%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG044+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 : n013.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 138.98s 18.01s
% Output : CNFRefutation 138.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 25 unt; 9 def)
% Number of atoms : 137 ( 17 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 111 ( 44 ~; 46 |; 9 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W1)
& aScalar0(W0) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0,W1,W2] :
( ( aScalar0(W2)
& aScalar0(W1)
& aScalar0(W0) )
=> ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f39,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f40,plain,
! [W0,W1] :
( aScalar0(sdtpldt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
! [X0,X1] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [W0,W1] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f43,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f60,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ aScalar0(X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(X0,X2),X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
aScalar0(xx),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f64,plain,
aScalar0(xy),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f65,plain,
aScalar0(xu),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f66,plain,
aScalar0(xv),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f67,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X1,sdtpldt0(X0,xv)) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X1,xv))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f61,f66]) ).
fof(f145,plain,
! [X0,X1] :
( sdtasdt0(sdtpldt0(X0,xy),X1) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(xy,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f64,f62]) ).
fof(f197,plain,
! [X0] :
( sdtasdt0(xy,sdtpldt0(X0,xv)) = sdtpldt0(sdtasdt0(xy,X0),sdtasdt0(xy,xv))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[f91,f64]) ).
fof(f198,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(sdtasdt0(xx,X0),sdtasdt0(xx,xv)) = sdtasdt0(xx,sdtpldt0(X0,xv)) ),
inference(resolution,[status(thm)],[f91,f63]) ).
fof(f302,plain,
aScalar0(sdtpldt0(xy,xy)),
inference(resolution,[status(thm)],[f41,f64]) ).
fof(f536,plain,
aScalar0(sdtasdt0(xx,xx)),
inference(resolution,[status(thm)],[f43,f63]) ).
fof(f538,plain,
aScalar0(sdtasdt0(xu,xu)),
inference(resolution,[status(thm)],[f43,f65]) ).
fof(f641,definition,
( sQ13_spl
<=> aScalar0(xu) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( sQ13_spl
| ~ aScalar0(xu) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f700,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f643,f65]) ).
fof(f701,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f745,definition,
( sQ27_spl
<=> aScalar0(xv) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f747,plain,
( sQ27_spl
| ~ aScalar0(xv) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f812,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f747,f66]) ).
fof(f813,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f812]) ).
fof(f888,definition,
( sQ45_spl
<=> aScalar0(xx) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( sQ45_spl
| ~ aScalar0(xx) ),
inference(component_clause,[status(thm)],[f888]) ).
fof(f952,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f890,f63]) ).
fof(f953,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f952]) ).
fof(f1004,definition,
( sQ62_spl
<=> aScalar0(sz0z00) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
( sQ62_spl
| ~ aScalar0(sz0z00) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1021,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1006,f39]) ).
fof(f1022,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f1021]) ).
fof(f1372,definition,
( sQ78_spl
<=> aScalar0(xy) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1374,plain,
( sQ78_spl
| ~ aScalar0(xy) ),
inference(component_clause,[status(thm)],[f1372]) ).
fof(f1375,definition,
( sQ79_spl
<=> aScalar0(sdtpldt0(xy,xy)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( sQ79_spl
| ~ aScalar0(sdtpldt0(xy,xy)) ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1455,plain,
( sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1377,f302]) ).
fof(f1456,plain,
sQ79_spl,
inference(contradiction_clause,[status(thm)],[f1455]) ).
fof(f1457,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1374,f64]) ).
fof(f1458,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f1457]) ).
fof(f1784,plain,
sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) = sdtasdt0(xy,sdtpldt0(xu,xv)),
inference(resolution,[status(thm)],[f197,f65]) ).
fof(f1789,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(backward_demodulation,[status(thm)],[f1784,f67]) ).
fof(f1832,definition,
( sQ122_spl
<=> aScalar0(sdtasdt0(xu,xu)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1834,plain,
( sQ122_spl
| ~ aScalar0(sdtasdt0(xu,xu)) ),
inference(component_clause,[status(thm)],[f1832]) ).
fof(f1847,plain,
( sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1834,f538]) ).
fof(f1848,plain,
sQ122_spl,
inference(contradiction_clause,[status(thm)],[f1847]) ).
fof(f1956,definition,
( sQ128_spl
<=> aScalar0(sdtasdt0(xx,xx)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1958,plain,
( sQ128_spl
| ~ aScalar0(sdtasdt0(xx,xx)) ),
inference(component_clause,[status(thm)],[f1956]) ).
fof(f1975,plain,
( sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1958,f536]) ).
fof(f1976,plain,
sQ128_spl,
inference(contradiction_clause,[status(thm)],[f1975]) ).
fof(f1982,plain,
sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),
inference(resolution,[status(thm)],[f198,f65]) ).
fof(f1989,plain,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(backward_demodulation,[status(thm)],[f1982,f1789]) ).
fof(f1995,plain,
( ~ aScalar0(sdtpldt0(xu,xv))
| ~ aScalar0(xx) ),
inference(resolution,[status(thm)],[f1989,f145]) ).
fof(f2004,definition,
( sQ134_spl
<=> aScalar0(sdtpldt0(xu,xv)) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2006,plain,
( sQ134_spl
| ~ aScalar0(sdtpldt0(xu,xv)) ),
inference(component_clause,[status(thm)],[f2004]) ).
fof(f2010,plain,
( ~ sQ134_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f1995,f888,f2004]) ).
fof(f2011,plain,
( sQ134_spl
| ~ aScalar0(xv)
| ~ aScalar0(xu) ),
inference(resolution,[status(thm)],[f2006,f41]) ).
fof(f2012,plain,
( sQ134_spl
| ~ sQ27_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2011,f641,f745,f2004]) ).
fof(f2013,plain,
$false,
inference(sat_refutation,[status(thm)],[f701,f813,f953,f1022,f1456,f1458,f1848,f1976,f2010,f2012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG044+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:14:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 138.98/18.01 % Refutation found
% 138.98/18.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 138.98/18.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 85.94/18.12 % Elapsed time: 17.722510 seconds
% 85.94/18.12 % CPU time: 140.286058 seconds
% 85.94/18.12 % Total memory used: 778.420 MB
% 85.94/18.12 % Net memory used: 711.307 MB
%------------------------------------------------------------------------------