TSTP Solution File: NUM504+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:29:26 EDT 2023
% Result : Theorem 2.79s 0.72s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 100 ( 25 unt; 2 def)
% Number of atoms : 276 ( 80 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 298 ( 122 ~; 111 |; 39 &)
% ( 19 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 38 (; 37 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> 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(f37,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( W1 = sz10
| W1 = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f62,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f109,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| W0 = W1 ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f141,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(f142,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)],[f141]) ).
fof(f143,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)],[f142]) ).
fof(f145,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)],[f143]) ).
fof(f157,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( isPrime0(W0)
<=> ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f158,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& W1 != sz10
& W1 != W0 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f157]) ).
fof(f159,plain,
! [W0] :
( ~ aNaturalNumber0(W0)
| ( ( ~ isPrime0(W0)
| ( W0 != sz00
& W0 != sz10
& ! [W1] :
( ~ aNaturalNumber0(W1)
| ~ doDivides0(W1,W0)
| W1 = sz10
| W1 = W0 ) ) )
& ( isPrime0(W0)
| W0 = sz00
| W0 = sz10
| ( aNaturalNumber0(sk0_2(W0))
& doDivides0(sk0_2(W0),W0)
& sk0_2(W0) != sz10
& sk0_2(W0) != W0 ) ) ) ),
inference(skolemization,[status(esa)],[f158]) ).
fof(f160,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| X0 != sz00 ),
inference(cnf_transformation,[status(esa)],[f159]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f173,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f174,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f177,plain,
isPrime0(xp),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f178,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f181,plain,
xn != xp,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f183,plain,
xm != xp,
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f185,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f186,plain,
( xk != sz00
& xk != sz10 ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f187,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f186]) ).
fof(f197,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f198,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f200,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f213,plain,
( spl0_2
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f215,plain,
( ~ aNaturalNumber0(xp)
| spl0_2 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( spl0_3
<=> xp = sz00 ),
introduced(split_symbol_definition) ).
fof(f219,plain,
( ~ aNaturalNumber0(xp)
| xp != sz00 ),
inference(resolution,[status(thm)],[f160,f177]) ).
fof(f220,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f219,f213,f216]) ).
fof(f221,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f174]) ).
fof(f222,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f235,plain,
( spl0_6
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f237,plain,
( ~ aNaturalNumber0(xm)
| spl0_6 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f243,plain,
( spl0_8
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f245,plain,
( ~ aNaturalNumber0(xn)
| spl0_8 ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f251,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f173]) ).
fof(f252,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f172]) ).
fof(f254,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f324,plain,
( spl0_18
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(split_symbol_definition) ).
fof(f326,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl0_18 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f335,plain,
( spl0_21
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f337,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl0_21 ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( spl0_22
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f340,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| spl0_22 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( spl0_23
<=> sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
introduced(split_symbol_definition) ).
fof(f342,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xn,xm)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ),
inference(resolution,[status(thm)],[f110,f198]) ).
fof(f345,plain,
( ~ spl0_18
| ~ spl0_21
| ~ spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f344,f324,f335,f338,f341]) ).
fof(f368,plain,
( spl0_30
<=> xp = xm ),
introduced(split_symbol_definition) ).
fof(f369,plain,
( xp = xm
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f376,plain,
( spl0_32
<=> xp = xn ),
introduced(split_symbol_definition) ).
fof(f377,plain,
( xp = xn
| ~ spl0_32 ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f403,plain,
( spl0_36
<=> xk = sz00 ),
introduced(split_symbol_definition) ).
fof(f404,plain,
( xk = sz00
| ~ spl0_36 ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f583,plain,
( spl0_55
<=> sz00 = sz10 ),
introduced(split_symbol_definition) ).
fof(f584,plain,
( sz00 = sz10
| ~ spl0_55 ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f600,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl0_21 ),
inference(resolution,[status(thm)],[f337,f63]) ).
fof(f601,plain,
( ~ spl0_8
| ~ spl0_6
| spl0_21 ),
inference(split_clause,[status(thm)],[f600,f243,f235,f335]) ).
fof(f617,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl0_18 ),
inference(resolution,[status(thm)],[f326,f63]) ).
fof(f618,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_18 ),
inference(split_clause,[status(thm)],[f617,f213,f235,f324]) ).
fof(f619,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f197]) ).
fof(f620,plain,
~ spl0_23,
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f912,plain,
( spl0_86
<=> isPrime0(xp) ),
introduced(split_symbol_definition) ).
fof(f914,plain,
( ~ isPrime0(xp)
| spl0_86 ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f915,plain,
( spl0_87
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f917,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| spl0_87 ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f1259,plain,
( $false
| spl0_87 ),
inference(forward_subsumption_resolution,[status(thm)],[f917,f178]) ).
fof(f1260,plain,
spl0_87,
inference(contradiction_clause,[status(thm)],[f1259]) ).
fof(f1261,plain,
( $false
| spl0_86 ),
inference(forward_subsumption_resolution,[status(thm)],[f914,f177]) ).
fof(f1262,plain,
spl0_86,
inference(contradiction_clause,[status(thm)],[f1261]) ).
fof(f1571,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f181]) ).
fof(f1572,plain,
~ spl0_32,
inference(contradiction_clause,[status(thm)],[f1571]) ).
fof(f2075,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f183]) ).
fof(f2076,plain,
~ spl0_30,
inference(contradiction_clause,[status(thm)],[f2075]) ).
fof(f2435,plain,
( $false
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f187]) ).
fof(f2436,plain,
~ spl0_36,
inference(contradiction_clause,[status(thm)],[f2435]) ).
fof(f2467,plain,
( $false
| ~ spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f59]) ).
fof(f2468,plain,
~ spl0_55,
inference(contradiction_clause,[status(thm)],[f2467]) ).
fof(f3699,plain,
( spl0_357
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(split_symbol_definition) ).
fof(f3700,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl0_357 ),
inference(component_clause,[status(thm)],[f3699]) ).
fof(f3702,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
inference(resolution,[status(thm)],[f185,f145]) ).
fof(f3703,plain,
( ~ spl0_2
| ~ spl0_21
| spl0_3
| ~ spl0_87
| spl0_357 ),
inference(split_clause,[status(thm)],[f3702,f213,f335,f216,f915,f3699]) ).
fof(f3723,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ spl0_357 ),
inference(backward_demodulation,[status(thm)],[f3700,f200]) ).
fof(f3724,plain,
( $false
| spl0_22
| ~ spl0_357 ),
inference(forward_subsumption_resolution,[status(thm)],[f3723,f340]) ).
fof(f3725,plain,
( spl0_22
| ~ spl0_357 ),
inference(contradiction_clause,[status(thm)],[f3724]) ).
fof(f3726,plain,
$false,
inference(sat_refutation,[status(thm)],[f220,f222,f252,f254,f345,f601,f618,f620,f1260,f1262,f1572,f2076,f2436,f2468,f3703,f3725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:26:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 2.79/0.72 % Refutation found
% 2.79/0.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.79/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.79/0.73 % Elapsed time: 0.388977 seconds
% 2.79/0.73 % CPU time: 2.948532 seconds
% 2.79/0.73 % Memory used: 84.985 MB
%------------------------------------------------------------------------------