TSTP Solution File: NUM529+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM529+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:35:01 EDT 2024
% Result : Theorem 1.71s 0.62s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 91 ( 24 unt; 1 def)
% Number of atoms : 288 ( 77 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 329 ( 132 ~; 145 |; 27 &)
% ( 15 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != W1
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
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(f39,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2)
& W0 != sz00
& W1 != sz00
& W2 != sz00 )
=> ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0)
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
( xm != xn
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f75,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f129,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| W0 = W1
| ~ sdtlseqdt0(W0,W1)
| iLess0(W0,W1) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| iLess0(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f137,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(f138,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)],[f137]) ).
fof(f139,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)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 != sdtsldt0(X1,X0)
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[status(esa)],[f139]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 != sdtsldt0(X1,X0)
| X1 = sdtasdt0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f139]) ).
fof(f168,plain,
! [W0,W1,W2] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W2)
| ~ isPrime0(W2)
| ~ doDivides0(W2,sdtasdt0(W0,W1))
| doDivides0(W2,W0)
| doDivides0(W2,W1) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| doDivides0(X2,X0)
| doDivides0(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f170,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f171,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f172,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f173,plain,
xn != sz00,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f174,plain,
xm != sz00,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f175,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f176,plain,
! [W0,W1,W2] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W2)
| W0 = sz00
| W1 = sz00
| W2 = sz00
| sdtasdt0(W2,sdtasdt0(W1,W1)) != sdtasdt0(W0,W0)
| ~ iLess0(W0,xn)
| ~ isPrime0(W2) ),
inference(pre_NNF_transformation,[status(esa)],[f41]) ).
fof(f177,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = sz00
| X2 = sz00
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f179,plain,
isPrime0(xp),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f180,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f182,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f183,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f184,plain,
xm != xn,
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f185,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f193,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f140]) ).
fof(f194,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X1 = sdtasdt0(X0,sdtsldt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f141]) ).
fof(f224,plain,
( spl0_4
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f226,plain,
( ~ aNaturalNumber0(xn)
| spl0_4 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,plain,
( spl0_5
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f229,plain,
( ~ aNaturalNumber0(xm)
| spl0_5 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f233,plain,
( spl0_7
<=> xn = xm ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( xn = xm
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f246,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f170]) ).
fof(f247,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f171]) ).
fof(f249,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f184]) ).
fof(f251,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f278,plain,
( spl0_13
<=> iLess0(xm,xn) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xm = xn
| iLess0(xm,xn) ),
inference(resolution,[status(thm)],[f130,f185]) ).
fof(f282,plain,
( ~ spl0_5
| ~ spl0_4
| spl0_7
| spl0_13 ),
inference(split_clause,[status(thm)],[f281,f227,f224,f233,f278]) ).
fof(f292,plain,
( spl0_15
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f294,plain,
( ~ aNaturalNumber0(xp)
| spl0_15 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f325,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f172]) ).
fof(f326,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f329,plain,
( spl0_22
<=> xm = sz00 ),
introduced(split_symbol_definition) ).
fof(f330,plain,
( xm = sz00
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f354,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f174]) ).
fof(f355,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f431,plain,
( spl0_39
<=> xp = sz00 ),
introduced(split_symbol_definition) ).
fof(f432,plain,
( xp = sz00
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f477,plain,
( $false
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f175]) ).
fof(f478,plain,
~ spl0_39,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f482,plain,
( spl0_47
<=> xn = sz00 ),
introduced(split_symbol_definition) ).
fof(f483,plain,
( xn = sz00
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f524,plain,
( $false
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f173]) ).
fof(f525,plain,
~ spl0_47,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f1653,plain,
( spl0_164
<=> aNaturalNumber0(xq) ),
introduced(split_symbol_definition) ).
fof(f1768,plain,
( spl0_183
<=> xq = sz00 ),
introduced(split_symbol_definition) ).
fof(f1769,plain,
( xq = sz00
| ~ spl0_183 ),
inference(component_clause,[status(thm)],[f1768]) ).
fof(f1771,plain,
( spl0_184
<=> isPrime0(xp) ),
introduced(split_symbol_definition) ).
fof(f1773,plain,
( ~ isPrime0(xp)
| spl0_184 ),
inference(component_clause,[status(thm)],[f1771]) ).
fof(f1774,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| xm = sz00
| xq = sz00
| xp = sz00
| ~ iLess0(xm,xn)
| ~ isPrime0(xp) ),
inference(resolution,[status(thm)],[f183,f177]) ).
fof(f1775,plain,
( ~ spl0_5
| ~ spl0_164
| ~ spl0_15
| spl0_22
| spl0_183
| spl0_39
| ~ spl0_13
| ~ spl0_184 ),
inference(split_clause,[status(thm)],[f1774,f227,f1653,f292,f329,f1768,f431,f278,f1771]) ).
fof(f1879,plain,
( $false
| spl0_184 ),
inference(forward_subsumption_resolution,[status(thm)],[f1773,f179]) ).
fof(f1880,plain,
spl0_184,
inference(contradiction_clause,[status(thm)],[f1879]) ).
fof(f1974,plain,
( spl0_219
<=> doDivides0(xp,xn) ),
introduced(split_symbol_definition) ).
fof(f1977,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| doDivides0(xp,xn) ),
inference(resolution,[status(thm)],[f180,f169]) ).
fof(f1978,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_184
| spl0_219 ),
inference(split_clause,[status(thm)],[f1977,f224,f292,f1771,f1974]) ).
fof(f1991,plain,
( spl0_222
<=> xn = sdtasdt0(xp,xq) ),
introduced(split_symbol_definition) ).
fof(f1992,plain,
( xn = sdtasdt0(xp,xq)
| ~ spl0_222 ),
inference(component_clause,[status(thm)],[f1991]) ).
fof(f1994,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xp = sz00
| ~ doDivides0(xp,xn)
| xn = sdtasdt0(xp,xq) ),
inference(paramodulation,[status(thm)],[f182,f194]) ).
fof(f1995,plain,
( ~ spl0_15
| ~ spl0_4
| spl0_39
| ~ spl0_219
| spl0_222 ),
inference(split_clause,[status(thm)],[f1994,f292,f224,f431,f1974,f1991]) ).
fof(f1996,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xp = sz00
| ~ doDivides0(xp,xn)
| aNaturalNumber0(xq) ),
inference(paramodulation,[status(thm)],[f182,f193]) ).
fof(f1997,plain,
( ~ spl0_15
| ~ spl0_4
| spl0_39
| ~ spl0_219
| spl0_164 ),
inference(split_clause,[status(thm)],[f1996,f292,f224,f431,f1974,f1653]) ).
fof(f2260,plain,
( xn = sdtasdt0(xp,sz00)
| ~ spl0_183
| ~ spl0_222 ),
inference(forward_demodulation,[status(thm)],[f1769,f1992]) ).
fof(f2261,plain,
( ~ aNaturalNumber0(xp)
| xn = sz00
| ~ spl0_183
| ~ spl0_222 ),
inference(paramodulation,[status(thm)],[f2260,f75]) ).
fof(f2262,plain,
( ~ spl0_15
| spl0_47
| ~ spl0_183
| ~ spl0_222 ),
inference(split_clause,[status(thm)],[f2261,f292,f482,f1768,f1991]) ).
fof(f2360,plain,
$false,
inference(sat_refutation,[status(thm)],[f247,f249,f251,f282,f326,f355,f478,f525,f1775,f1880,f1978,f1995,f1997,f2262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM529+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 20:58:03 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.37 % Drodi V3.6.0
% 1.71/0.62 % Refutation found
% 1.71/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.71/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.71/0.64 % Elapsed time: 0.282268 seconds
% 1.71/0.64 % CPU time: 2.012304 seconds
% 1.71/0.64 % Total memory used: 82.632 MB
% 1.71/0.64 % Net memory used: 80.781 MB
%------------------------------------------------------------------------------