TSTP Solution File: NUM432+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM432+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 12:29:07 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 71 ( 19 unt; 2 def)
% Number of atoms : 208 ( 34 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 221 ( 84 ~; 90 |; 30 &)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 50 (; 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,definition,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f36,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f68,plain,
! [W0] :
( ~ aInteger0(W0)
| ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f69,plain,
! [W0] :
( ~ aInteger0(W0)
| ! [W1] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [W0] :
( ~ aInteger0(W0)
| ( ! [W1] :
( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) )
& ! [W1] :
( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(miniscoping,[status(esa)],[f69]) ).
fof(f71,plain,
! [W0] :
( ~ aInteger0(W0)
| ( ! [W1] :
( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& W1 != sz00
& aInteger0(sk0_0(W1,W0))
& sdtasdt0(W1,sk0_0(W1,W0)) = W0 ) )
& ! [W1] :
( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| W1 = sz00
| ! [W2] :
( ~ aInteger0(W2)
| sdtasdt0(W1,W2) != W0 ) ) ) ),
inference(skolemization,[status(esa)],[f70]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| X1 = sz00
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ),
inference(cnf_transformation,[status(esa)],[f71]) ).
fof(f77,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| W2 = sz00
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f78,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| W2 = sz00
| ( ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
& ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ),
inference(NNF_transformation,[status(esa)],[f77]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f85,plain,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f87,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f88,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f89,plain,
aInteger0(xc),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f92,plain,
aInteger0(xn),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f94,plain,
aInteger0(xm),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f96,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f97,plain,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aInteger0(sdtasdt0(X0,X1))
| aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| X0 = sz00
| ~ aInteger0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f76]) ).
fof(f103,plain,
( spl0_1
<=> aInteger0(xc) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( ~ aInteger0(xc)
| spl0_1 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( spl0_2
<=> aInteger0(xq) ),
introduced(split_symbol_definition) ).
fof(f108,plain,
( ~ aInteger0(xq)
| spl0_2 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( spl0_3
<=> xq = sz00 ),
introduced(split_symbol_definition) ).
fof(f110,plain,
( xq = sz00
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f117,plain,
( spl0_5
<=> aInteger0(xa) ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( ~ aInteger0(xa)
| spl0_5 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f127,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f85]) ).
fof(f128,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f89]) ).
fof(f130,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f87]) ).
fof(f132,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f148,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f88]) ).
fof(f149,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f213,plain,
! [X0,X1] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| X0 = sz00
| ~ aInteger0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f39]) ).
fof(f219,plain,
( spl0_23
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) ),
introduced(split_symbol_definition) ).
fof(f220,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( spl0_24
<=> aInteger0(sdtpldt0(xn,xm)) ),
introduced(split_symbol_definition) ).
fof(f224,plain,
( ~ aInteger0(sdtpldt0(xn,xm))
| spl0_24 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ~ aInteger0(xq)
| xq = sz00
| ~ aInteger0(sdtpldt0(xn,xm)) ),
inference(paramodulation,[status(thm)],[f96,f213]) ).
fof(f226,plain,
( spl0_23
| ~ spl0_2
| spl0_3
| ~ spl0_24 ),
inference(split_clause,[status(thm)],[f225,f219,f106,f109,f222]) ).
fof(f265,plain,
( spl0_33
<=> aInteger0(xn) ),
introduced(split_symbol_definition) ).
fof(f267,plain,
( ~ aInteger0(xn)
| spl0_33 ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( spl0_34
<=> aInteger0(xm) ),
introduced(split_symbol_definition) ).
fof(f270,plain,
( ~ aInteger0(xm)
| spl0_34 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( ~ aInteger0(xn)
| ~ aInteger0(xm)
| spl0_24 ),
inference(resolution,[status(thm)],[f224,f37]) ).
fof(f272,plain,
( ~ spl0_33
| ~ spl0_34
| spl0_24 ),
inference(split_clause,[status(thm)],[f271,f265,f268,f222]) ).
fof(f273,plain,
( $false
| spl0_33 ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f92]) ).
fof(f274,plain,
spl0_33,
inference(contradiction_clause,[status(thm)],[f273]) ).
fof(f275,plain,
( $false
| spl0_34 ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f94]) ).
fof(f276,plain,
spl0_34,
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f394,plain,
( spl0_57
<=> sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
introduced(split_symbol_definition) ).
fof(f395,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f80,f220]) ).
fof(f398,plain,
( ~ spl0_5
| ~ spl0_1
| ~ spl0_2
| spl0_3
| spl0_57
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f397,f117,f103,f106,f109,f394,f219]) ).
fof(f409,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f97]) ).
fof(f410,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f411,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f130,f132,f149,f226,f272,f274,f276,f398,f410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM432+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n001.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 10:31:00 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.55 % Elapsed time: 0.039342 seconds
% 0.14/0.55 % CPU time: 0.019739 seconds
% 0.14/0.55 % Memory used: 3.991 MB
%------------------------------------------------------------------------------