TSTP Solution File: NUM434+3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM434+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 0.10s 0.35s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 7 unt; 1 def)
% Number of atoms : 143 ( 27 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 156 ( 60 ~; 52 |; 34 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 37 (; 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(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(f23,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( sdtasdt0(xp,xq) != sz00
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f32,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f33,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f66,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(f67,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)],[f66]) ).
fof(f68,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)],[f67]) ).
fof(f69,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)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sk0_0(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sk0_0(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f85,plain,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f86,plain,
aInteger0(xb),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f91,plain,
( sdtasdt0(xp,xq) != sz00
& aInteger0(sk0_1)
& sdtasdt0(sdtasdt0(xp,xq),sk0_1) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f95,plain,
aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f97,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtasdt0(sdtasdt0(xp,xq),W0) != sdtpldt0(xa,smndt0(xb)) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f98,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f101,plain,
( spl0_0
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f103,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( spl0_1
<=> aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
introduced(split_symbol_definition) ).
fof(f106,plain,
( ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( spl0_2
<=> aInteger0(sk0_0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))) ),
introduced(split_symbol_definition) ).
fof(f109,plain,
( ~ aInteger0(sk0_0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))))
| spl0_2 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sk0_0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))) ),
inference(resolution,[status(thm)],[f73,f98]) ).
fof(f111,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f110,f101,f104,f107]) ).
fof(f112,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| spl0_2 ),
inference(resolution,[status(thm)],[f109,f72]) ).
fof(f113,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f112,f101,f104,f107]) ).
fof(f114,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f106]) ).
fof(f115,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( spl0_3
<=> aInteger0(xa) ),
introduced(split_symbol_definition) ).
fof(f118,plain,
( ~ aInteger0(xa)
| spl0_3 ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( spl0_4
<=> aInteger0(smndt0(xb)) ),
introduced(split_symbol_definition) ).
fof(f121,plain,
( ~ aInteger0(smndt0(xb))
| spl0_4 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| spl0_0 ),
inference(resolution,[status(thm)],[f103,f35]) ).
fof(f123,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_0 ),
inference(split_clause,[status(thm)],[f122,f116,f119,f101]) ).
fof(f124,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f85]) ).
fof(f125,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f126,plain,
( ~ aInteger0(xb)
| spl0_4 ),
inference(resolution,[status(thm)],[f121,f33]) ).
fof(f127,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f86]) ).
fof(f128,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
$false,
inference(sat_refutation,[status(thm)],[f111,f113,f115,f123,f125,f128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM434+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n011.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Tue May 30 09:52:12 EDT 2023
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V3.5.1
% 0.10/0.35 % Refutation found
% 0.10/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.014430 seconds
% 0.17/0.58 % CPU time: 0.013813 seconds
% 0.17/0.58 % Memory used: 3.734 MB
%------------------------------------------------------------------------------