TSTP Solution File: RNG073+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG073+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:32:47 EDT 2023
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 182 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 71 ~; 74 |; 11 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 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(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtlseqdt0(sz0z00,W0)
& sdtlseqdt0(sz0z00,W1)
& sdtasdt0(W0,W0) = sdtasdt0(W1,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
& sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,conjecture,
sdtpldt0(xR,xS) = sdtpldt0(xP,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f87,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| aScalar0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f87]) ).
fof(f89,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| aScalar0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f89]) ).
fof(f121,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f122,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f136,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| ~ sdtlseqdt0(sz0z00,W0)
| ~ sdtlseqdt0(sz0z00,W1)
| sdtasdt0(W0,W0) != sdtasdt0(W1,W1)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f136]) ).
fof(f196,plain,
aScalar0(xR),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f198,plain,
aScalar0(xP),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f200,plain,
aScalar0(xS),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f207,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f210,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f211,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f212,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f213,plain,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f229,plain,
( spl0_4
<=> aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
introduced(split_symbol_definition) ).
fof(f231,plain,
( ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| spl0_4 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( spl0_5
<=> aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( spl0_6
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
introduced(split_symbol_definition) ).
fof(f237,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| spl0_6 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( spl0_7
<=> sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) ),
introduced(split_symbol_definition) ).
fof(f239,plain,
( sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) ),
inference(resolution,[status(thm)],[f122,f212]) ).
fof(f242,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f241,f229,f232,f235,f238]) ).
fof(f262,plain,
( spl0_13
<=> aScalar0(sdtpldt0(xP,xP)) ),
introduced(split_symbol_definition) ).
fof(f264,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| spl0_13 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( spl0_14
<=> aScalar0(sdtpldt0(xR,xS)) ),
introduced(split_symbol_definition) ).
fof(f267,plain,
( ~ aScalar0(sdtpldt0(xR,xS))
| spl0_14 ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f271,plain,
( spl0_16
<=> sdtpldt0(xP,xP) = sdtpldt0(xR,xS) ),
introduced(split_symbol_definition) ).
fof(f272,plain,
( sdtpldt0(xP,xP) = sdtpldt0(xR,xS)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f307,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f207]) ).
fof(f308,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f322,plain,
( spl0_27
<=> aScalar0(xR) ),
introduced(split_symbol_definition) ).
fof(f324,plain,
( ~ aScalar0(xR)
| spl0_27 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( spl0_28
<=> aScalar0(xS) ),
introduced(split_symbol_definition) ).
fof(f327,plain,
( ~ aScalar0(xS)
| spl0_28 ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xS)
| spl0_14 ),
inference(resolution,[status(thm)],[f267,f88]) ).
fof(f329,plain,
( ~ spl0_27
| ~ spl0_28
| spl0_14 ),
inference(split_clause,[status(thm)],[f328,f322,f325,f265]) ).
fof(f330,plain,
( $false
| spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f200]) ).
fof(f331,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f332,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f196]) ).
fof(f333,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f334,plain,
( spl0_29
<=> aScalar0(xP) ),
introduced(split_symbol_definition) ).
fof(f336,plain,
( ~ aScalar0(xP)
| spl0_29 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| spl0_13 ),
inference(resolution,[status(thm)],[f264,f88]) ).
fof(f338,plain,
( ~ spl0_29
| spl0_13 ),
inference(split_clause,[status(thm)],[f337,f334,f262]) ).
fof(f339,plain,
( $false
| spl0_29 ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f198]) ).
fof(f340,plain,
spl0_29,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f366,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xP,xP))
| spl0_4 ),
inference(resolution,[status(thm)],[f90,f231]) ).
fof(f367,plain,
( ~ spl0_13
| spl0_4 ),
inference(split_clause,[status(thm)],[f366,f262,f229]) ).
fof(f439,plain,
( ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xR,xS))
| spl0_5 ),
inference(resolution,[status(thm)],[f234,f90]) ).
fof(f440,plain,
( ~ spl0_14
| spl0_5 ),
inference(split_clause,[status(thm)],[f439,f265,f232]) ).
fof(f443,plain,
( spl0_42
<=> sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
introduced(split_symbol_definition) ).
fof(f445,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| spl0_42 ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( spl0_43
<=> sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
introduced(split_symbol_definition) ).
fof(f448,plain,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| spl0_43 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| sdtpldt0(xP,xP) = sdtpldt0(xR,xS)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f239,f137]) ).
fof(f450,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_42
| ~ spl0_43
| spl0_16
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f449,f262,f265,f443,f446,f271,f238]) ).
fof(f509,plain,
( $false
| spl0_42 ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f211]) ).
fof(f510,plain,
spl0_42,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( $false
| spl0_43 ),
inference(forward_subsumption_resolution,[status(thm)],[f448,f210]) ).
fof(f512,plain,
spl0_43,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f213]) ).
fof(f514,plain,
~ spl0_16,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
$false,
inference(sat_refutation,[status(thm)],[f242,f308,f329,f331,f333,f338,f340,f367,f440,f450,f510,f512,f514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG073+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n008.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 10:39:08 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.47 % Elapsed time: 0.166334 seconds
% 0.15/0.47 % CPU time: 0.733740 seconds
% 0.15/0.47 % Memory used: 69.887 MB
%------------------------------------------------------------------------------