TSTP Solution File: RNG067+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG067+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 : Tue Apr 30 20:37:52 EDT 2024
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 24
% Syntax : Number of formulae : 82 ( 17 unt; 0 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(W0)
& aScalar0(W1) )
=> aScalar0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [W0,W1,W2,W3] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W2,W3) )
=> sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox/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/sandbox/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(W0)
| ~ aScalar0(W1)
| aScalar0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f84,plain,
! [W0,W1] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| aScalar0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f120,plain,
! [W0,W1,W2,W3] :
( ~ aScalar0(W0)
| ~ aScalar0(W1)
| ~ aScalar0(W2)
| ~ aScalar0(W3)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W2,W3)
| sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W3)) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X2,X3)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f191,plain,
aScalar0(xR),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f193,plain,
aScalar0(xP),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f195,plain,
aScalar0(xS),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f198,plain,
xN = sdtasdt0(xR,xS),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f200,plain,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f201,plain,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(cnf_transformation,[status(esa)],[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(esa)],[f60]) ).
fof(f225,plain,
( spl0_4
<=> aScalar0(xR) ),
introduced(split_symbol_definition) ).
fof(f227,plain,
( ~ aScalar0(xR)
| spl0_4 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( spl0_5
<=> aScalar0(xS) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( ~ aScalar0(xS)
| spl0_5 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( spl0_6
<=> aScalar0(xN) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xS)
| aScalar0(xN) ),
inference(paramodulation,[status(thm)],[f198,f85]) ).
fof(f235,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f234,f225,f228,f231]) ).
fof(f236,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f195]) ).
fof(f237,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f191]) ).
fof(f239,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f251,plain,
( spl0_10
<=> aScalar0(sdtasdt0(xP,xP)) ),
introduced(split_symbol_definition) ).
fof(f253,plain,
( ~ aScalar0(sdtasdt0(xP,xP))
| spl0_10 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f306,plain,
( spl0_17
<=> aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))) ),
introduced(split_symbol_definition) ).
fof(f308,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| spl0_17 ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( spl0_18
<=> aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
introduced(split_symbol_definition) ).
fof(f311,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| spl0_18 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f330,plain,
( spl0_23
<=> aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP))) ),
introduced(split_symbol_definition) ).
fof(f332,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)))
| spl0_23 ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( spl0_24
<=> aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
introduced(split_symbol_definition) ).
fof(f335,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| spl0_24 ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( spl0_25
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN)) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| spl0_25 ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( spl0_26
<=> sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| spl0_26 ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(xN)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN) ),
inference(resolution,[status(thm)],[f121,f202]) ).
fof(f343,plain,
( ~ spl0_23
| ~ spl0_24
| ~ spl0_10
| ~ spl0_6
| ~ spl0_25
| ~ spl0_26 ),
inference(split_clause,[status(thm)],[f342,f330,f333,f251,f231,f336,f339]) ).
fof(f350,plain,
( $false
| spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f200]) ).
fof(f351,plain,
spl0_26,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f352,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(xN)
| spl0_24 ),
inference(resolution,[status(thm)],[f335,f83]) ).
fof(f353,plain,
( ~ spl0_18
| ~ spl0_6
| spl0_24 ),
inference(split_clause,[status(thm)],[f352,f309,f231,f333]) ).
fof(f354,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP))
| spl0_23 ),
inference(resolution,[status(thm)],[f332,f83]) ).
fof(f355,plain,
( ~ spl0_17
| ~ spl0_10
| spl0_23 ),
inference(split_clause,[status(thm)],[f354,f306,f251,f330]) ).
fof(f360,plain,
( spl0_27
<=> sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) ),
introduced(split_symbol_definition) ).
fof(f362,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| spl0_27 ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(xN)
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),xN)
| spl0_25 ),
inference(resolution,[status(thm)],[f338,f121]) ).
fof(f364,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_10
| ~ spl0_6
| ~ spl0_27
| ~ spl0_26
| spl0_25 ),
inference(split_clause,[status(thm)],[f363,f306,f309,f251,f231,f360,f339,f336]) ).
fof(f377,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f201]) ).
fof(f378,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f379,plain,
( spl0_30
<=> aScalar0(xP) ),
introduced(split_symbol_definition) ).
fof(f381,plain,
( ~ aScalar0(xP)
| spl0_30 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( ~ aScalar0(xP)
| ~ aScalar0(xP)
| spl0_10 ),
inference(resolution,[status(thm)],[f253,f85]) ).
fof(f383,plain,
( ~ spl0_30
| spl0_10 ),
inference(split_clause,[status(thm)],[f382,f379,f251]) ).
fof(f384,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f193]) ).
fof(f385,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f456,plain,
( spl0_39
<=> aScalar0(sdtasdt0(xR,xR)) ),
introduced(split_symbol_definition) ).
fof(f458,plain,
( ~ aScalar0(sdtasdt0(xR,xR))
| spl0_39 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( spl0_40
<=> aScalar0(sdtasdt0(xS,xS)) ),
introduced(split_symbol_definition) ).
fof(f461,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| spl0_40 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtasdt0(xS,xS))
| spl0_18 ),
inference(resolution,[status(thm)],[f311,f83]) ).
fof(f463,plain,
( ~ spl0_39
| ~ spl0_40
| spl0_18 ),
inference(split_clause,[status(thm)],[f462,f456,f459,f309]) ).
fof(f464,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| spl0_39 ),
inference(resolution,[status(thm)],[f458,f85]) ).
fof(f465,plain,
( ~ spl0_4
| spl0_39 ),
inference(split_clause,[status(thm)],[f464,f225,f456]) ).
fof(f466,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xS)
| spl0_40 ),
inference(resolution,[status(thm)],[f461,f85]) ).
fof(f467,plain,
( ~ spl0_5
| spl0_40 ),
inference(split_clause,[status(thm)],[f466,f228,f459]) ).
fof(f468,plain,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP))
| spl0_17 ),
inference(resolution,[status(thm)],[f308,f83]) ).
fof(f469,plain,
( ~ spl0_10
| spl0_17 ),
inference(split_clause,[status(thm)],[f468,f251,f306]) ).
fof(f470,plain,
$false,
inference(sat_refutation,[status(thm)],[f235,f237,f239,f343,f351,f353,f355,f364,f378,f383,f385,f463,f465,f467,f469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG067+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 22:41:29 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 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
% 0.19/0.42 % Elapsed time: 0.066224 seconds
% 0.19/0.42 % CPU time: 0.400371 seconds
% 0.19/0.42 % Total memory used: 67.748 MB
% 0.19/0.42 % Net memory used: 67.381 MB
%------------------------------------------------------------------------------