/0.43 % Elapsed time: 0.058284 seconds
% 0.12/0.43 % CPU time: 0.169278 seconds
% 0.12/0.43 % Total memory used: 104.602 MB
% 0.12/0.43 % Net memory used: 104.490 MB
%------------------------------------------------------------------------------