%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG067+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 : n017.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 02:04:50 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 17 unt; 14 def)
% Number of atoms : 198 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 203 ( 87 ~; 88 |; 10 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W3)
& aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( ( sdtlseqdt0(W2,W3)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,conjecture,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f82,plain,
! [W0,W1] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f83,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f85,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f120,plain,
! [W0,W1,W2,W3] :
( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3))
| ~ sdtlseqdt0(W2,W3)
| ~ sdtlseqdt0(W0,W1)
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f191,plain,
aScalar0(xR),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f193,plain,
aScalar0(xP),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f195,plain,
aScalar0(xS),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f198,plain,
xN = sdtasdt0(xR,xS),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f200,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f201,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f202,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f254,plain,
( aScalar0(xN)
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(paramodulation,[status(thm)],[f198,f85]) ).
fof(f255,definition,
( sQ7_spl
<=> aScalar0(xR) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ7_spl
| ~ aScalar0(xR) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ8_spl
<=> aScalar0(xS) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ8_spl
| ~ aScalar0(xS) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ9_spl
<=> aScalar0(xN) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f254,f255,f258,f261]) ).
fof(f265,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f195]) ).
fof(f266,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f267,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f191]) ).
fof(f268,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(xN)
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP))) ),
inference(resolution,[status(thm)],[f121,f202]) ).
fof(f270,definition,
( sQ10_spl
<=> aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ10_spl
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP))) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ11_spl
<=> aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ11_spl
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,definition,
( sQ12_spl
<=> aScalar0(sdtasdt0(xP,xP)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ12_spl
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ13_spl
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ13_spl
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ14_spl
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ14_spl
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f269,f270,f273,f276,f261,f279,f282]) ).
fof(f286,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f200]) ).
fof(f287,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ13_spl
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(xN)
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(resolution,[status(thm)],[f281,f121]) ).
fof(f290,definition,
( sQ15_spl
<=> aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ15_spl
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
( sQ16_spl
<=> aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ16_spl
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ17_spl
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ17_spl
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f288,f290,f293,f276,f261,f296,f282,f279]) ).
fof(f304,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f201]) ).
fof(f305,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ12_spl
| ~ aScalar0(xP)
| ~ aScalar0(xP) ),
inference(resolution,[status(thm)],[f278,f85]) ).
fof(f307,definition,
( sQ19_spl
<=> aScalar0(xP) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ19_spl
| ~ aScalar0(xP) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( sQ12_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f306,f307,f276]) ).
fof(f311,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f193]) ).
fof(f312,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ15_spl
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(resolution,[status(thm)],[f83,f292]) ).
fof(f314,plain,
( sQ16_spl
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(resolution,[status(thm)],[f83,f295]) ).
fof(f315,plain,
( sQ10_spl
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
inference(resolution,[status(thm)],[f83,f272]) ).
fof(f316,plain,
( sQ11_spl
| ~ aScalar0(xN)
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
inference(resolution,[status(thm)],[f83,f275]) ).
fof(f317,plain,
( sQ15_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f313,f276,f290]) ).
fof(f318,definition,
( sQ20_spl
<=> aScalar0(sdtasdt0(xR,xR)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ20_spl
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,definition,
( sQ21_spl
<=> aScalar0(sdtasdt0(xS,xS)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ21_spl
| ~ aScalar0(sdtasdt0(xS,xS)) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,plain,
( sQ16_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f314,f318,f321,f293]) ).
fof(f325,plain,
( sQ10_spl
| ~ sQ12_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f315,f290,f276,f270]) ).
fof(f326,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f316,f293,f261,f273]) ).
fof(f327,plain,
( sQ20_spl
| ~ aScalar0(xR)
| ~ aScalar0(xR) ),
inference(resolution,[status(thm)],[f320,f85]) ).
fof(f328,plain,
( sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f327,f255,f318]) ).
fof(f329,plain,
( sQ21_spl
| ~ aScalar0(xS)
| ~ aScalar0(xS) ),
inference(resolution,[status(thm)],[f323,f85]) ).
fof(f330,plain,
( sQ21_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f329,f258,f321]) ).
fof(f331,plain,
$false,
inference(sat_refutation,[status(thm)],[f264,f266,f268,f285,f287,f299,f305,f310,f312,f317,f324,f325,f326,f328,f330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG067+2 : 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 : n017.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 04:12:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.082128 seconds
% 0.14/0.45 % CPU time: 0.234954 seconds
% 0.14/0.45 % Total memory used: 63.794 MB
% 0.14/0.45 % Net memory used: 63.697 MB
%------------------------------------------------------------------------------