TSTP Solution File: NUM480+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM480+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:29:19 EDT 2023
% Result : Theorem 0.06s 0.28s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 16 unt; 1 def)
% Number of atoms : 187 ( 59 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 199 ( 77 ~; 80 |; 27 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 (; 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00
& doDivides0(W0,W1) )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
( xl != sz00
& ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xl,W0) )
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f50,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f61,plain,
! [W0,W1,W2] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W2)
| sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f129,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f130,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ! [W2] :
( ( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(NNF_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = sz00
| ~ doDivides0(W0,W1)
| ( ! [W2] :
( W2 != sdtsldt0(W1,W0)
| ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ! [W2] :
( W2 = sdtsldt0(W1,W0)
| ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ),
inference(miniscoping,[status(esa)],[f130]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f143,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f145,plain,
( xl != sz00
& aNaturalNumber0(sk0_2)
& xm = sdtasdt0(xl,sk0_2)
& doDivides0(xl,xm) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f146,plain,
xl != sz00,
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f147,plain,
aNaturalNumber0(sk0_2),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f148,plain,
xm = sdtasdt0(xl,sk0_2),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f149,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f150,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f154,plain,
sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f155,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f156,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl) ),
inference(pre_NNF_transformation,[status(esa)],[f41]) ).
fof(f159,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cnf_transformation,[status(esa)],[f156]) ).
fof(f170,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| X0 = sz00
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ aNaturalNumber0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f134]) ).
fof(f171,plain,
( spl0_0
<=> aNaturalNumber0(xl) ),
introduced(split_symbol_definition) ).
fof(f173,plain,
( ~ aNaturalNumber0(xl)
| spl0_0 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f184,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f143]) ).
fof(f185,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f196,plain,
( spl0_5
<=> xl = sz00 ),
introduced(split_symbol_definition) ).
fof(f197,plain,
( xl = sz00
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f225,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ doDivides0(X0,sdtasdt0(X0,X1))
| X1 = sdtsldt0(sdtasdt0(X0,X1),X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f51]) ).
fof(f244,plain,
( spl0_16
<=> doDivides0(xl,sdtasdt0(xl,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f246,plain,
( ~ doDivides0(xl,sdtasdt0(xl,sk0_2))
| spl0_16 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( spl0_17
<=> sk0_2 = sdtsldt0(xm,xl) ),
introduced(split_symbol_definition) ).
fof(f248,plain,
( sk0_2 = sdtsldt0(xm,xl)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( spl0_18
<=> aNaturalNumber0(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f252,plain,
( ~ aNaturalNumber0(sk0_2)
| spl0_18 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ aNaturalNumber0(xl)
| xl = sz00
| ~ doDivides0(xl,sdtasdt0(xl,sk0_2))
| sk0_2 = sdtsldt0(xm,xl)
| ~ aNaturalNumber0(sk0_2) ),
inference(paramodulation,[status(thm)],[f148,f225]) ).
fof(f254,plain,
( ~ spl0_0
| spl0_5
| ~ spl0_16
| spl0_17
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f253,f171,f196,f244,f247,f250]) ).
fof(f262,plain,
( ~ doDivides0(xl,xm)
| spl0_16 ),
inference(forward_demodulation,[status(thm)],[f148,f246]) ).
fof(f263,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f149]) ).
fof(f264,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f265,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f147]) ).
fof(f266,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f146]) ).
fof(f269,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f308,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sk0_2))
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f248,f159]) ).
fof(f318,plain,
( sdtasdt0(sdtasdt0(xl,xn),sk0_2) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f248,f155]) ).
fof(f319,plain,
( sdtasdt0(sdtasdt0(xl,xn),sk0_2) = sdtasdt0(xn,xm)
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f154,f318]) ).
fof(f320,plain,
( spl0_27
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f322,plain,
( ~ aNaturalNumber0(xn)
| spl0_27 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( spl0_28
<=> sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f324,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sk0_2))
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sk0_2)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sk0_2))
| ~ spl0_17 ),
inference(paramodulation,[status(thm)],[f319,f62]) ).
fof(f327,plain,
( ~ spl0_0
| ~ spl0_27
| ~ spl0_18
| spl0_28
| ~ spl0_17 ),
inference(split_clause,[status(thm)],[f326,f171,f320,f250,f323,f247]) ).
fof(f366,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f150]) ).
fof(f367,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( $false
| ~ spl0_17
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f308]) ).
fof(f369,plain,
( ~ spl0_17
| ~ spl0_28 ),
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f370,plain,
$false,
inference(sat_refutation,[status(thm)],[f185,f254,f264,f266,f269,f327,f367,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM480+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 30 10:02:16 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.06/0.27 % Drodi V3.5.1
% 0.06/0.28 % Refutation found
% 0.06/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.29 % Elapsed time: 0.022808 seconds
% 0.06/0.29 % CPU time: 0.042917 seconds
% 0.06/0.29 % Memory used: 15.104 MB
%------------------------------------------------------------------------------