%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG046+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:04:46 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 11 unt; 4 def)
% Number of atoms : 98 ( 34 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 88 ( 32 ~; 31 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [W0] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aScalar0(W0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
( aScalar0(xy)
& aScalar0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f46,plain,
! [W0] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
! [X0] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [W0] :
( ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(W0)) = W0
& sdtpldt0(smndt0(W0),W0) = sz0z00
& sdtpldt0(W0,smndt0(W0)) = sz0z00
& sdtasdt0(sz0z00,W0) = sz0z00
& sdtasdt0(W0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,W0) = W0
& sdtpldt0(W0,sz0z00) = W0 )
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f55,plain,
! [X0] :
( smndt0(smndt0(X0)) = X0
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f67,plain,
! [W0,W1] :
( ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1))
& sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
aScalar0(xx),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f71,plain,
aScalar0(xy),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f72,plain,
sdtasdt0(smndt0(xx),smndt0(xy)) != sdtasdt0(xx,xy),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f90,plain,
smndt0(smndt0(xy)) = xy,
inference(resolution,[status(thm)],[f55,f71]) ).
fof(f91,plain,
smndt0(smndt0(xx)) = xx,
inference(resolution,[status(thm)],[f55,f70]) ).
fof(f93,definition,
( sQ4_spl
<=> aScalar0(smndt0(xy)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ4_spl
| aScalar0(smndt0(xy)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f95,plain,
( sQ4_spl
| ~ aScalar0(smndt0(xy)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f100,plain,
( sQ4_spl
| ~ aScalar0(xy) ),
inference(resolution,[status(thm)],[f95,f47]) ).
fof(f101,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f71]) ).
fof(f102,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( aScalar0(xx)
| ~ aScalar0(smndt0(xx)) ),
inference(paramodulation,[status(thm)],[f91,f47]) ).
fof(f105,definition,
( sQ6_spl
<=> aScalar0(smndt0(xx)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( sQ6_spl
| ~ aScalar0(smndt0(xx)) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ7_spl
<=> aScalar0(xx) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f104,f105,f108]) ).
fof(f112,plain,
! [X0] :
( ~ sQ4_spl
| sdtasdt0(X0,smndt0(smndt0(xy))) = smndt0(sdtasdt0(X0,smndt0(xy)))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f68,f94]) ).
fof(f117,plain,
! [X0] :
( ~ sQ4_spl
| sdtasdt0(X0,xy) = smndt0(sdtasdt0(X0,smndt0(xy)))
| ~ aScalar0(X0) ),
inference(forward_demodulation,[status(thm)],[f90,f112]) ).
fof(f133,plain,
( sQ6_spl
| ~ aScalar0(xx) ),
inference(resolution,[status(thm)],[f47,f107]) ).
fof(f137,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f70]) ).
fof(f138,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f165,plain,
( ~ sQ4_spl
| sdtasdt0(xx,xy) = smndt0(sdtasdt0(xx,smndt0(xy))) ),
inference(resolution,[status(thm)],[f117,f70]) ).
fof(f168,plain,
( ~ sQ4_spl
| sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy)
| ~ aScalar0(smndt0(xy))
| ~ aScalar0(xx) ),
inference(paramodulation,[status(thm)],[f165,f69]) ).
fof(f170,definition,
( sQ11_spl
<=> sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ11_spl
| sdtasdt0(smndt0(xx),smndt0(xy)) = sdtasdt0(xx,xy) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f168,f108,f93,f170]) ).
fof(f181,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f72]) ).
fof(f182,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f183,plain,
$false,
inference(sat_refutation,[status(thm)],[f102,f111,f138,f173,f182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG046+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.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 04:15:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.037323 seconds
% 0.10/0.41 % CPU time: 0.128104 seconds
% 0.10/0.41 % Total memory used: 65.913 MB
% 0.10/0.41 % Net memory used: 65.753 MB
%------------------------------------------------------------------------------