TSTP Solution File: NUM475+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM475+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 12:29:18 EDT 2023
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 99 ( 29 unt; 2 def)
% Number of atoms : 273 ( 60 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 291 ( 117 ~; 125 |; 23 &)
% ( 18 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 57 (; 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
| sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f50,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f74,plain,
! [W0,W1,W2] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W1) != sdtpldt0(W0,W2)
& sdtpldt0(W1,W0) != sdtpldt0(W2,W0) )
| W1 = W2 ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f91,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f92,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ! [W2] :
( ( W2 != sdtmndt0(W1,W0)
| ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ( W2 = sdtmndt0(W1,W0)
| ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ),
inference(NNF_transformation,[status(esa)],[f91]) ).
fof(f93,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ( ! [W2] :
( W2 != sdtmndt0(W1,W0)
| ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) )
& ! [W2] :
( W2 = sdtmndt0(W1,W0)
| ~ aNaturalNumber0(W2)
| sdtpldt0(W0,W2) != W1 ) ) ),
inference(miniscoping,[status(esa)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| X2 != sdtmndt0(X1,X0)
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[status(esa)],[f93]) ).
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) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f132,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)],[f131]) ).
fof(f133,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)],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| X2 != sdtsldt0(X1,X0)
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f141,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f142,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f143,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f144,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f145,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f146,plain,
xl != sz00,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f147,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f148,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f149,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f150,plain,
xr = sdtmndt0(xq,xp),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f151,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f152,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f154,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f94]) ).
fof(f160,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f134]) ).
fof(f163,plain,
( spl0_0
<=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
introduced(split_symbol_definition) ).
fof(f165,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xp))
| spl0_0 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( spl0_1
<=> aNaturalNumber0(sdtasdt0(xl,xr)) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| spl0_1 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f208,plain,
( spl0_9
<=> aNaturalNumber0(xl) ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( ~ aNaturalNumber0(xl)
| spl0_9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( spl0_10
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( spl0_11
<=> aNaturalNumber0(xr) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f141]) ).
fof(f223,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f224,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr)
| spl0_1 ),
inference(resolution,[status(thm)],[f168,f53]) ).
fof(f225,plain,
( ~ spl0_9
| ~ spl0_11
| spl0_1 ),
inference(split_clause,[status(thm)],[f224,f208,f214,f166]) ).
fof(f226,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| spl0_0 ),
inference(resolution,[status(thm)],[f165,f53]) ).
fof(f227,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_0 ),
inference(split_clause,[status(thm)],[f226,f208,f211,f163]) ).
fof(f269,plain,
( spl0_18
<=> aNaturalNumber0(xq) ),
introduced(split_symbol_definition) ).
fof(f272,plain,
( spl0_19
<=> sdtlseqdt0(xp,xq) ),
introduced(split_symbol_definition) ).
fof(f274,plain,
( ~ sdtlseqdt0(xp,xq)
| spl0_19 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ sdtlseqdt0(xp,xq)
| aNaturalNumber0(xr) ),
inference(paramodulation,[status(thm)],[f150,f154]) ).
fof(f276,plain,
( ~ spl0_10
| ~ spl0_18
| ~ spl0_19
| spl0_11 ),
inference(split_clause,[status(thm)],[f275,f211,f269,f272,f214]) ).
fof(f277,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f149]) ).
fof(f278,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f279,plain,
( spl0_20
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f281,plain,
( ~ aNaturalNumber0(xn)
| spl0_20 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( spl0_21
<=> sdtasdt0(xl,xr) = xn ),
introduced(split_symbol_definition) ).
fof(f283,plain,
( sdtasdt0(xl,xr) = xn
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xn)
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[f75,f151]) ).
fof(f286,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_20
| spl0_21 ),
inference(split_clause,[status(thm)],[f285,f163,f166,f279,f282]) ).
fof(f311,plain,
( $false
| spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f143]) ).
fof(f312,plain,
spl0_20,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f314,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f152]) ).
fof(f315,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f487,plain,
( spl0_48
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(split_symbol_definition) ).
fof(f489,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl0_48 ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( spl0_49
<=> xl = sz00 ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( xl = sz00
| ~ spl0_49 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( spl0_50
<=> doDivides0(xl,sdtpldt0(xm,xn)) ),
introduced(split_symbol_definition) ).
fof(f495,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| spl0_50 ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| xl = sz00
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| aNaturalNumber0(xq) ),
inference(paramodulation,[status(thm)],[f148,f160]) ).
fof(f497,plain,
( ~ spl0_9
| ~ spl0_48
| spl0_49
| ~ spl0_50
| spl0_18 ),
inference(split_clause,[status(thm)],[f496,f208,f487,f490,f493,f269]) ).
fof(f498,plain,
( spl0_51
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f500,plain,
( ~ aNaturalNumber0(xm)
| spl0_51 ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( spl0_52
<=> doDivides0(xl,xm) ),
introduced(split_symbol_definition) ).
fof(f503,plain,
( ~ doDivides0(xl,xm)
| spl0_52 ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| xl = sz00
| ~ doDivides0(xl,xm)
| aNaturalNumber0(xp) ),
inference(paramodulation,[status(thm)],[f147,f160]) ).
fof(f505,plain,
( ~ spl0_9
| ~ spl0_51
| spl0_49
| ~ spl0_52
| spl0_10 ),
inference(split_clause,[status(thm)],[f504,f208,f498,f490,f501,f211]) ).
fof(f506,plain,
( $false
| spl0_52 ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f144]) ).
fof(f507,plain,
spl0_52,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f508,plain,
( $false
| spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f142]) ).
fof(f509,plain,
spl0_51,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( $false
| ~ spl0_49 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f146]) ).
fof(f511,plain,
~ spl0_49,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f577,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl0_48 ),
inference(resolution,[status(thm)],[f489,f51]) ).
fof(f578,plain,
( ~ spl0_51
| ~ spl0_20
| spl0_48 ),
inference(split_clause,[status(thm)],[f577,f498,f279,f487]) ).
fof(f579,plain,
( $false
| spl0_50 ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f145]) ).
fof(f580,plain,
spl0_50,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
$false,
inference(sat_refutation,[status(thm)],[f223,f225,f227,f276,f278,f286,f312,f315,f497,f505,f507,f509,f511,f578,f580]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % 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 10:21:15 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.50 % Refutation found
% 0.19/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.52 % Elapsed time: 0.172468 seconds
% 0.19/0.52 % CPU time: 1.249568 seconds
% 0.19/0.52 % Memory used: 70.601 MB
%------------------------------------------------------------------------------