TSTP Solution File: NUM523+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 20:35:00 EDT 2024
% Result : Theorem 16.61s 2.44s
% Output : CNFRefutation 16.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 12 unt; 1 def)
% Number of atoms : 153 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 166 ( 67 ~; 68 |; 18 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f54,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| aNaturalNumber0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f127,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f128,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ doDivides0(W0,W1)
| ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) )
& ( doDivides0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f127]) ).
fof(f129,plain,
! [W0,W1] :
( ~ aNaturalNumber0(W0)
| ~ aNaturalNumber0(W1)
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(sk0_1(W1,W0))
& W1 = sdtasdt0(W0,sk0_1(W1,W0)) ) )
& ( doDivides0(W0,W1)
| ! [W2] :
( ~ aNaturalNumber0(W2)
| W1 != sdtasdt0(W0,W2) ) ) ) ),
inference(skolemization,[status(esa)],[f128]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f164,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(f165,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)],[f164]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f168,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f174,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f175,plain,
isPrime0(xp),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f176,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f177,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(cnf_transformation,[status(esa)],[f176]) ).
fof(f178,plain,
( spl0_0
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
introduced(split_symbol_definition) ).
fof(f179,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( spl0_1
<=> doDivides0(xp,xn) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f177,f178,f181]) ).
fof(f191,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f132]) ).
fof(f197,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f55]) ).
fof(f270,plain,
( spl0_2
<=> aNaturalNumber0(xp) ),
introduced(split_symbol_definition) ).
fof(f272,plain,
( ~ aNaturalNumber0(xp)
| spl0_2 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( spl0_3
<=> aNaturalNumber0(xn) ),
introduced(split_symbol_definition) ).
fof(f275,plain,
( ~ aNaturalNumber0(xn)
| spl0_3 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f291,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f166]) ).
fof(f292,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f303,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f168]) ).
fof(f304,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f2036,plain,
( spl0_197
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(split_symbol_definition) ).
fof(f2038,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl0_197 ),
inference(component_clause,[status(thm)],[f2036]) ).
fof(f2085,plain,
( ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(paramodulation,[status(thm)],[f174,f197]) ).
fof(f2086,plain,
( ~ spl0_2
| spl0_0
| ~ spl0_197 ),
inference(split_clause,[status(thm)],[f2085,f270,f178,f2036]) ).
fof(f2219,plain,
( spl0_213
<=> aNaturalNumber0(xm) ),
introduced(split_symbol_definition) ).
fof(f2221,plain,
( ~ aNaturalNumber0(xm)
| spl0_213 ),
inference(component_clause,[status(thm)],[f2219]) ).
fof(f2222,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| spl0_197 ),
inference(resolution,[status(thm)],[f2038,f55]) ).
fof(f2223,plain,
( ~ spl0_213
| spl0_197 ),
inference(split_clause,[status(thm)],[f2222,f2219,f2036]) ).
fof(f2224,plain,
( $false
| spl0_213 ),
inference(forward_subsumption_resolution,[status(thm)],[f2221,f167]) ).
fof(f2225,plain,
spl0_213,
inference(contradiction_clause,[status(thm)],[f2224]) ).
fof(f2840,plain,
( spl0_252
<=> isPrime0(xp) ),
introduced(split_symbol_definition) ).
fof(f2842,plain,
( ~ isPrime0(xp)
| spl0_252 ),
inference(component_clause,[status(thm)],[f2840]) ).
fof(f2869,plain,
( $false
| spl0_252 ),
inference(forward_subsumption_resolution,[status(thm)],[f2842,f175]) ).
fof(f2870,plain,
spl0_252,
inference(contradiction_clause,[status(thm)],[f2869]) ).
fof(f5831,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| doDivides0(xp,xn)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f179,f165]) ).
fof(f5832,plain,
( ~ spl0_3
| ~ spl0_2
| ~ spl0_252
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f5831,f273,f270,f2840,f181,f178]) ).
fof(f5859,plain,
$false,
inference(sat_refutation,[status(thm)],[f184,f292,f304,f2086,f2223,f2225,f2870,f5832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n017.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Mon Apr 29 20:19:03 EDT 2024
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.6.0
% 16.61/2.44 % Refutation found
% 16.61/2.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.61/2.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.61/2.47 % Elapsed time: 2.132294 seconds
% 16.61/2.47 % CPU time: 16.758839 seconds
% 16.61/2.47 % Total memory used: 144.996 MB
% 16.61/2.47 % Net memory used: 140.920 MB
%------------------------------------------------------------------------------